- constant: busy-beaver-shift-1
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-1
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-2
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-2
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-3
  type: lower_bound
  value:
    latex: '21'
    decimal_approx: 21
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-4
  type: lower_bound
  value:
    latex: '107'
    decimal_approx: 107
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-5
  type: lower_bound
  value:
    latex: '47176870'
    decimal_approx: 47176870
    alt_display: 47,176,870
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-5
  type: upper_bound
  value:
    latex: '47176870'
    decimal_approx: 47176870
    alt_display: 47,176,870
  date: null
  primary_source: null
  secondary_source: oeis-A060843
- constant: busy-beaver-shift-7
  type: lower_bound
  value:
    latex: 10^{2\times10^{10^{10^{18705353}}}}
    decimal_approx: null
    alt_display: null
  date: null
  primary_source: null
  secondary_source: aaronson-2020
- constant: busy-beaver-ones-7
  type: lower_bound
  value:
    latex: 10^{10^{10^{10^{18705353}}}}
    decimal_approx: null
    alt_display: null
  date: null
  primary_source: null
  secondary_source: aaronson-2020
- constant: busy-beaver-ones-1
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A028444
- constant: busy-beaver-ones-1
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A028444
- constant: busy-beaver-ones-2
  type: lower_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A028444
- constant: busy-beaver-ones-2
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A028444
- constant: busy-beaver-ones-3
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A028444
- constant: busy-beaver-ones-4
  type: lower_bound
  value:
    latex: '13'
    decimal_approx: 13
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-A028444
- constant: cage-3-3
  type: lower_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-3-3
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-3-4
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-3-4
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-3
  type: lower_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-3
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-4
  type: lower_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-4
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-5-3
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-5-3
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-5-4
  type: lower_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-5-4
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-6-3
  type: lower_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-6-3
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-6-4
  type: lower_bound
  value:
    latex: '12'
    decimal_approx: 12
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-6-4
  type: upper_bound
  value:
    latex: '12'
    decimal_approx: 12
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-7-3
  type: lower_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-7-3
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-7-4
  type: lower_bound
  value:
    latex: '14'
    decimal_approx: 14
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-7-4
  type: upper_bound
  value:
    latex: '14'
    decimal_approx: 14
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-7
  type: lower_bound
  value:
    latex: '67'
    decimal_approx: 67
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-8
  type: lower_bound
  value:
    latex: '80'
    decimal_approx: 80
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-5-8
  type: lower_bound
  value:
    latex: '170'
    decimal_approx: 170
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-age
- constant: cage-6-8
  type: lower_bound
  value:
    latex: '312'
    decimal_approx: 312
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-4-12
  type: lower_bound
  value:
    latex: '728'
    decimal_approx: 728
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-5-12
  type: lower_bound
  value:
    latex: '2730'
    decimal_approx: 2730
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-6-12
  type: lower_bound
  value:
    latex: '7812'
    decimal_approx: 7812
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-cage
- constant: cage-3-5
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-6
  type: upper_bound
  value:
    latex: '14'
    decimal_approx: 14
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-7
  type: upper_bound
  value:
    latex: '24'
    decimal_approx: 24
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-8
  type: upper_bound
  value:
    latex: '30'
    decimal_approx: 30
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-9
  type: upper_bound
  value:
    latex: '58'
    decimal_approx: 58
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-10
  type: upper_bound
  value:
    latex: '70'
    decimal_approx: 70
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-11
  type: upper_bound
  value:
    latex: '112'
    decimal_approx: 112
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-12
  type: upper_bound
  value:
    latex: '126'
    decimal_approx: 126
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-13
  type: upper_bound
  value:
    latex: '272'
    decimal_approx: 272
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-14
  type: upper_bound
  value:
    latex: '384'
    decimal_approx: 384
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-15
  type: upper_bound
  value:
    latex: '620'
    decimal_approx: 620
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-16
  type: upper_bound
  value:
    latex: '960'
    decimal_approx: 960
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-5
  type: upper_bound
  value:
    latex: '19'
    decimal_approx: 19
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-6
  type: upper_bound
  value:
    latex: '26'
    decimal_approx: 26
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-7
  type: upper_bound
  value:
    latex: '67'
    decimal_approx: 67
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-8
  type: upper_bound
  value:
    latex: '80'
    decimal_approx: 80
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-12
  type: upper_bound
  value:
    latex: '728'
    decimal_approx: 728
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-5
  type: upper_bound
  value:
    latex: '30'
    decimal_approx: 30
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-6
  type: upper_bound
  value:
    latex: '42'
    decimal_approx: 42
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-7
  type: upper_bound
  value:
    latex: '152'
    decimal_approx: 152
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-8
  type: upper_bound
  value:
    latex: '170'
    decimal_approx: 170
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-12
  type: upper_bound
  value:
    latex: '2730'
    decimal_approx: 2730
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-5
  type: upper_bound
  value:
    latex: '40'
    decimal_approx: 40
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-6
  type: upper_bound
  value:
    latex: '62'
    decimal_approx: 62
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-7
  type: upper_bound
  value:
    latex: '294'
    decimal_approx: 294
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-8
  type: upper_bound
  value:
    latex: '312'
    decimal_approx: 312
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-12
  type: upper_bound
  value:
    latex: '7812'
    decimal_approx: 7812
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-7-5
  type: upper_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-7-6
  type: upper_bound
  value:
    latex: '90'
    decimal_approx: 90
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-7-8
  type: upper_bound
  value:
    latex: '672'
    decimal_approx: 672
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-7-12
  type: upper_bound
  value:
    latex: '32928'
    decimal_approx: 32928
    alt_display: 32,928
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-8-5
  type: upper_bound
  value:
    latex: '80'
    decimal_approx: 80
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-8-6
  type: upper_bound
  value:
    latex: '114'
    decimal_approx: 114
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-8-8
  type: upper_bound
  value:
    latex: '800'
    decimal_approx: 800
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-8-12
  type: upper_bound
  value:
    latex: '39216'
    decimal_approx: 39216
    alt_display: 39,216
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-9-5
  type: upper_bound
  value:
    latex: '96'
    decimal_approx: 96
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-9-6
  type: upper_bound
  value:
    latex: '146'
    decimal_approx: 146
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-9-8
  type: upper_bound
  value:
    latex: '1170'
    decimal_approx: 1170
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-9-12
  type: upper_bound
  value:
    latex: '74898'
    decimal_approx: 74898
    alt_display: 74,898
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-10-5
  type: upper_bound
  value:
    latex: '124'
    decimal_approx: 124
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-10-6
  type: upper_bound
  value:
    latex: '182'
    decimal_approx: 182
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-10-8
  type: upper_bound
  value:
    latex: '1640'
    decimal_approx: 1640
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-10-12
  type: upper_bound
  value:
    latex: '132860'
    decimal_approx: 132860
    alt_display: 132,860
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-11-5
  type: upper_bound
  value:
    latex: '154'
    decimal_approx: 154
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-11-6
  type: upper_bound
  value:
    latex: '240'
    decimal_approx: 240
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-11-8
  type: upper_bound
  value:
    latex: '2618'
    decimal_approx: 2618
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-11-12
  type: upper_bound
  value:
    latex: '319440'
    decimal_approx: 319440
    alt_display: 319,440
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-12-5
  type: upper_bound
  value:
    latex: '203'
    decimal_approx: 203
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-12-6
  type: upper_bound
  value:
    latex: '266'
    decimal_approx: 266
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-12-8
  type: upper_bound
  value:
    latex: '2928'
    decimal_approx: 2928
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-12-12
  type: upper_bound
  value:
    latex: '354312'
    decimal_approx: 354312
    alt_display: 354,312
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-13-5
  type: upper_bound
  value:
    latex: '230'
    decimal_approx: 230
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-13-6
  type: upper_bound
  value:
    latex: '336'
    decimal_approx: 336
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-13-8
  type: upper_bound
  value:
    latex: '4342'
    decimal_approx: 4342
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-13-12
  type: upper_bound
  value:
    latex: '738192'
    decimal_approx: 738192
    alt_display: 738,192
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-14-5
  type: upper_bound
  value:
    latex: '288'
    decimal_approx: 288
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-14-6
  type: upper_bound
  value:
    latex: '366'
    decimal_approx: 366
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-14-8
  type: upper_bound
  value:
    latex: '4760'
    decimal_approx: 4760
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-14-12
  type: upper_bound
  value:
    latex: '804468'
    decimal_approx: 804468
    alt_display: 804,468
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-15-5
  type: upper_bound
  value:
    latex: '312'
    decimal_approx: 312
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-15-6
  type: upper_bound
  value:
    latex: '462'
    decimal_approx: 462
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-15-8
  type: upper_bound
  value:
    latex: '7648'
    decimal_approx: 7648
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-15-12
  type: upper_bound
  value:
    latex: '1957376'
    decimal_approx: 1957376
    alt_display: 1,957,376
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-16-5
  type: upper_bound
  value:
    latex: '336'
    decimal_approx: 336
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-16-6
  type: upper_bound
  value:
    latex: '504'
    decimal_approx: 504
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-16-8
  type: upper_bound
  value:
    latex: '8092'
    decimal_approx: 8092
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-16-12
  type: upper_bound
  value:
    latex: '2088960'
    decimal_approx: 2088960
    alt_display: 2,088,960
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-17-5
  type: upper_bound
  value:
    latex: '448'
    decimal_approx: 448
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-17-6
  type: upper_bound
  value:
    latex: '546'
    decimal_approx: 546
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-17-8
  type: upper_bound
  value:
    latex: '8738'
    decimal_approx: 8738
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-17-12
  type: upper_bound
  value:
    latex: '2236962'
    decimal_approx: 2236962
    alt_display: 2,236,962
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-18-5
  type: upper_bound
  value:
    latex: '480'
    decimal_approx: 480
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-18-6
  type: upper_bound
  value:
    latex: '614'
    decimal_approx: 614
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-18-8
  type: upper_bound
  value:
    latex: '10440'
    decimal_approx: 10440
    alt_display: 10,440
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-18-12
  type: upper_bound
  value:
    latex: '3017196'
    decimal_approx: 3017196
    alt_display: 3,017,196
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-19-5
  type: upper_bound
  value:
    latex: '512'
    decimal_approx: 512
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-19-6
  type: upper_bound
  value:
    latex: '720'
    decimal_approx: 720
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-19-8
  type: upper_bound
  value:
    latex: '13642'
    decimal_approx: 13642
    alt_display: 13,642
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-19-12
  type: upper_bound
  value:
    latex: '4938480'
    decimal_approx: 4938480
    alt_display: 4,938,480
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-20-5
  type: upper_bound
  value:
    latex: '576'
    decimal_approx: 576
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-20-6
  type: upper_bound
  value:
    latex: '762'
    decimal_approx: 762
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-20-8
  type: upper_bound
  value:
    latex: '14480'
    decimal_approx: 14480
    alt_display: 14,480
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-20-12
  type: upper_bound
  value:
    latex: '5227320'
    decimal_approx: 5227320
    alt_display: 5,227,320
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-5
  type: lower_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-6
  type: lower_bound
  value:
    latex: '14'
    decimal_approx: 14
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-7
  type: lower_bound
  value:
    latex: '24'
    decimal_approx: 24
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-8
  type: lower_bound
  value:
    latex: '30'
    decimal_approx: 30
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-9
  type: lower_bound
  value:
    latex: '58'
    decimal_approx: 58
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-10
  type: lower_bound
  value:
    latex: '70'
    decimal_approx: 70
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-11
  type: lower_bound
  value:
    latex: '112'
    decimal_approx: 112
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-12
  type: lower_bound
  value:
    latex: '126'
    decimal_approx: 126
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-13
  type: lower_bound
  value:
    latex: '202'
    decimal_approx: 202
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-14
  type: lower_bound
  value:
    latex: '258'
    decimal_approx: 258
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-15
  type: lower_bound
  value:
    latex: '384'
    decimal_approx: 384
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-3-16
  type: lower_bound
  value:
    latex: '512'
    decimal_approx: 512
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-5
  type: lower_bound
  value:
    latex: '19'
    decimal_approx: 19
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-5
  type: lower_bound
  value:
    latex: '30'
    decimal_approx: 30
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-5
  type: lower_bound
  value:
    latex: '40'
    decimal_approx: 40
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-7-5
  type: lower_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-8-5
  type: lower_bound
  value:
    latex: '67'
    decimal_approx: 67
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-9-5
  type: lower_bound
  value:
    latex: '86'
    decimal_approx: 86
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-10-5
  type: lower_bound
  value:
    latex: '103'
    decimal_approx: 103
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-11-5
  type: lower_bound
  value:
    latex: '124'
    decimal_approx: 124
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-12-5
  type: lower_bound
  value:
    latex: '147'
    decimal_approx: 147
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-13-5
  type: lower_bound
  value:
    latex: '174'
    decimal_approx: 174
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-14-5
  type: lower_bound
  value:
    latex: '199'
    decimal_approx: 199
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-15-5
  type: lower_bound
  value:
    latex: '230'
    decimal_approx: 230
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-16-5
  type: lower_bound
  value:
    latex: '259'
    decimal_approx: 259
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-17-5
  type: lower_bound
  value:
    latex: '294'
    decimal_approx: 294
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-18-5
  type: lower_bound
  value:
    latex: '327'
    decimal_approx: 327
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-19-5
  type: lower_bound
  value:
    latex: '364'
    decimal_approx: 364
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-20-5
  type: lower_bound
  value:
    latex: '403'
    decimal_approx: 403
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-4-6
  type: lower_bound
  value:
    latex: '26'
    decimal_approx: 26
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-5-6
  type: lower_bound
  value:
    latex: '42'
    decimal_approx: 42
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-6-6
  type: lower_bound
  value:
    latex: '62'
    decimal_approx: 62
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-7-6
  type: lower_bound
  value:
    latex: '90'
    decimal_approx: 90
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-8-6
  type: lower_bound
  value:
    latex: '114'
    decimal_approx: 114
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-9-6
  type: lower_bound
  value:
    latex: '146'
    decimal_approx: 146
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-10-6
  type: lower_bound
  value:
    latex: '182'
    decimal_approx: 182
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-11-6
  type: lower_bound
  value:
    latex: '224'
    decimal_approx: 224
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-12-6
  type: lower_bound
  value:
    latex: '266'
    decimal_approx: 266
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-13-6
  type: lower_bound
  value:
    latex: '314'
    decimal_approx: 314
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-14-6
  type: lower_bound
  value:
    latex: '366'
    decimal_approx: 366
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-15-6
  type: lower_bound
  value:
    latex: '422'
    decimal_approx: 422
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-16-6
  type: lower_bound
  value:
    latex: '482'
    decimal_approx: 482
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-17-6
  type: lower_bound
  value:
    latex: '546'
    decimal_approx: 546
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-18-6
  type: lower_bound
  value:
    latex: '614'
    decimal_approx: 614
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-19-6
  type: lower_bound
  value:
    latex: '686'
    decimal_approx: 686
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: cage-20-6
  type: lower_bound
  value:
    latex: '762'
    decimal_approx: 762
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds16-cages
- constant: circle-in-equilateral-1
  type: lower_bound
  value:
    latex: 2\sqrt{3}
    decimal_approx: 3.464102
    alt_display: "\u22483.464102"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-1
  type: upper_bound
  value:
    latex: 2\sqrt{3}
    decimal_approx: 3.464102
    alt_display: "\u22483.464102"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-2
  type: lower_bound
  value:
    latex: 2+2\sqrt{3}
    decimal_approx: 5.464102
    alt_display: "\u22485.464102"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-2
  type: upper_bound
  value:
    latex: 2+2\sqrt{3}
    decimal_approx: 5.464102
    alt_display: "\u22485.464102"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-3
  type: lower_bound
  value:
    latex: 2+2\sqrt{3}
    decimal_approx: 5.464102
    alt_display: "\u22485.464102"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-3
  type: upper_bound
  value:
    latex: 2+2\sqrt{3}
    decimal_approx: 5.464102
    alt_display: "\u22485.464102"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-4
  type: upper_bound
  value:
    latex: 4\sqrt{3}
    decimal_approx: 6.928203
    alt_display: "\u22486.928203"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-5
  type: upper_bound
  value:
    latex: 4+2\sqrt{3}
    decimal_approx: 7.464102
    alt_display: "\u22487.464102"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-6
  type: upper_bound
  value:
    latex: 4+2\sqrt{3}
    decimal_approx: 7.464102
    alt_display: "\u22487.464102"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-7
  type: upper_bound
  value:
    latex: 2+4\sqrt{3}
    decimal_approx: 8.928203
    alt_display: "\u22488.928203"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-8
  type: upper_bound
  value:
    latex: 2+2\sqrt{3}+\frac{2\sqrt{33}}{3}
    decimal_approx: 9.29381
    alt_display: "\u22489.29381"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-9
  type: upper_bound
  value:
    latex: 6+2\sqrt{3}
    decimal_approx: 9.464102
    alt_display: "\u22489.464102"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-10
  type: upper_bound
  value:
    latex: 6+2\sqrt{3}
    decimal_approx: 9.464102
    alt_display: "\u22489.464102"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-11
  type: upper_bound
  value:
    latex: 4+2\sqrt{3}+\frac{4\sqrt{6}}{3}
    decimal_approx: 10.73009
    alt_display: "\u224810.73009"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-12
  type: upper_bound
  value:
    latex: 4+4\sqrt{3}
    decimal_approx: 10.9282
    alt_display: "\u224810.9282"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-15
  type: upper_bound
  value:
    latex: 8+2\sqrt{3}
    decimal_approx: 11.4641
    alt_display: "\u224811.4641"
  date: null
  primary_source: null
  secondary_source: friedman-circles-in-triangles
- constant: degree-diameter-3-2
  type: lower_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-3-2
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-3-6
  type: lower_bound
  value:
    latex: '132'
    decimal_approx: 132
    alt_display: null
  date: null
  primary_source: exoographs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-3-9
  type: lower_bound
  value:
    latex: '600'
    decimal_approx: 600
    alt_display: null
  date: null
  primary_source: exoographs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-4
  type: lower_bound
  value:
    latex: '212'
    decimal_approx: 212
    alt_display: null
  date: null
  primary_source: exoographs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-2
  type: lower_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-2
  type: upper_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-2
  type: lower_bound
  value:
    latex: '104'
    decimal_approx: 104
    alt_display: null
  date: null
  primary_source: exoographs
  secondary_source: wikipedia-degree-diameter
- constant: disk-covering-1
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-1
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-2
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: wikipedia-disk-covering
- constant: disk-covering-2
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: wikipedia-disk-covering
- constant: disk-covering-3
  type: lower_bound
  value:
    latex: \frac{\sqrt{3}}{2}
    decimal_approx: 0.8660254
    alt_display: "\u22480.8660254"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-3
  type: upper_bound
  value:
    latex: \frac{\sqrt{3}}{2}
    decimal_approx: 0.8660254
    alt_display: "\u22480.8660254"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-4
  type: lower_bound
  value:
    latex: \frac{\sqrt{2}}{2}
    decimal_approx: 0.7071068
    alt_display: "\u22480.7071068"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-4
  type: upper_bound
  value:
    latex: \frac{\sqrt{2}}{2}
    decimal_approx: 0.7071068
    alt_display: "\u22480.7071068"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-5
  type: upper_bound
  value:
    latex: '{\approx}0.609382'
    decimal_approx: 0.609382
    alt_display: null
  date: null
  primary_source: null
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-6
  type: upper_bound
  value:
    latex: '{\approx}0.555905'
    decimal_approx: 0.555905
    alt_display: null
  date: null
  primary_source: null
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-7
  type: lower_bound
  value:
    latex: \frac{1}{2}
    decimal_approx: 0.5
    alt_display: "\u22480.5"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-7
  type: upper_bound
  value:
    latex: \frac{1}{2}
    decimal_approx: 0.5
    alt_display: "\u22480.5"
  date: null
  primary_source: trivial
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-8
  type: upper_bound
  value:
    latex: '{\approx}0.445041'
    decimal_approx: 0.445041
    alt_display: null
  date: null
  primary_source: null
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-9
  type: upper_bound
  value:
    latex: '{\approx}0.414213'
    decimal_approx: 0.414213
    alt_display: null
  date: null
  primary_source: null
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-10
  type: upper_bound
  value:
    latex: '{\approx}0.394930'
    decimal_approx: 0.39493
    alt_display: null
  date: null
  primary_source: null
  secondary_source: friedman-circles-covering-circles
- constant: kissing-number-1
  type: lower_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-1
  type: upper_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-2
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-2
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-3
  type: lower_bound
  value:
    latex: '12'
    decimal_approx: 12
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-3
  type: upper_bound
  value:
    latex: '12'
    decimal_approx: 12
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-4
  type: lower_bound
  value:
    latex: '24'
    decimal_approx: 24
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-4
  type: upper_bound
  value:
    latex: '24'
    decimal_approx: 24
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-5
  type: lower_bound
  value:
    latex: '40'
    decimal_approx: 40
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-5
  type: upper_bound
  value:
    latex: '44'
    decimal_approx: 44
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-6
  type: lower_bound
  value:
    latex: '72'
    decimal_approx: 72
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-6
  type: upper_bound
  value:
    latex: '77'
    decimal_approx: 77
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-7
  type: lower_bound
  value:
    latex: '126'
    decimal_approx: 126
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-7
  type: upper_bound
  value:
    latex: '134'
    decimal_approx: 134
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-8
  type: lower_bound
  value:
    latex: '240'
    decimal_approx: 240
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-8
  type: upper_bound
  value:
    latex: '240'
    decimal_approx: 240
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-9
  type: lower_bound
  value:
    latex: '306'
    decimal_approx: 306
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-9
  type: upper_bound
  value:
    latex: '363'
    decimal_approx: 363
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-10
  type: lower_bound
  value:
    latex: '510'
    decimal_approx: 510
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-10
  type: upper_bound
  value:
    latex: '553'
    decimal_approx: 553
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-11
  type: lower_bound
  value:
    latex: '592'
    decimal_approx: 592
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-11
  type: upper_bound
  value:
    latex: '868'
    decimal_approx: 868
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-12
  type: lower_bound
  value:
    latex: '840'
    decimal_approx: 840
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-12
  type: upper_bound
  value:
    latex: '1355'
    decimal_approx: 1355
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-13
  type: lower_bound
  value:
    latex: '1154'
    decimal_approx: 1154
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-13
  type: upper_bound
  value:
    latex: '2064'
    decimal_approx: 2064
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-14
  type: lower_bound
  value:
    latex: '1932'
    decimal_approx: 1932
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-14
  type: upper_bound
  value:
    latex: '3174'
    decimal_approx: 3174
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-15
  type: lower_bound
  value:
    latex: '2564'
    decimal_approx: 2564
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-15
  type: upper_bound
  value:
    latex: '4853'
    decimal_approx: 4853
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-16
  type: lower_bound
  value:
    latex: '4320'
    decimal_approx: 4320
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-16
  type: upper_bound
  value:
    latex: '7320'
    decimal_approx: 7320
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-17
  type: lower_bound
  value:
    latex: '5730'
    decimal_approx: 5730
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-17
  type: upper_bound
  value:
    latex: '10978'
    decimal_approx: 10978
    alt_display: 10,978
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-18
  type: lower_bound
  value:
    latex: '7654'
    decimal_approx: 7654
    alt_display: null
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-18
  type: upper_bound
  value:
    latex: '16406'
    decimal_approx: 16406
    alt_display: 16,406
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-19
  type: lower_bound
  value:
    latex: '11692'
    decimal_approx: 11692
    alt_display: 11,692
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-19
  type: upper_bound
  value:
    latex: '24417'
    decimal_approx: 24417
    alt_display: 24,417
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-20
  type: lower_bound
  value:
    latex: '19448'
    decimal_approx: 19448
    alt_display: 19,448
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-20
  type: upper_bound
  value:
    latex: '36195'
    decimal_approx: 36195
    alt_display: 36,195
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-21
  type: lower_bound
  value:
    latex: '29768'
    decimal_approx: 29768
    alt_display: 29,768
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-21
  type: upper_bound
  value:
    latex: '53524'
    decimal_approx: 53524
    alt_display: 53,524
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-22
  type: lower_bound
  value:
    latex: '49896'
    decimal_approx: 49896
    alt_display: 49,896
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-22
  type: upper_bound
  value:
    latex: '80810'
    decimal_approx: 80810
    alt_display: 80,810
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-23
  type: lower_bound
  value:
    latex: '93150'
    decimal_approx: 93150
    alt_display: 93,150
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-23
  type: upper_bound
  value:
    latex: '122351'
    decimal_approx: 122351
    alt_display: 122,351
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-24
  type: lower_bound
  value:
    latex: '196560'
    decimal_approx: 196560
    alt_display: 196,560
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: kissing-number-24
  type: upper_bound
  value:
    latex: '196560'
    decimal_approx: 196560
    alt_display: 196,560
  date: null
  primary_source: null
  secondary_source: wikipedia-kissing-number
- constant: map-folding-2-2
  type: lower_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-2-2
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-3-3
  type: lower_bound
  value:
    latex: '1368'
    decimal_approx: 1368
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-3-3
  type: upper_bound
  value:
    latex: '1368'
    decimal_approx: 1368
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-4-4
  type: lower_bound
  value:
    latex: '300608'
    decimal_approx: 300608
    alt_display: 300,608
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-4-4
  type: upper_bound
  value:
    latex: '300608'
    decimal_approx: 300608
    alt_display: 300,608
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-5-5
  type: lower_bound
  value:
    latex: '186086600'
    decimal_approx: 186086600
    alt_display: 186,086,600
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-5-5
  type: upper_bound
  value:
    latex: '186086600'
    decimal_approx: 186086600
    alt_display: 186,086,600
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-6-6
  type: lower_bound
  value:
    latex: '123912532224'
    decimal_approx: 123912532224
    alt_display: 123,912,532,224
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-6-6
  type: upper_bound
  value:
    latex: '123912532224'
    decimal_approx: 123912532224
    alt_display: 123,912,532,224
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-7-7
  type: lower_bound
  value:
    latex: '129950723279272'
    decimal_approx: 129950723279272
    alt_display: 129,950,723,279,272
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-7-7
  type: upper_bound
  value:
    latex: '129950723279272'
    decimal_approx: 129950723279272
    alt_display: 129,950,723,279,272
  date: null
  primary_source: null
  secondary_source: oeis-a001418-map-folding-n-n
- constant: map-folding-2-3
  type: lower_bound
  value:
    latex: '60'
    decimal_approx: 60
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-3
  type: upper_bound
  value:
    latex: '60'
    decimal_approx: 60
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-4
  type: lower_bound
  value:
    latex: '320'
    decimal_approx: 320
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-4
  type: upper_bound
  value:
    latex: '320'
    decimal_approx: 320
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-5
  type: lower_bound
  value:
    latex: '1980'
    decimal_approx: 1980
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-5
  type: upper_bound
  value:
    latex: '1980'
    decimal_approx: 1980
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-6
  type: lower_bound
  value:
    latex: '10512'
    decimal_approx: 10512
    alt_display: 10,512
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-6
  type: upper_bound
  value:
    latex: '10512'
    decimal_approx: 10512
    alt_display: 10,512
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-7
  type: lower_bound
  value:
    latex: '60788'
    decimal_approx: 60788
    alt_display: 60,788
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-7
  type: upper_bound
  value:
    latex: '60788'
    decimal_approx: 60788
    alt_display: 60,788
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-8
  type: lower_bound
  value:
    latex: '320896'
    decimal_approx: 320896
    alt_display: 320,896
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-8
  type: upper_bound
  value:
    latex: '320896'
    decimal_approx: 320896
    alt_display: 320,896
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-9
  type: lower_bound
  value:
    latex: '1787904'
    decimal_approx: 1787904
    alt_display: 1,787,904
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-9
  type: upper_bound
  value:
    latex: '1787904'
    decimal_approx: 1787904
    alt_display: 1,787,904
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-10
  type: lower_bound
  value:
    latex: '9381840'
    decimal_approx: 9381840
    alt_display: 9,381,840
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-10
  type: upper_bound
  value:
    latex: '9381840'
    decimal_approx: 9381840
    alt_display: 9,381,840
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-11
  type: lower_bound
  value:
    latex: '51081844'
    decimal_approx: 51081844
    alt_display: 51,081,844
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-11
  type: upper_bound
  value:
    latex: '51081844'
    decimal_approx: 51081844
    alt_display: 51,081,844
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-12
  type: lower_bound
  value:
    latex: '266680992'
    decimal_approx: 266680992
    alt_display: 266,680,992
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-12
  type: upper_bound
  value:
    latex: '266680992'
    decimal_approx: 266680992
    alt_display: 266,680,992
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-13
  type: lower_bound
  value:
    latex: '1429703548'
    decimal_approx: 1429703548
    alt_display: 1,429,703,548
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-13
  type: upper_bound
  value:
    latex: '1429703548'
    decimal_approx: 1429703548
    alt_display: 1,429,703,548
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-14
  type: lower_bound
  value:
    latex: '7432424160'
    decimal_approx: 7432424160
    alt_display: 7,432,424,160
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-14
  type: upper_bound
  value:
    latex: '7432424160'
    decimal_approx: 7432424160
    alt_display: 7,432,424,160
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-15
  type: lower_bound
  value:
    latex: '39409195740'
    decimal_approx: 39409195740
    alt_display: 39,409,195,740
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-15
  type: upper_bound
  value:
    latex: '39409195740'
    decimal_approx: 39409195740
    alt_display: 39,409,195,740
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-16
  type: lower_bound
  value:
    latex: '204150606976'
    decimal_approx: 204150606976
    alt_display: 204,150,606,976
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-16
  type: upper_bound
  value:
    latex: '204150606976'
    decimal_approx: 204150606976
    alt_display: 204,150,606,976
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-17
  type: lower_bound
  value:
    latex: '1073644675448'
    decimal_approx: 1073644675448
    alt_display: 1,073,644,675,448
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-17
  type: upper_bound
  value:
    latex: '1073644675448'
    decimal_approx: 1073644675448
    alt_display: 1,073,644,675,448
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-18
  type: lower_bound
  value:
    latex: '5545305620064'
    decimal_approx: 5545305620064
    alt_display: 5,545,305,620,064
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: map-folding-2-18
  type: upper_bound
  value:
    latex: '5545305620064'
    decimal_approx: 5545305620064
    alt_display: 5,545,305,620,064
  date: null
  primary_source: null
  secondary_source: oeis-a001415-map-folding-2-n
- constant: minimal-superpermutation-1
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-1
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-2
  type: lower_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-2
  type: upper_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-3
  type: lower_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-3
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-4
  type: lower_bound
  value:
    latex: '33'
    decimal_approx: 33
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-4
  type: upper_bound
  value:
    latex: '33'
    decimal_approx: 33
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-5
  type: upper_bound
  value:
    latex: '153'
    decimal_approx: 153
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-6
  type: upper_bound
  value:
    latex: '873'
    decimal_approx: 873
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-7
  type: upper_bound
  value:
    latex: '5913'
    decimal_approx: 5913
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-8
  type: upper_bound
  value:
    latex: '46233'
    decimal_approx: 46233
    alt_display: 46,233
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-9
  type: upper_bound
  value:
    latex: '409113'
    decimal_approx: 409113
    alt_display: 409,113
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-7
  type: upper_bound
  value:
    latex: '5908'
    decimal_approx: 5908
    alt_display: null
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-8
  type: upper_bound
  value:
    latex: '46205'
    decimal_approx: 46205
    alt_display: 46,205
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-9
  type: upper_bound
  value:
    latex: '408966'
    decimal_approx: 408966
    alt_display: 408,966
  date: null
  primary_source: null
  secondary_source: egan-superpermutations
- constant: ramsey-3-3
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-3
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-15
  type: lower_bound
  value:
    latex: '275'
    decimal_approx: 275
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-15
  type: lower_bound
  value:
    latex: '401'
    decimal_approx: 401
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-9
  type: upper_bound
  value:
    latex: '3583'
    decimal_approx: 3583
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-11
  type: lower_bound
  value:
    latex: '457'
    decimal_approx: 457
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-15
  type: lower_bound
  value:
    latex: '873'
    decimal_approx: 873
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-10
  type: upper_bound
  value:
    latex: '12677'
    decimal_approx: 12677
    alt_display: 12,677
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-10-15
  type: lower_bound
  value:
    latex: '1313'
    decimal_approx: 1313
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: square-packing-in-square-1
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-2
  type: upper_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-3
  type: upper_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-4
  type: upper_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-6
  type: upper_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-7
  type: upper_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-8
  type: upper_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-9
  type: upper_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-11
  type: upper_bound
  value:
    latex: '{\approx}3.8771'
    decimal_approx: 3.8771
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-12
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-13
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-14
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-15
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-16
  type: upper_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-17
  type: upper_bound
  value:
    latex: '{\approx}4.6756'
    decimal_approx: 4.6756
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-18
  type: upper_bound
  value:
    latex: \frac{7+\sqrt{7}}{2}
    decimal_approx: 4.822876
    alt_display: "\u22484.822876"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-19
  type: upper_bound
  value:
    latex: 3+\frac{4\sqrt{2}}{3}
    decimal_approx: 4.885618
    alt_display: "\u22484.885618"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-20
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-21
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-22
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-23
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-24
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-25
  type: upper_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-26
  type: upper_bound
  value:
    latex: \frac{7}{2}+\frac{3\sqrt{2}}{2}
    decimal_approx: 5.62132
    alt_display: "\u22485.62132"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-28
  type: upper_bound
  value:
    latex: 3+2\sqrt{2}
    decimal_approx: 5.828427
    alt_display: "\u22485.828427"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-29
  type: upper_bound
  value:
    latex: '{\approx}5.9344'
    decimal_approx: 5.9344
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-30
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-31
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-32
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-33
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-34
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-35
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-36
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-37
  type: upper_bound
  value:
    latex: '{\approx}6.5987'
    decimal_approx: 6.5987
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-39
  type: upper_bound
  value:
    latex: '{\approx}6.8189'
    decimal_approx: 6.8189
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-40
  type: upper_bound
  value:
    latex: 4+2\sqrt{2}
    decimal_approx: 6.828427
    alt_display: "\u22486.828427"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-41
  type: upper_bound
  value:
    latex: '{\approx}6.9473'
    decimal_approx: 6.9473
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-42
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-43
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-44
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-45
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-46
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-47
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-48
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-49
  type: upper_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-50
  type: upper_bound
  value:
    latex: '{\approx}7.5987'
    decimal_approx: 7.5987
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-51
  type: upper_bound
  value:
    latex: '{\approx}7.7044'
    decimal_approx: 7.7044
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-53
  type: upper_bound
  value:
    latex: '{\approx}7.8231'
    decimal_approx: 7.8231
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-54
  type: upper_bound
  value:
    latex: '{\approx}7.8488'
    decimal_approx: 7.8488
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-55
  type: upper_bound
  value:
    latex: '{\approx}7.9871'
    decimal_approx: 7.9871
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-56
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-57
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-58
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-59
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-60
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-61
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-62
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-63
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-64
  type: upper_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-65
  type: upper_bound
  value:
    latex: 5+\frac{5}{\sqrt{2}}
    decimal_approx: 8.535534
    alt_display: "\u22488.535534"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-66
  type: upper_bound
  value:
    latex: 3+4\sqrt{2}
    decimal_approx: 8.656854
    alt_display: "\u22488.656854"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-68
  type: upper_bound
  value:
    latex: \frac{15}{2}+\frac{\sqrt{7}}{2}
    decimal_approx: 8.822876
    alt_display: "\u22488.822876"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-69
  type: upper_bound
  value:
    latex: '{\approx}8.8562'
    decimal_approx: 8.8562
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-70
  type: upper_bound
  value:
    latex: '{\approx}8.9121'
    decimal_approx: 8.9121
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-71
  type: upper_bound
  value:
    latex: '{\approx}8.9633'
    decimal_approx: 8.9633
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-72
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-73
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-74
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-75
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-76
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-77
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-78
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-79
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-80
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-81
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-82
  type: upper_bound
  value:
    latex: 6+\frac{5}{\sqrt{2}}
    decimal_approx: 9.535534
    alt_display: "\u22489.535534"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-83
  type: upper_bound
  value:
    latex: 4+4\sqrt{2}
    decimal_approx: 9.656854
    alt_display: "\u22489.656854"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-85
  type: upper_bound
  value:
    latex: \frac{11}{2}+3\sqrt{2}
    decimal_approx: 9.742641
    alt_display: "\u22489.742641"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-86
  type: upper_bound
  value:
    latex: \frac{17+\sqrt{7}}{2}
    decimal_approx: 9.822876
    alt_display: "\u22489.822876"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-87
  type: upper_bound
  value:
    latex: '{\approx}9.8520'
    decimal_approx: 9.852
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-88
  type: upper_bound
  value:
    latex: '{\approx}9.9018'
    decimal_approx: 9.9018
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-89
  type: upper_bound
  value:
    latex: 5+\frac{7}{\sqrt{2}}
    decimal_approx: 9.949747
    alt_display: "\u22489.949747"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-90
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-91
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-92
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-93
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-94
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-95
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-96
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-97
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-98
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-99
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-100
  type: upper_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-1
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-2
  type: lower_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-3
  type: lower_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-4
  type: lower_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-6
  type: lower_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-7
  type: lower_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-8
  type: lower_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-9
  type: lower_bound
  value:
    latex: '3'
    decimal_approx: 3
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-10
  type: lower_bound
  value:
    latex: 3 + \frac{1}{\sqrt{2}}
    decimal_approx: 3.707107
    alt_display: "\u22483.707107"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-11
  type: lower_bound
  value:
    latex: 2 + \frac{4}{\sqrt{5}}
    decimal_approx: 3.788854
    alt_display: "\u22483.788854"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-12
  type: lower_bound
  value:
    latex: 2 + \frac{4}{\sqrt{5}}
    decimal_approx: 3.788854
    alt_display: "\u22483.788854"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-13
  type: lower_bound
  value:
    latex: '3.8437'
    decimal_approx: 3.8437
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-14
  type: lower_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-15
  type: lower_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-16
  type: lower_bound
  value:
    latex: '4'
    decimal_approx: 4
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-17
  type: lower_bound
  value:
    latex: \frac{40\sqrt{2}+19}{17}
    decimal_approx: 4.445208
    alt_display: "\u22484.445208"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-18
  type: lower_bound
  value:
    latex: \frac{40\sqrt{2}+19}{17}
    decimal_approx: 4.445208
    alt_display: "\u22484.445208"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-19
  type: lower_bound
  value:
    latex: 6\sqrt{2}-4
    decimal_approx: 4.485281
    alt_display: "\u22484.485281"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-20
  type: lower_bound
  value:
    latex: 6\sqrt{2}-4
    decimal_approx: 4.485281
    alt_display: "\u22484.485281"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-21
  type: lower_bound
  value:
    latex: '4.7438'
    decimal_approx: 4.7438
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-22
  type: lower_bound
  value:
    latex: 2\sqrt{2}+2
    decimal_approx: 4.828427
    alt_display: "\u22484.828427"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-23
  type: lower_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-24
  type: lower_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-25
  type: lower_bound
  value:
    latex: '5'
    decimal_approx: 5
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-26
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{27+2\sqrt{10}}{13}
    decimal_approx: 5.391854
    alt_display: "\u22485.391854"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-27
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{27+2\sqrt{10}}{13}
    decimal_approx: 5.391854
    alt_display: "\u22485.391854"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-28
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{6}{\sqrt{5}}
    decimal_approx: 5.511709
    alt_display: "\u22485.511709"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-29
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{6}{\sqrt{5}}
    decimal_approx: 5.511709
    alt_display: "\u22485.511709"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-30
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{6}{\sqrt{5}}
    decimal_approx: 5.511709
    alt_display: "\u22485.511709"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-31
  type: lower_bound
  value:
    latex: '5.6415'
    decimal_approx: 5.6415
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-34
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-35
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-36
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-37
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{113+10\sqrt{3}}{37}
    decimal_approx: 6.350603
    alt_display: "\u22486.350603"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-38
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{113+10\sqrt{3}}{37}
    decimal_approx: 6.350603
    alt_display: "\u22486.350603"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-39
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{113+10\sqrt{3}}{37}
    decimal_approx: 6.350603
    alt_display: "\u22486.350603"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-40
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{8}{\sqrt{5}}
    decimal_approx: 6.406136
    alt_display: "\u22486.406136"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-41
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{8}{\sqrt{5}}
    decimal_approx: 6.406136
    alt_display: "\u22486.406136"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-47
  type: lower_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-48
  type: lower_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-49
  type: lower_bound
  value:
    latex: '7'
    decimal_approx: 7
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-50
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{101+3\sqrt{14}}{25}
    decimal_approx: 7.317426
    alt_display: "\u22487.317426"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-51
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{101+3\sqrt{14}}{25}
    decimal_approx: 7.317426
    alt_display: "\u22487.317426"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-52
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{101+3\sqrt{14}}{25}
    decimal_approx: 7.317426
    alt_display: "\u22487.317426"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-53
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{101+3\sqrt{14}}{25}
    decimal_approx: 7.317426
    alt_display: "\u22487.317426"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-62
  type: lower_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-63
  type: lower_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-64
  type: lower_bound
  value:
    latex: '8'
    decimal_approx: 8
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-65
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{71}{13}
    decimal_approx: 8.289966
    alt_display: "\u22488.289966"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-66
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{71}{13}
    decimal_approx: 8.289966
    alt_display: "\u22488.289966"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-67
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{71}{13}
    decimal_approx: 8.289966
    alt_display: "\u22488.289966"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-68
  type: lower_bound
  value:
    latex: 2\sqrt{2}+\frac{71}{13}
    decimal_approx: 8.289966
    alt_display: "\u22488.289966"
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-79
  type: lower_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-80
  type: lower_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-81
  type: lower_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-82
  type: lower_bound
  value:
    latex: '{\approx}9.2667'
    decimal_approx: 9.2667
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-83
  type: lower_bound
  value:
    latex: '{\approx}9.2667'
    decimal_approx: 9.2667
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-84
  type: lower_bound
  value:
    latex: '{\approx}9.2667'
    decimal_approx: 9.2667
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-85
  type: lower_bound
  value:
    latex: '{\approx}9.2667'
    decimal_approx: 9.2667
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-98
  type: lower_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-99
  type: lower_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-100
  type: lower_bound
  value:
    latex: '10'
    decimal_approx: 10
    alt_display: null
  date: null
  primary_source: null
  secondary_source: ejc-ds7-packing-unit-squares
- constant: stamp-folding-1
  type: lower_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-1
  type: upper_bound
  value:
    latex: '1'
    decimal_approx: 1
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-2
  type: lower_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-2
  type: upper_bound
  value:
    latex: '2'
    decimal_approx: 2
    alt_display: null
  date: null
  primary_source: trivial
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-3
  type: lower_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-3
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-4
  type: lower_bound
  value:
    latex: '16'
    decimal_approx: 16
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-4
  type: upper_bound
  value:
    latex: '16'
    decimal_approx: 16
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-5
  type: lower_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-5
  type: upper_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-6
  type: lower_bound
  value:
    latex: '144'
    decimal_approx: 144
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-6
  type: upper_bound
  value:
    latex: '144'
    decimal_approx: 144
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-7
  type: lower_bound
  value:
    latex: '462'
    decimal_approx: 462
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-7
  type: upper_bound
  value:
    latex: '462'
    decimal_approx: 462
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-8
  type: lower_bound
  value:
    latex: '1392'
    decimal_approx: 1392
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-8
  type: upper_bound
  value:
    latex: '1392'
    decimal_approx: 1392
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-9
  type: lower_bound
  value:
    latex: '4536'
    decimal_approx: 4536
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-9
  type: upper_bound
  value:
    latex: '4536'
    decimal_approx: 4536
    alt_display: null
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-10
  type: lower_bound
  value:
    latex: '14060'
    decimal_approx: 14060
    alt_display: 14,060
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-10
  type: upper_bound
  value:
    latex: '14060'
    decimal_approx: 14060
    alt_display: 14,060
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-11
  type: lower_bound
  value:
    latex: '46310'
    decimal_approx: 46310
    alt_display: 46,310
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-11
  type: upper_bound
  value:
    latex: '46310'
    decimal_approx: 46310
    alt_display: 46,310
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-12
  type: lower_bound
  value:
    latex: '146376'
    decimal_approx: 146376
    alt_display: 146,376
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-12
  type: upper_bound
  value:
    latex: '146376'
    decimal_approx: 146376
    alt_display: 146,376
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-13
  type: lower_bound
  value:
    latex: '485914'
    decimal_approx: 485914
    alt_display: 485,914
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-13
  type: upper_bound
  value:
    latex: '485914'
    decimal_approx: 485914
    alt_display: 485,914
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-14
  type: lower_bound
  value:
    latex: '1557892'
    decimal_approx: 1557892
    alt_display: 1,557,892
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-14
  type: upper_bound
  value:
    latex: '1557892'
    decimal_approx: 1557892
    alt_display: 1,557,892
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-15
  type: lower_bound
  value:
    latex: '5202690'
    decimal_approx: 5202690
    alt_display: 5,202,690
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-15
  type: upper_bound
  value:
    latex: '5202690'
    decimal_approx: 5202690
    alt_display: 5,202,690
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-16
  type: lower_bound
  value:
    latex: '16861984'
    decimal_approx: 16861984
    alt_display: 16,861,984
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-16
  type: upper_bound
  value:
    latex: '16861984'
    decimal_approx: 16861984
    alt_display: 16,861,984
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-17
  type: lower_bound
  value:
    latex: '56579196'
    decimal_approx: 56579196
    alt_display: 56,579,196
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-17
  type: upper_bound
  value:
    latex: '56579196'
    decimal_approx: 56579196
    alt_display: 56,579,196
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-18
  type: lower_bound
  value:
    latex: '184940388'
    decimal_approx: 184940388
    alt_display: 184,940,388
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-18
  type: upper_bound
  value:
    latex: '184940388'
    decimal_approx: 184940388
    alt_display: 184,940,388
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-19
  type: lower_bound
  value:
    latex: '622945970'
    decimal_approx: 622945970
    alt_display: 622,945,970
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-19
  type: upper_bound
  value:
    latex: '622945970'
    decimal_approx: 622945970
    alt_display: 622,945,970
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-20
  type: lower_bound
  value:
    latex: '2050228360'
    decimal_approx: 2050228360
    alt_display: 2,050,228,360
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-20
  type: upper_bound
  value:
    latex: '2050228360'
    decimal_approx: 2050228360
    alt_display: 2,050,228,360
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-21
  type: lower_bound
  value:
    latex: '6927964218'
    decimal_approx: 6927964218
    alt_display: 6,927,964,218
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-21
  type: upper_bound
  value:
    latex: '6927964218'
    decimal_approx: 6927964218
    alt_display: 6,927,964,218
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-22
  type: lower_bound
  value:
    latex: '22930109884'
    decimal_approx: 22930109884
    alt_display: 22,930,109,884
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-22
  type: upper_bound
  value:
    latex: '22930109884'
    decimal_approx: 22930109884
    alt_display: 22,930,109,884
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-23
  type: lower_bound
  value:
    latex: '77692142980'
    decimal_approx: 77692142980
    alt_display: 77,692,142,980
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-23
  type: upper_bound
  value:
    latex: '77692142980'
    decimal_approx: 77692142980
    alt_display: 77,692,142,980
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-24
  type: lower_bound
  value:
    latex: '258360586368'
    decimal_approx: 258360586368
    alt_display: 258,360,586,368
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-24
  type: upper_bound
  value:
    latex: '258360586368'
    decimal_approx: 258360586368
    alt_display: 258,360,586,368
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-25
  type: lower_bound
  value:
    latex: '877395996200'
    decimal_approx: 877395996200
    alt_display: 877,395,996,200
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-25
  type: upper_bound
  value:
    latex: '877395996200'
    decimal_approx: 877395996200
    alt_display: 877,395,996,200
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-26
  type: lower_bound
  value:
    latex: '2929432171328'
    decimal_approx: 2929432171328
    alt_display: 2,929,432,171,328
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-26
  type: upper_bound
  value:
    latex: '2929432171328'
    decimal_approx: 2929432171328
    alt_display: 2,929,432,171,328
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-27
  type: lower_bound
  value:
    latex: '9968202968958'
    decimal_approx: 9968202968958
    alt_display: 9,968,202,968,958
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-27
  type: upper_bound
  value:
    latex: '9968202968958'
    decimal_approx: 9968202968958
    alt_display: 9,968,202,968,958
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-28
  type: lower_bound
  value:
    latex: '33396290888520'
    decimal_approx: 33396290888520
    alt_display: 33,396,290,888,520
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-28
  type: upper_bound
  value:
    latex: '33396290888520'
    decimal_approx: 33396290888520
    alt_display: 33,396,290,888,520
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-29
  type: lower_bound
  value:
    latex: '113837957337750'
    decimal_approx: 113837957337750
    alt_display: 113,837,957,337,750
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: stamp-folding-29
  type: upper_bound
  value:
    latex: '113837957337750'
    decimal_approx: 113837957337750
    alt_display: 113,837,957,337,750
  date: null
  primary_source: null
  secondary_source: oeis-a000136-stamp-folding
- constant: van-der-waerden-4-6
  type: lower_bound
  value:
    latex: '91332'
    decimal_approx: 91332
    alt_display: 91,332
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-4-7
  type: lower_bound
  value:
    latex: '420218'
    decimal_approx: 420218
    alt_display: 420,218
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-4-8
  type: lower_bound
  value:
    latex: '2388318'
    decimal_approx: 2388318
    alt_display: 2,388,318
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-4-9
  type: lower_bound
  value:
    latex: '10898730'
    decimal_approx: 10898730
    alt_display: 10,898,730
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-4-10
  type: lower_bound
  value:
    latex: '76049219'
    decimal_approx: 76049219
    alt_display: 76,049,219
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-4-11
  type: lower_bound
  value:
    latex: '329263782'
    decimal_approx: 329263782
    alt_display: 329,263,782
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-5-6
  type: lower_bound
  value:
    latex: '540026'
    decimal_approx: 540026
    alt_display: 540,026
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-5-9
  type: lower_bound
  value:
    latex: '79706010'
    decimal_approx: 79706010
    alt_display: 79,706,010
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-5-10
  type: lower_bound
  value:
    latex: '542694971'
    decimal_approx: 542694971
    alt_display: 542,694,971
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: van-der-waerden-6-6
  type: lower_bound
  value:
    latex: '816982'
    decimal_approx: 816982
    alt_display: 816,982
  date: null
  primary_source: null
  secondary_source: blankenship-c-t-2018
- constant: debruijn-newman
  type: upper_bound
  value:
    latex: \le 0.5
    decimal_approx: 0.5
    alt_display: null
  date: 1950-09
  primary_source: debruijn-1950
  secondary_source: wikipedia-debruijn-newman
- constant: ramsey-3-4
  type: lower_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: '1955'
  primary_source: greenwood-gleason-1955
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-4
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: '1955'
  primary_source: greenwood-gleason-1955
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-5
  type: lower_bound
  value:
    latex: '14'
    decimal_approx: 14
    alt_display: null
  date: '1955'
  primary_source: greenwood-gleason-1955
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-5
  type: upper_bound
  value:
    latex: '14'
    decimal_approx: 14
    alt_display: null
  date: '1955'
  primary_source: greenwood-gleason-1955
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-4
  type: lower_bound
  value:
    latex: '18'
    decimal_approx: 18
    alt_display: null
  date: '1955'
  primary_source: greenwood-gleason-1955
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-4
  type: upper_bound
  value:
    latex: '18'
    decimal_approx: 18
    alt_display: null
  date: '1955'
  primary_source: greenwood-gleason-1955
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: circle-in-equilateral-6
  type: lower_bound
  value:
    latex: 4+2\sqrt{3}
    decimal_approx: 7.464102
    alt_display: "\u22487.464102"
  date: '1961'
  primary_source: oler-groemer-1961
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-10
  type: lower_bound
  value:
    latex: 6+2\sqrt{3}
    decimal_approx: 9.464102
    alt_display: "\u22489.464102"
  date: '1961'
  primary_source: oler-groemer-1961
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-14
  type: upper_bound
  value:
    latex: 8+2\sqrt{3}
    decimal_approx: 11.4641
    alt_display: "\u224811.4641"
  date: '1961'
  primary_source: erdos-oler-1961
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-15
  type: lower_bound
  value:
    latex: 8+2\sqrt{3}
    decimal_approx: 11.4641
    alt_display: "\u224811.4641"
  date: '1961'
  primary_source: erdos-groemer-1961
  secondary_source: friedman-circles-in-triangles
- constant: ramsey-3-6
  type: lower_bound
  value:
    latex: '18'
    decimal_approx: 18
    alt_display: null
  date: '1964'
  primary_source: kery-1964
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-6
  type: upper_bound
  value:
    latex: '18'
    decimal_approx: 18
    alt_display: null
  date: '1964'
  primary_source: kery-1964
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-3-3
  type: lower_bound
  value:
    latex: '20'
    decimal_approx: 20
    alt_display: null
  date: 1964-11
  primary_source: elspasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-3-3
  type: upper_bound
  value:
    latex: '20'
    decimal_approx: 20
    alt_display: null
  date: 1964-11
  primary_source: elspasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-2
  type: lower_bound
  value:
    latex: '15'
    decimal_approx: 15
    alt_display: null
  date: 1964-11
  primary_source: elspasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-2
  type: upper_bound
  value:
    latex: '15'
    decimal_approx: 15
    alt_display: null
  date: 1964-11
  primary_source: elspasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-2
  type: lower_bound
  value:
    latex: '24'
    decimal_approx: 24
    alt_display: null
  date: 1964-11
  primary_source: elspasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-2
  type: upper_bound
  value:
    latex: '24'
    decimal_approx: 24
    alt_display: null
  date: 1964-11
  primary_source: elspasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-4-5
  type: lower_bound
  value:
    latex: '25'
    decimal_approx: 25
    alt_display: null
  date: '1965'
  primary_source: kalbfleisch-1965
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: busy-beaver-shift-3
  type: upper_bound
  value:
    latex: '21'
    decimal_approx: 21
    alt_display: null
  date: '1965-04-01'
  primary_source: lin-1965
  secondary_source: oeis-A060843
- constant: busy-beaver-ones-3
  type: upper_bound
  value:
    latex: '6'
    decimal_approx: 6
    alt_display: null
  date: '1965-04-01'
  primary_source: lin-1965
  secondary_source: oeis-A028444
- constant: degree-diameter-17-2
  type: lower_bound
  value:
    latex: '274'
    decimal_approx: 274
    alt_display: null
  date: '1966'
  primary_source: brown-1966
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-2
  type: lower_bound
  value:
    latex: '274'
    decimal_approx: 274
    alt_display: null
  date: '1966'
  primary_source: brown-1966
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-2
  type: lower_bound
  value:
    latex: '381'
    decimal_approx: 381
    alt_display: null
  date: '1966'
  primary_source: brown-1966
  secondary_source: combi-wiki-degree-diameter
- constant: ramsey-3-7
  type: lower_bound
  value:
    latex: '23'
    decimal_approx: 23
    alt_display: null
  date: 1966-01
  primary_source: kalbfleisch-1966
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-9
  type: lower_bound
  value:
    latex: '36'
    decimal_approx: 36
    alt_display: null
  date: 1966-01
  primary_source: kalbfleisch-1966
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-6
  type: lower_bound
  value:
    latex: '102'
    decimal_approx: 102
    alt_display: null
  date: 1966-01
  primary_source: kalbfleisch-1966
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-7
  type: upper_bound
  value:
    latex: '23'
    decimal_approx: 23
    alt_display: null
  date: '1968'
  primary_source: graver-yackel-1968
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: van-der-waerden-2-3
  type: lower_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: '1970'
  primary_source: chvatal-1970
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-3
  type: upper_bound
  value:
    latex: '9'
    decimal_approx: 9
    alt_display: null
  date: '1970'
  primary_source: chvatal-1970
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-4
  type: lower_bound
  value:
    latex: '35'
    decimal_approx: 35
    alt_display: null
  date: '1970'
  primary_source: chvatal-1970
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-4
  type: upper_bound
  value:
    latex: '35'
    decimal_approx: 35
    alt_display: null
  date: '1970'
  primary_source: chvatal-1970
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-3
  type: lower_bound
  value:
    latex: '27'
    decimal_approx: 27
    alt_display: null
  date: '1970'
  primary_source: chvatal-1970
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-3
  type: upper_bound
  value:
    latex: '27'
    decimal_approx: 27
    alt_display: null
  date: '1970'
  primary_source: chvatal-1970
  secondary_source: wikipedia-van-der-waerden
- constant: degree-diameter-8-2
  type: lower_bound
  value:
    latex: '57'
    decimal_approx: 57
    alt_display: null
  date: '1970-12-31'
  primary_source: storwickgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-2
  type: lower_bound
  value:
    latex: '74'
    decimal_approx: 74
    alt_display: null
  date: '1970-12-31'
  primary_source: storwickgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-2
  type: lower_bound
  value:
    latex: '91'
    decimal_approx: 91
    alt_display: null
  date: '1970-12-31'
  primary_source: storwickgraphs
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-8-8
  type: lower_bound
  value:
    latex: '282'
    decimal_approx: 282
    alt_display: null
  date: '1972'
  primary_source: burling-reyner-1972
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-6-2
  type: lower_bound
  value:
    latex: '32'
    decimal_approx: 32
    alt_display: null
  date: '1977'
  primary_source: wegnergraph
  secondary_source: wikipedia-degree-diameter
- constant: van-der-waerden-2-5
  type: lower_bound
  value:
    latex: '178'
    decimal_approx: 178
    alt_display: null
  date: 1978-04
  primary_source: stevens-shantaram-1978
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-5
  type: upper_bound
  value:
    latex: '178'
    decimal_approx: 178
    alt_display: null
  date: 1978-04
  primary_source: stevens-shantaram-1978
  secondary_source: wikipedia-van-der-waerden
- constant: disk-covering-6
  type: lower_bound
  value:
    latex: '{\approx}0.555905'
    decimal_approx: 0.555905
    alt_display: null
  date: '1979'
  primary_source: bezdek-1979
  secondary_source: friedman-circles-covering-circles
- constant: square-packing-in-square-5
  type: upper_bound
  value:
    latex: 2 + \frac{1}{\sqrt{2}}
    decimal_approx: 2.707107
    alt_display: "\u22482.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-10
  type: upper_bound
  value:
    latex: 3 + \frac{1}{\sqrt{2}}
    decimal_approx: 3.707107
    alt_display: "\u22483.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-27
  type: upper_bound
  value:
    latex: 5+\frac{1}{\sqrt{2}}
    decimal_approx: 5.707107
    alt_display: "\u22485.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-38
  type: upper_bound
  value:
    latex: 6+\frac{1}{\sqrt{2}}
    decimal_approx: 6.707107
    alt_display: "\u22486.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-52
  type: upper_bound
  value:
    latex: 7+\frac{1}{\sqrt{2}}
    decimal_approx: 7.707107
    alt_display: "\u22487.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-67
  type: upper_bound
  value:
    latex: 8+\frac{1}{\sqrt{2}}
    decimal_approx: 8.707107
    alt_display: "\u22488.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-84
  type: upper_bound
  value:
    latex: 9+\frac{1}{\sqrt{2}}
    decimal_approx: 9.707107
    alt_display: "\u22489.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: square-packing-in-square-5
  type: lower_bound
  value:
    latex: 2 + \frac{1}{\sqrt{2}}
    decimal_approx: 2.707107
    alt_display: "\u22482.707107"
  date: '1979'
  primary_source: gobel-1979
  secondary_source: ejc-ds7-packing-unit-squares
- constant: van-der-waerden-4-3
  type: upper_bound
  value:
    latex: '76'
    decimal_approx: 76
    alt_display: null
  date: '1979'
  primary_source: beeler-oneil-1979
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-3
  type: lower_bound
  value:
    latex: '76'
    decimal_approx: 76
    alt_display: null
  date: '1979-03-01'
  primary_source: rabung-1979
  secondary_source: beeler-oneil-1979
- constant: degree-diameter-12-4
  type: lower_bound
  value:
    latex: '4680'
    decimal_approx: 4680
    alt_display: null
  date: '1982'
  primary_source: bdfgraph
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-3-8
  type: lower_bound
  value:
    latex: '28'
    decimal_approx: 28
    alt_display: null
  date: '1982'
  primary_source: grinstead-roberts-1982
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-9
  type: upper_bound
  value:
    latex: '36'
    decimal_approx: 36
    alt_display: null
  date: '1982'
  primary_source: grinstead-roberts-1982
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-3-4
  type: lower_bound
  value:
    latex: '38'
    decimal_approx: 38
    alt_display: null
  date: 1982-10
  primary_source: dotygraph
  secondary_source: wikipedia-degree-diameter
- constant: disk-covering-5
  type: lower_bound
  value:
    latex: '{\approx}0.609382'
    decimal_approx: 0.609382
    alt_display: null
  date: '1983'
  primary_source: bezdek-1983
  secondary_source: friedman-circles-covering-circles
- constant: busy-beaver-shift-4
  type: upper_bound
  value:
    latex: '107'
    decimal_approx: 107
    alt_display: null
  date: 1983-04
  primary_source: brady-1983
  secondary_source: oeis-A060843
- constant: busy-beaver-ones-4
  type: upper_bound
  value:
    latex: '13'
    decimal_approx: 13
    alt_display: null
  date: 1983-04
  primary_source: brady-1983
  secondary_source: oeis-A028444
- constant: degree-diameter-12-2
  type: lower_bound
  value:
    latex: '133'
    decimal_approx: 133
    alt_display: null
  date: '1984-09-30'
  primary_source: dfgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-2
  type: lower_bound
  value:
    latex: '183'
    decimal_approx: 183
    alt_display: null
  date: '1984-09-30'
  primary_source: dfgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-4
  type: lower_bound
  value:
    latex: '3200'
    decimal_approx: 3200
    alt_display: null
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-6
  type: lower_bound
  value:
    latex: '156864'
    decimal_approx: 156864
    alt_display: 156,864
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-4
  type: lower_bound
  value:
    latex: '6560'
    decimal_approx: 6560
    alt_display: null
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-6
  type: lower_bound
  value:
    latex: '531440'
    decimal_approx: 531440
    alt_display: 531,440
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-4
  type: lower_bound
  value:
    latex: '8200'
    decimal_approx: 8200
    alt_display: null
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-3
  type: lower_bound
  value:
    latex: '1215'
    decimal_approx: 1215
    alt_display: null
  date: '1985'
  primary_source: delorme85bgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-4
  type: lower_bound
  value:
    latex: '11712'
    decimal_approx: 11712
    alt_display: 11,712
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-6
  type: lower_bound
  value:
    latex: '1417248'
    decimal_approx: 1417248
    alt_display: 1,417,248
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-3
  type: lower_bound
  value:
    latex: '1600'
    decimal_approx: 1600
    alt_display: null
  date: '1985'
  primary_source: delorme85bgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-4
  type: lower_bound
  value:
    latex: '14640'
    decimal_approx: 14640
    alt_display: 14,640
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-5
  type: lower_bound
  value:
    latex: '132496'
    decimal_approx: 132496
    alt_display: 132,496
  date: '1985'
  primary_source: delorme85bgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-6
  type: lower_bound
  value:
    latex: '1771560'
    decimal_approx: 1771560
    alt_display: 1,771,560
  date: '1985'
  primary_source: gomezfiolgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-5
  type: lower_bound
  value:
    latex: '364'
    decimal_approx: 364
    alt_display: null
  date: 1985-12
  primary_source: delorme85agraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-3
  type: lower_bound
  value:
    latex: '585'
    decimal_approx: 585
    alt_display: null
  date: 1985-12
  primary_source: delorme85agraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-3
  type: lower_bound
  value:
    latex: '650'
    decimal_approx: 650
    alt_display: null
  date: 1985-12
  primary_source: delorme85agraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-3
  type: lower_bound
  value:
    latex: '715'
    decimal_approx: 715
    alt_display: null
  date: 1985-12
  primary_source: delorme85agraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-3-5
  type: lower_bound
  value:
    latex: '70'
    decimal_approx: 70
    alt_display: null
  date: '1986'
  primary_source: afygraph
  secondary_source: wikipedia-degree-diameter
- constant: circle-in-equilateral-4
  type: lower_bound
  value:
    latex: 4\sqrt{3}
    decimal_approx: 6.928203
    alt_display: "\u22486.928203"
  date: '1987'
  primary_source: milano-1987
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-5
  type: lower_bound
  value:
    latex: 4+2\sqrt{3}
    decimal_approx: 7.464102
    alt_display: "\u22487.464102"
  date: '1987'
  primary_source: milano-1987
  secondary_source: friedman-circles-in-triangles
- constant: ramsey-7-7
  type: lower_bound
  value:
    latex: '205'
    decimal_approx: 205
    alt_display: null
  date: '1987'
  primary_source: mathon-1987
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-9
  type: lower_bound
  value:
    latex: '565'
    decimal_approx: 565
    alt_display: null
  date: '1987'
  primary_source: mathon-1987
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-10-10
  type: lower_bound
  value:
    latex: '798'
    decimal_approx: 798
    alt_display: null
  date: '1987'
  primary_source: mathon-1987
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: '-50'
    decimal_approx: -50.0
    alt_display: null
  date: 1987-09
  primary_source: csordas-norfolk-varga-1987
  secondary_source: wikipedia-debruijn-newman
- constant: ramsey-3-10
  type: lower_bound
  value:
    latex: '40'
    decimal_approx: 40
    alt_display: null
  date: '1989'
  primary_source: exoo-1989c
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-7
  type: lower_bound
  value:
    latex: '49'
    decimal_approx: 49
    alt_display: null
  date: '1989'
  primary_source: exoo-1989a
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-5
  type: lower_bound
  value:
    latex: '43'
    decimal_approx: 43
    alt_display: null
  date: '1989'
  primary_source: exoo-1989b
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: busy-beaver-ones-5
  type: lower_bound
  value:
    latex: '4098'
    decimal_approx: 4098
    alt_display: null
  date: 1990-02
  primary_source: marxen-1990
  secondary_source: aaronson-2020
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: '-5'
    decimal_approx: -5.0
    alt_display: null
  date: 1990-12
  primary_source: teriele-1990
  secondary_source: wikipedia-debruijn-newman
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: '-0.0991'
    decimal_approx: -0.0991
    alt_display: null
  date: 1991-06
  primary_source: csordas-ruttan-varga-1991
  secondary_source: wikipedia-debruijn-newman
- constant: ramsey-3-8
  type: upper_bound
  value:
    latex: '28'
    decimal_approx: 28
    alt_display: null
  date: '1992'
  primary_source: mckay-zhang-1992
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-4-3
  type: lower_bound
  value:
    latex: '41'
    decimal_approx: 41
    alt_display: null
  date: '1992-07-15'
  primary_source: allwrightgraph
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-5-6
  type: upper_bound
  value:
    latex: '87'
    decimal_approx: 87
    alt_display: null
  date: '1993'
  primary_source: huang-zhang-1993
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-7
  type: upper_bound
  value:
    latex: '143'
    decimal_approx: 143
    alt_display: null
  date: '1993'
  primary_source: huang-zhang-1993
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-7
  type: upper_bound
  value:
    latex: '298'
    decimal_approx: 298
    alt_display: null
  date: '1993'
  primary_source: huang-zhang-1993
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-8
  type: upper_bound
  value:
    latex: '1031'
    decimal_approx: 1031
    alt_display: null
  date: '1993'
  primary_source: huang-zhang-1993
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-14-7
  type: lower_bound
  value:
    latex: '6200460'
    decimal_approx: 6200460
    alt_display: 6,200,460
  date: '1993-04-28'
  primary_source: gfsgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-7
  type: lower_bound
  value:
    latex: '14882658'
    decimal_approx: 14882658
    alt_display: 14,882,658
  date: '1993-04-28'
  primary_source: gfsgraphs
  secondary_source: wikipedia-degree-diameter
- constant: circle-in-equilateral-7
  type: lower_bound
  value:
    latex: 2+4\sqrt{3}
    decimal_approx: 8.928203
    alt_display: "\u22488.928203"
  date: 1993-12
  primary_source: melissen-1993
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-8
  type: lower_bound
  value:
    latex: 2+2\sqrt{3}+\frac{2\sqrt{33}}{3}
    decimal_approx: 9.29381
    alt_display: "\u22489.29381"
  date: 1993-12
  primary_source: melissen-1993
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-9
  type: lower_bound
  value:
    latex: 6+2\sqrt{3}
    decimal_approx: 9.464102
    alt_display: "\u22489.464102"
  date: 1993-12
  primary_source: melissen-1993
  secondary_source: friedman-circles-in-triangles
- constant: circle-in-equilateral-13
  type: upper_bound
  value:
    latex: 4+\frac{2\sqrt{6}}{3} + \frac{10\sqrt{3}}{3}
    decimal_approx: 11.4065
    alt_display: "\u224811.4065"
  date: 1993-12
  primary_source: melissen-1993
  secondary_source: friedman-circles-in-triangles
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: -5.895 \times 10^{-9}
    decimal_approx: -5.895e-09
    alt_display: "\u2248-5.895e-09"
  date: 1993-12
  primary_source: csordas-o-s-v-1993
  secondary_source: wikipedia-debruijn-newman
- constant: circle-in-equilateral-12
  type: lower_bound
  value:
    latex: 4+4\sqrt{3}
    decimal_approx: 10.9282
    alt_display: "\u224810.9282"
  date: '1994'
  primary_source: melissen-1994b
  secondary_source: friedman-circles-in-triangles
- constant: ramsey-4-7
  type: upper_bound
  value:
    latex: '61'
    decimal_approx: 61
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-8
  type: upper_bound
  value:
    latex: '84'
    decimal_approx: 84
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-9
  type: upper_bound
  value:
    latex: '115'
    decimal_approx: 115
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-10
  type: upper_bound
  value:
    latex: '149'
    decimal_approx: 149
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-11
  type: upper_bound
  value:
    latex: '191'
    decimal_approx: 191
    alt_display: null
  date: '1994'
  primary_source: spencer-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-12
  type: upper_bound
  value:
    latex: '238'
    decimal_approx: 238
    alt_display: null
  date: '1994'
  primary_source: spencer-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-13
  type: upper_bound
  value:
    latex: '291'
    decimal_approx: 291
    alt_display: null
  date: '1994'
  primary_source: spencer-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-14
  type: upper_bound
  value:
    latex: '349'
    decimal_approx: 349
    alt_display: null
  date: '1994'
  primary_source: spencer-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-15
  type: upper_bound
  value:
    latex: '417'
    decimal_approx: 417
    alt_display: null
  date: '1994'
  primary_source: spencer-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-8
  type: upper_bound
  value:
    latex: '216'
    decimal_approx: 216
    alt_display: null
  date: '1994'
  primary_source: spencer-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-9
  type: upper_bound
  value:
    latex: '316'
    decimal_approx: 316
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-10
  type: upper_bound
  value:
    latex: '442'
    decimal_approx: 442
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-6
  type: upper_bound
  value:
    latex: '165'
    decimal_approx: 165
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-8
  type: upper_bound
  value:
    latex: '495'
    decimal_approx: 495
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-9
  type: upper_bound
  value:
    latex: '780'
    decimal_approx: 780
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-10
  type: upper_bound
  value:
    latex: '1171'
    decimal_approx: 1171
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-7
  type: upper_bound
  value:
    latex: '540'
    decimal_approx: 540
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-10
  type: upper_bound
  value:
    latex: '2826'
    decimal_approx: 2826
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-8
  type: upper_bound
  value:
    latex: '1870'
    decimal_approx: 1870
    alt_display: null
  date: '1994'
  primary_source: mackey-1994
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-7-5
  type: lower_bound
  value:
    latex: '2756'
    decimal_approx: 2756
    alt_display: null
  date: 1994-10
  primary_source: dinneen-hafner-1994
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-6
  type: lower_bound
  value:
    latex: '740'
    decimal_approx: 740
    alt_display: null
  date: '1994-11-03'
  primary_source: comellas-gomez-1994
  secondary_source: wikipedia-degree-diameter
- constant: circle-in-equilateral-11
  type: lower_bound
  value:
    latex: 4+2\sqrt{3}+\frac{4\sqrt{6}}{3}
    decimal_approx: 10.73009
    alt_display: "\u224810.73009"
  date: '1994-12-01'
  primary_source: melissen-1994a
  secondary_source: friedman-circles-in-triangles
- constant: degree-diameter-8-3
  type: lower_bound
  value:
    latex: '253'
    decimal_approx: 253
    alt_display: null
  date: '1995'
  primary_source: mitjana-comellas-1995
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-4-5
  type: upper_bound
  value:
    latex: '25'
    decimal_approx: 25
    alt_display: null
  date: '1995'
  primary_source: mckay-radziszowski-1995
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: disk-covering-8
  type: lower_bound
  value:
    latex: '{\approx}0.445041'
    decimal_approx: 0.445041
    alt_display: null
  date: '1996'
  primary_source: toth-1996
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-9
  type: lower_bound
  value:
    latex: '{\approx}0.414213'
    decimal_approx: 0.414213
    alt_display: null
  date: '1996'
  primary_source: toth-1996
  secondary_source: friedman-circles-covering-circles
- constant: degree-diameter-7-4
  type: lower_bound
  value:
    latex: '672'
    decimal_approx: 672
    alt_display: null
  date: '1997'
  primary_source: sampels-1997
  secondary_source: wikipedia-degree-diameter
- constant: disk-covering-11
  type: upper_bound
  value:
    latex: '{\approx}0.380083'
    decimal_approx: 0.380083
    alt_display: null
  date: '1997'
  primary_source: melissen-1997
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-12
  type: upper_bound
  value:
    latex: '{\approx}0.361141'
    decimal_approx: 0.361141
    alt_display: null
  date: '1997'
  primary_source: melissen-1997
  secondary_source: friedman-circles-covering-circles
- constant: ramsey-4-6
  type: upper_bound
  value:
    latex: '41'
    decimal_approx: 41
    alt_display: null
  date: '1997'
  primary_source: mckay-radziszowski-1997
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-7
  type: lower_bound
  value:
    latex: '80'
    decimal_approx: 80
    alt_display: null
  date: '1997'
  primary_source: calkin-erdos-tovey-1997
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-12
  type: lower_bound
  value:
    latex: '128'
    decimal_approx: 128
    alt_display: null
  date: '1998'
  primary_source: su-luo-li-1998
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-9
  type: upper_bound
  value:
    latex: '1713'
    decimal_approx: 1713
    alt_display: null
  date: '1998'
  primary_source: huang-zhang-1998
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-10
  type: upper_bound
  value:
    latex: '6090'
    decimal_approx: 6090
    alt_display: null
  date: '1998'
  primary_source: huang-zhang-1998
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-13-2
  type: lower_bound
  value:
    latex: '162'
    decimal_approx: 162
    alt_display: null
  date: 1998-09
  primary_source: mmsgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-19-2
  type: lower_bound
  value:
    latex: '338'
    decimal_approx: 338
    alt_display: null
  date: 1998-09
  primary_source: mmsgraphs
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-3-4
  type: upper_bound
  value:
    latex: '38'
    decimal_approx: 38
    alt_display: null
  date: '2000-04-15'
  primary_source: buset-2000
  secondary_source: wikipedia-degree-diameter
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: -2.7 \times 10^{-9}
    decimal_approx: -2.7e-09
    alt_display: "\u2248-2.7e-09"
  date: 2000-09
  primary_source: odlyzko-2000
  secondary_source: wikipedia-debruijn-newman
- constant: ramsey-3-12
  type: upper_bound
  value:
    latex: '59'
    decimal_approx: 59
    alt_display: null
  date: '2001'
  primary_source: lesser-2001
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-9
  type: upper_bound
  value:
    latex: '6588'
    decimal_approx: 6588
    alt_display: null
  date: '2001'
  primary_source: shi-zhang-2001
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-3-7
  type: lower_bound
  value:
    latex: '190'
    decimal_approx: 190
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-3-8
  type: lower_bound
  value:
    latex: '330'
    decimal_approx: 330
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-4-4
  type: lower_bound
  value:
    latex: '96'
    decimal_approx: 96
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-5-3
  type: lower_bound
  value:
    latex: '72'
    decimal_approx: 72
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-6-3
  type: lower_bound
  value:
    latex: '110'
    decimal_approx: 110
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-6-4
  type: lower_bound
  value:
    latex: '380'
    decimal_approx: 380
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-7-3
  type: lower_bound
  value:
    latex: '148'
    decimal_approx: 148
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-14-3
  type: lower_bound
  value:
    latex: '912'
    decimal_approx: 912
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-16-2
  type: lower_bound
  value:
    latex: '198'
    decimal_approx: 198
    alt_display: null
  date: '2001-05-25'
  primary_source: exoo-2001
  secondary_source: null
- constant: degree-diameter-3-7
  type: lower_bound
  value:
    latex: '196'
    decimal_approx: 196
    alt_display: null
  date: 2001-06
  primary_source: exoo-post-2001
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-4
  type: lower_bound
  value:
    latex: '98'
    decimal_approx: 98
    alt_display: null
  date: 2001-06
  primary_source: exoo-post-2001
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-3
  type: lower_bound
  value:
    latex: '111'
    decimal_approx: 111
    alt_display: null
  date: 2001-06
  primary_source: exoo-post-2001
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-3
  type: lower_bound
  value:
    latex: '168'
    decimal_approx: 168
    alt_display: null
  date: 2001-06
  primary_source: exoo-post-2001
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-4-10
  type: lower_bound
  value:
    latex: '92'
    decimal_approx: 92
    alt_display: null
  date: '2003'
  primary_source: harborth-krause-2003
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-8
  type: lower_bound
  value:
    latex: '101'
    decimal_approx: 101
    alt_display: null
  date: '2003'
  primary_source: harborth-krause-2003
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-10-10
  type: upper_bound
  value:
    latex: '23556'
    decimal_approx: 23556
    alt_display: 23,556
  date: '2003'
  primary_source: shi-2003
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-11
  type: lower_bound
  value:
    latex: '405'
    decimal_approx: 405
    alt_display: null
  date: '2004'
  primary_source: xu-xie-e-r-2004
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-13
  type: lower_bound
  value:
    latex: '511'
    decimal_approx: 511
    alt_display: null
  date: '2004'
  primary_source: xu-xie-radziszowski-2004
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-13
  type: lower_bound
  value:
    latex: '817'
    decimal_approx: 817
    alt_display: null
  date: '2004'
  primary_source: xu-xie-e-r-2004
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: disk-covering-10
  type: lower_bound
  value:
    latex: '{\approx}0.394930'
    decimal_approx: 0.39493
    alt_display: null
  date: '2005'
  primary_source: toth-2005
  secondary_source: friedman-circles-covering-circles
- constant: ramsey-4-9
  type: lower_bound
  value:
    latex: '73'
    decimal_approx: 73
    alt_display: null
  date: '2005'
  primary_source: exoo-2005
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-6-2
  type: upper_bound
  value:
    latex: '32'
    decimal_approx: 32
    alt_display: null
  date: '2006'
  primary_source: molodtsov-2006
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-6
  type: lower_bound
  value:
    latex: '2772'
    decimal_approx: 2772
    alt_display: null
  date: '2006-07-15'
  primary_source: pinedagraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-6
  type: lower_bound
  value:
    latex: '7917'
    decimal_approx: 7917
    alt_display: null
  date: '2006-07-15'
  primary_source: pinedagraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-6
  type: lower_bound
  value:
    latex: '75893'
    decimal_approx: 75893
    alt_display: 75,893
  date: '2006-07-15'
  primary_source: pinedagraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-6
  type: lower_bound
  value:
    latex: '359772'
    decimal_approx: 359772
    alt_display: 359,772
  date: '2006-07-15'
  primary_source: pinedagraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-6
  type: lower_bound
  value:
    latex: '816294'
    decimal_approx: 816294
    alt_display: 816,294
  date: '2006-07-15'
  primary_source: pinedagraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-3-10
  type: lower_bound
  value:
    latex: '1250'
    decimal_approx: 1250
    alt_display: null
  date: '2006-08-17'
  primary_source: conder-2006
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-5-11
  type: upper_bound
  value:
    latex: '633'
    decimal_approx: 633
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-12
  type: upper_bound
  value:
    latex: '848'
    decimal_approx: 848
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-13
  type: upper_bound
  value:
    latex: '1138'
    decimal_approx: 1138
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-14
  type: upper_bound
  value:
    latex: '1461'
    decimal_approx: 1461
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-15
  type: upper_bound
  value:
    latex: '1878'
    decimal_approx: 1878
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-11
  type: upper_bound
  value:
    latex: '1804'
    decimal_approx: 1804
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-12
  type: upper_bound
  value:
    latex: '2566'
    decimal_approx: 2566
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-13
  type: upper_bound
  value:
    latex: '3703'
    decimal_approx: 3703
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-14
  type: upper_bound
  value:
    latex: '5033'
    decimal_approx: 5033
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-15
  type: upper_bound
  value:
    latex: '6911'
    decimal_approx: 6911
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-11
  type: upper_bound
  value:
    latex: '4553'
    decimal_approx: 4553
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-12
  type: upper_bound
  value:
    latex: '6954'
    decimal_approx: 6954
    alt_display: null
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-13
  type: upper_bound
  value:
    latex: '10578'
    decimal_approx: 10578
    alt_display: 10,578
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-14
  type: upper_bound
  value:
    latex: '15263'
    decimal_approx: 15263
    alt_display: 15,263
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-15
  type: upper_bound
  value:
    latex: '22112'
    decimal_approx: 22112
    alt_display: 22,112
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-11
  type: upper_bound
  value:
    latex: '10630'
    decimal_approx: 10630
    alt_display: 10,630
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-12
  type: upper_bound
  value:
    latex: '16944'
    decimal_approx: 16944
    alt_display: 16,944
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-13
  type: upper_bound
  value:
    latex: '27485'
    decimal_approx: 27485
    alt_display: 27,485
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-14
  type: upper_bound
  value:
    latex: '41525'
    decimal_approx: 41525
    alt_display: 41,525
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-15
  type: upper_bound
  value:
    latex: '63609'
    decimal_approx: 63609
    alt_display: 63,609
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-11
  type: upper_bound
  value:
    latex: '22325'
    decimal_approx: 22325
    alt_display: 22,325
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-12
  type: upper_bound
  value:
    latex: '38832'
    decimal_approx: 38832
    alt_display: 38,832
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-13
  type: upper_bound
  value:
    latex: '64864'
    decimal_approx: 64864
    alt_display: 64,864
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-10-11
  type: upper_bound
  value:
    latex: '45881'
    decimal_approx: 45881
    alt_display: 45,881
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-10-12
  type: upper_bound
  value:
    latex: '81123'
    decimal_approx: 81123
    alt_display: 81,123
  date: '2007'
  primary_source: huang-w-s-y-z-h-2007
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: cage-4-9
  type: upper_bound
  value:
    latex: '275'
    decimal_approx: 275
    alt_display: null
  date: '2008'
  primary_source: exoo-circa-2008
  secondary_source: ejc-ds16-cages
- constant: cage-4-10
  type: upper_bound
  value:
    latex: '384'
    decimal_approx: 384
    alt_display: null
  date: '2008'
  primary_source: exoo-circa-2008
  secondary_source: ejc-ds16-cages
- constant: degree-diameter-4-7
  type: lower_bound
  value:
    latex: '1320'
    decimal_approx: 1320
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-8
  type: lower_bound
  value:
    latex: '3243'
    decimal_approx: 3243
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-9
  type: lower_bound
  value:
    latex: '7575'
    decimal_approx: 7575
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-4-10
  type: lower_bound
  value:
    latex: '17703'
    decimal_approx: 17703
    alt_display: 17,703
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-5
  type: lower_bound
  value:
    latex: '624'
    decimal_approx: 624
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-7
  type: lower_bound
  value:
    latex: '5516'
    decimal_approx: 5516
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-8
  type: lower_bound
  value:
    latex: '17030'
    decimal_approx: 17030
    alt_display: 17,030
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-9
  type: lower_bound
  value:
    latex: '57840'
    decimal_approx: 57840
    alt_display: 57,840
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-5-10
  type: lower_bound
  value:
    latex: '187056'
    decimal_approx: 187056
    alt_display: 187,056
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-4
  type: lower_bound
  value:
    latex: '390'
    decimal_approx: 390
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-5
  type: lower_bound
  value:
    latex: '1404'
    decimal_approx: 1404
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-7
  type: lower_bound
  value:
    latex: '19383'
    decimal_approx: 19383
    alt_display: 19,383
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-10
  type: lower_bound
  value:
    latex: '1253615'
    decimal_approx: 1253615
    alt_display: 1,253,615
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-8
  type: lower_bound
  value:
    latex: '249660'
    decimal_approx: 249660
    alt_display: 249,660
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-9
  type: lower_bound
  value:
    latex: '1223050'
    decimal_approx: 1223050
    alt_display: 1,223,050
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-10
  type: lower_bound
  value:
    latex: '6007230'
    decimal_approx: 6007230
    alt_display: 6,007,230
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-8-4
  type: lower_bound
  value:
    latex: '1100'
    decimal_approx: 1100
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-8-7
  type: lower_bound
  value:
    latex: '131137'
    decimal_approx: 131137
    alt_display: 131,137
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-8-8
  type: lower_bound
  value:
    latex: '734820'
    decimal_approx: 734820
    alt_display: 734,820
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-8-9
  type: lower_bound
  value:
    latex: '4243100'
    decimal_approx: 4243100
    alt_display: 4,243,100
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-8-10
  type: lower_bound
  value:
    latex: '24897161'
    decimal_approx: 24897161
    alt_display: 24,897,161
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-7
  type: lower_bound
  value:
    latex: '279616'
    decimal_approx: 279616
    alt_display: 279,616
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-9
  type: lower_bound
  value:
    latex: '12123288'
    decimal_approx: 12123288
    alt_display: 12,123,288
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-10
  type: lower_bound
  value:
    latex: '65866350'
    decimal_approx: 65866350
    alt_display: 65,866,350
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-7
  type: lower_bound
  value:
    latex: '583083'
    decimal_approx: 583083
    alt_display: 583,083
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-8
  type: lower_bound
  value:
    latex: '4293452'
    decimal_approx: 4293452
    alt_display: 4,293,452
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-9
  type: lower_bound
  value:
    latex: '27997191'
    decimal_approx: 27997191
    alt_display: 27,997,191
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-10
  type: lower_bound
  value:
    latex: '201038922'
    decimal_approx: 201038922
    alt_display: 201,038,922
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-7
  type: lower_bound
  value:
    latex: '1001268'
    decimal_approx: 1001268
    alt_display: 1,001,268
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-8
  type: lower_bound
  value:
    latex: '7442328'
    decimal_approx: 7442328
    alt_display: 7,442,328
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-9
  type: lower_bound
  value:
    latex: '72933102'
    decimal_approx: 72933102
    alt_display: 72,933,102
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-10
  type: lower_bound
  value:
    latex: '600380000'
    decimal_approx: 600380000
    alt_display: 600,380,000
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-7
  type: lower_bound
  value:
    latex: '1999500'
    decimal_approx: 1999500
    alt_display: 1,999,500
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-8
  type: lower_bound
  value:
    latex: '15924326'
    decimal_approx: 15924326
    alt_display: 15,924,326
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-9
  type: lower_bound
  value:
    latex: '158158875'
    decimal_approx: 158158875
    alt_display: 158,158,875
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-10
  type: lower_bound
  value:
    latex: '1506252500'
    decimal_approx: 1506252500
    alt_display: 1,506,252,500
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-7
  type: lower_bound
  value:
    latex: '3322080'
    decimal_approx: 3322080
    alt_display: 3,322,080
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-8
  type: lower_bound
  value:
    latex: '29927790'
    decimal_approx: 29927790
    alt_display: 29,927,790
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-9
  type: lower_bound
  value:
    latex: '249155760'
    decimal_approx: 249155760
    alt_display: 249,155,760
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-10
  type: lower_bound
  value:
    latex: '3077200700'
    decimal_approx: 3077200700
    alt_display: 3,077,200,700
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-8
  type: lower_bound
  value:
    latex: '55913932'
    decimal_approx: 55913932
    alt_display: 55,913,932
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-9
  type: lower_bound
  value:
    latex: '600123780'
    decimal_approx: 600123780
    alt_display: 600,123,780
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-10
  type: lower_bound
  value:
    latex: '7041746081'
    decimal_approx: 7041746081
    alt_display: 7,041,746,081
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-7
  type: lower_bound
  value:
    latex: '8599986'
    decimal_approx: 8599986
    alt_display: 8,599,986
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-8
  type: lower_bound
  value:
    latex: '90001236'
    decimal_approx: 90001236
    alt_display: 90,001,236
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-9
  type: lower_bound
  value:
    latex: '1171998164'
    decimal_approx: 1171998164
    alt_display: 1,171,998,164
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-10
  type: lower_bound
  value:
    latex: '10012349898'
    decimal_approx: 10012349898
    alt_display: 10,012,349,898
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-8
  type: lower_bound
  value:
    latex: '140559416'
    decimal_approx: 140559416
    alt_display: 140,559,416
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-9
  type: lower_bound
  value:
    latex: '2025125476'
    decimal_approx: 2025125476
    alt_display: 2,025,125,476
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-16-10
  type: lower_bound
  value:
    latex: '12951451931'
    decimal_approx: 12951451931
    alt_display: 12,951,451,931
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-6-8
  type: lower_bound
  value:
    latex: '76461'
    decimal_approx: 76461
    alt_display: 76,461
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-6-9
  type: lower_bound
  value:
    latex: '307845'
    decimal_approx: 307845
    alt_display: 307,845
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-7-6
  type: lower_bound
  value:
    latex: '11988'
    decimal_approx: 11988
    alt_display: 11,988
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-7-7
  type: lower_bound
  value:
    latex: '52768'
    decimal_approx: 52768
    alt_display: 52,768
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-8-5
  type: lower_bound
  value:
    latex: '5060'
    decimal_approx: 5060
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-9-4
  type: lower_bound
  value:
    latex: '1550'
    decimal_approx: 1550
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-9-5
  type: lower_bound
  value:
    latex: '8200'
    decimal_approx: 8200
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-9-8
  type: lower_bound
  value:
    latex: '1686600'
    decimal_approx: 1686600
    alt_display: 1,686,600
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-10-4
  type: lower_bound
  value:
    latex: '2286'
    decimal_approx: 2286
    alt_display: null
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-10-5
  type: lower_bound
  value:
    latex: '13140'
    decimal_approx: 13140
    alt_display: 13,140
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-11-5
  type: lower_bound
  value:
    latex: '19500'
    decimal_approx: 19500
    alt_display: 19,500
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-12-5
  type: lower_bound
  value:
    latex: '29470'
    decimal_approx: 29470
    alt_display: 29,470
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-13-5
  type: lower_bound
  value:
    latex: '40260'
    decimal_approx: 40260
    alt_display: 40,260
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-14-5
  type: lower_bound
  value:
    latex: '57837'
    decimal_approx: 57837
    alt_display: 57,837
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-15-5
  type: lower_bound
  value:
    latex: '76518'
    decimal_approx: 76518
    alt_display: 76,518
  date: '2008'
  primary_source: loz-siran-2008
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-8-6
  type: lower_bound
  value:
    latex: '39672'
    decimal_approx: 39672
    alt_display: 39,672
  date: '2008-06-03'
  primary_source: gomez09graphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-6
  type: lower_bound
  value:
    latex: '134690'
    decimal_approx: 134690
    alt_display: 134,690
  date: '2008-06-03'
  primary_source: gomez09graphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-3
  type: lower_bound
  value:
    latex: '786'
    decimal_approx: 786
    alt_display: null
  date: '2008-06-03'
  primary_source: gomez09graphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-3
  type: lower_bound
  value:
    latex: '916'
    decimal_approx: 916
    alt_display: null
  date: '2008-06-03'
  primary_source: gomez09graphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-3
  type: lower_bound
  value:
    latex: '851'
    decimal_approx: 851
    alt_display: null
  date: '2008-06-03'
  primary_source: gomez09graphs
  secondary_source: null
- constant: debruijn-newman
  type: upper_bound
  value:
    latex: \lt 0.5
    decimal_approx: 0.5
    alt_display: null
  date: '2009-09-10'
  primary_source: ki-kim-lee-2009
  secondary_source: wikipedia-debruijn-newman
- constant: cage-5-11
  type: upper_bound
  value:
    latex: '2688'
    decimal_approx: 2688
    alt_display: null
  date: '2010'
  primary_source: araujopardo-2010
  secondary_source: ejc-ds16-cages
- constant: cage-9-7
  type: upper_bound
  value:
    latex: '1152'
    decimal_approx: 1152
    alt_display: null
  date: '2010'
  primary_source: araujopardo-2010
  secondary_source: ejc-ds16-cages
- constant: cage-9-11
  type: upper_bound
  value:
    latex: '74752'
    decimal_approx: 74752
    alt_display: 74,752
  date: '2010'
  primary_source: araujopardo-2010
  secondary_source: ejc-ds16-cages
- constant: degree-diameter-17-3
  type: lower_bound
  value:
    latex: '1610'
    decimal_approx: 1610
    alt_display: null
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-4
  type: lower_bound
  value:
    latex: '19040'
    decimal_approx: 19040
    alt_display: 19,040
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-5
  type: lower_bound
  value:
    latex: '133144'
    decimal_approx: 133144
    alt_display: 133,144
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-6
  type: lower_bound
  value:
    latex: '3217872'
    decimal_approx: 3217872
    alt_display: 3,217,872
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-7
  type: lower_bound
  value:
    latex: '18495162'
    decimal_approx: 18495162
    alt_display: 18,495,162
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-8
  type: lower_bound
  value:
    latex: '220990700'
    decimal_approx: 220990700
    alt_display: 220,990,700
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-9
  type: lower_bound
  value:
    latex: '3372648954'
    decimal_approx: 3372648954
    alt_display: 3,372,648,954
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-17-10
  type: lower_bound
  value:
    latex: '15317070720'
    decimal_approx: 15317070720
    alt_display: 15,317,070,720
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-3
  type: lower_bound
  value:
    latex: '1620'
    decimal_approx: 1620
    alt_display: null
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-4
  type: lower_bound
  value:
    latex: '23800'
    decimal_approx: 23800
    alt_display: 23,800
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-5
  type: lower_bound
  value:
    latex: '171828'
    decimal_approx: 171828
    alt_display: 171,828
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-6
  type: lower_bound
  value:
    latex: '4022340'
    decimal_approx: 4022340
    alt_display: 4,022,340
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-7
  type: lower_bound
  value:
    latex: '26515120'
    decimal_approx: 26515120
    alt_display: 26,515,120
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-8
  type: lower_bound
  value:
    latex: '323037476'
    decimal_approx: 323037476
    alt_display: 323,037,476
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-9
  type: lower_bound
  value:
    latex: '5768971167'
    decimal_approx: 5768971167
    alt_display: 5,768,971,167
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-18-10
  type: lower_bound
  value:
    latex: '16659077632'
    decimal_approx: 16659077632
    alt_display: 16,659,077,632
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-3
  type: lower_bound
  value:
    latex: '1638'
    decimal_approx: 1638
    alt_display: null
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-4
  type: lower_bound
  value:
    latex: '23970'
    decimal_approx: 23970
    alt_display: 23,970
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-5
  type: lower_bound
  value:
    latex: '221676'
    decimal_approx: 221676
    alt_display: 221,676
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-6
  type: lower_bound
  value:
    latex: '4024707'
    decimal_approx: 4024707
    alt_display: 4,024,707
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-7
  type: lower_bound
  value:
    latex: '39123116'
    decimal_approx: 39123116
    alt_display: 39,123,116
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-8
  type: lower_bound
  value:
    latex: '501001000'
    decimal_approx: 501001000
    alt_display: 501,001,000
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-9
  type: lower_bound
  value:
    latex: '8855580344'
    decimal_approx: 8855580344
    alt_display: 8,855,580,344
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-19-10
  type: lower_bound
  value:
    latex: '18155097232'
    decimal_approx: 18155097232
    alt_display: 18,155,097,232
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-3
  type: lower_bound
  value:
    latex: '1958'
    decimal_approx: 1958
    alt_display: null
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-4
  type: lower_bound
  value:
    latex: '34952'
    decimal_approx: 34952
    alt_display: 34,952
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-5
  type: lower_bound
  value:
    latex: '281820'
    decimal_approx: 281820
    alt_display: 281,820
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-6
  type: lower_bound
  value:
    latex: '8947848'
    decimal_approx: 8947848
    alt_display: 8,947,848
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-7
  type: lower_bound
  value:
    latex: '55625185'
    decimal_approx: 55625185
    alt_display: 55,625,185
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-8
  type: lower_bound
  value:
    latex: '762374779'
    decimal_approx: 762374779
    alt_display: 762,374,779
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-9
  type: lower_bound
  value:
    latex: '12951451931'
    decimal_approx: 12951451931
    alt_display: 12,951,451,931
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: degree-diameter-20-10
  type: lower_bound
  value:
    latex: '78186295824'
    decimal_approx: 78186295824
    alt_display: 78,186,295,824
  date: 2010-09
  primary_source: loz-pineda-2010
  secondary_source: combi-wiki-degree-diameter
- constant: busy-beaver-shift-6
  type: lower_bound
  value:
    latex: 7.4\times10^{36524}
    decimal_approx: null
    alt_display: null
  date: '2011'
  primary_source: kropitz-2011
  secondary_source: aaronson-2020
- constant: busy-beaver-ones-6
  type: lower_bound
  value:
    latex: 3.5\times10^{18267}
    decimal_approx: null
    alt_display: null
  date: '2011'
  primary_source: kropitz-2011
  secondary_source: aaronson-2020
- constant: ramsey-7-12
  type: lower_bound
  value:
    latex: '417'
    decimal_approx: 417
    alt_display: null
  date: '2011'
  primary_source: xiaodong-s-r-2011
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-10
  type: lower_bound
  value:
    latex: '581'
    decimal_approx: 581
    alt_display: null
  date: '2011'
  primary_source: xiaodong-s-r-2011
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: van-der-waerden-2-6
  type: lower_bound
  value:
    latex: '1132'
    decimal_approx: 1132
    alt_display: null
  date: '2011-01-29'
  primary_source: kouril-pre-2011
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-6
  type: upper_bound
  value:
    latex: '1132'
    decimal_approx: 1132
    alt_display: null
  date: '2011-01-30'
  primary_source: kouril-paul-2011
  secondary_source: wikipedia-van-der-waerden
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: -1.1 \times 10^{-11}
    decimal_approx: -1.1e-11
    alt_display: "\u2248-1.1e-11"
  date: '2011-03-09'
  primary_source: saouter-gourdon-demichel-2011
  secondary_source: wikipedia-debruijn-newman
- constant: cage-5-10
  type: upper_bound
  value:
    latex: '1296'
    decimal_approx: 1296
    alt_display: null
  date: '2012'
  primary_source: exoo-circa-2012
  secondary_source: ejc-ds16-cages
- constant: degree-diameter-15-2
  type: lower_bound
  value:
    latex: '187'
    decimal_approx: 187
    alt_display: null
  date: '2012'
  primary_source: canale-2012
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-4-6
  type: lower_bound
  value:
    latex: '36'
    decimal_approx: 36
    alt_display: null
  date: '2012'
  primary_source: exoo-2012
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: van-der-waerden-3-4
  type: lower_bound
  value:
    latex: '293'
    decimal_approx: 293
    alt_display: null
  date: '2012'
  primary_source: kouril-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-4
  type: upper_bound
  value:
    latex: '293'
    decimal_approx: 293
    alt_display: null
  date: '2012'
  primary_source: kouril-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-7
  type: lower_bound
  value:
    latex: '3704'
    decimal_approx: 3704
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-8
  type: lower_bound
  value:
    latex: '11496'
    decimal_approx: 11496
    alt_display: 11,496
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-9
  type: lower_bound
  value:
    latex: '41266'
    decimal_approx: 41266
    alt_display: 41,266
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-10
  type: lower_bound
  value:
    latex: '103475'
    decimal_approx: 103475
    alt_display: 103,475
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-2-11
  type: lower_bound
  value:
    latex: '193942'
    decimal_approx: 193942
    alt_display: 193,942
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-5
  type: lower_bound
  value:
    latex: '2174'
    decimal_approx: 2174
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-6
  type: lower_bound
  value:
    latex: '11192'
    decimal_approx: 11192
    alt_display: 11,192
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-7
  type: lower_bound
  value:
    latex: '48812'
    decimal_approx: 48812
    alt_display: 48,812
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-8
  type: lower_bound
  value:
    latex: '238401'
    decimal_approx: 238401
    alt_display: 238,401
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-9
  type: lower_bound
  value:
    latex: '932746'
    decimal_approx: 932746
    alt_display: 932,746
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-10
  type: lower_bound
  value:
    latex: '4173725'
    decimal_approx: 4173725
    alt_display: 4,173,725
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-3-11
  type: lower_bound
  value:
    latex: '18603732'
    decimal_approx: 18603732
    alt_display: 18,603,732
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-4
  type: lower_bound
  value:
    latex: '1049'
    decimal_approx: 1049
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-5
  type: lower_bound
  value:
    latex: '17706'
    decimal_approx: 17706
    alt_display: 17,706
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-3
  type: lower_bound
  value:
    latex: '171'
    decimal_approx: 171
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-4
  type: lower_bound
  value:
    latex: '2255'
    decimal_approx: 2255
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-3
  type: lower_bound
  value:
    latex: '226'
    decimal_approx: 226
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-4
  type: lower_bound
  value:
    latex: '9779'
    decimal_approx: 9779
    alt_display: null
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-5
  type: lower_bound
  value:
    latex: '98749'
    decimal_approx: 98749
    alt_display: 98,749
  date: '2012-06-06'
  primary_source: rabung-lotts-2012
  secondary_source: wikipedia-van-der-waerden
- constant: degree-diameter-6-9
  type: lower_bound
  value:
    latex: '331387'
    decimal_approx: 331387
    alt_display: 331,387
  date: '2012-12-11'
  primary_source: canale12graphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-5
  type: lower_bound
  value:
    latex: '8268'
    decimal_approx: 8268
    alt_display: null
  date: '2012-12-11'
  primary_source: canale12graphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-8
  type: lower_bound
  value:
    latex: '1697688'
    decimal_approx: 1697688
    alt_display: 1,697,688
  date: '2012-12-11'
  primary_source: canale12graphs
  secondary_source: wikipedia-degree-diameter
- constant: ramsey-3-11
  type: lower_bound
  value:
    latex: '47'
    decimal_approx: 47
    alt_display: null
  date: '2013'
  primary_source: exoo-2013
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-11
  type: upper_bound
  value:
    latex: '50'
    decimal_approx: 50
    alt_display: null
  date: '2013'
  primary_source: goedgebeur-radziszowski-2013
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-13
  type: upper_bound
  value:
    latex: '68'
    decimal_approx: 68
    alt_display: null
  date: '2013'
  primary_source: goedgebeur-radziszowski-2013
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-14
  type: upper_bound
  value:
    latex: '77'
    decimal_approx: 77
    alt_display: null
  date: '2013'
  primary_source: goedgebeur-radziszowski-2013
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-15
  type: upper_bound
  value:
    latex: '87'
    decimal_approx: 87
    alt_display: null
  date: '2013'
  primary_source: goedgebeur-radziszowski-2013
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: minimal-superpermutation-5
  type: lower_bound
  value:
    latex: '153'
    decimal_approx: 153
    alt_display: null
  date: '2014'
  primary_source: chaffin-2014
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-6
  type: upper_bound
  value:
    latex: '872'
    decimal_approx: 872
    alt_display: null
  date: '2014-08-21'
  primary_source: houston-2014
  secondary_source: egan-superpermutations
- constant: ramsey-3-12
  type: lower_bound
  value:
    latex: '53'
    decimal_approx: 53
    alt_display: null
  date: '2015'
  primary_source: kolodyazhny-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-13
  type: lower_bound
  value:
    latex: '60'
    decimal_approx: 60
    alt_display: null
  date: '2015'
  primary_source: kolodyazhny-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-8
  type: lower_bound
  value:
    latex: '59'
    decimal_approx: 59
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-11
  type: lower_bound
  value:
    latex: '102'
    decimal_approx: 102
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-13
  type: lower_bound
  value:
    latex: '138'
    decimal_approx: 138
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-14
  type: lower_bound
  value:
    latex: '147'
    decimal_approx: 147
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-10
  type: lower_bound
  value:
    latex: '149'
    decimal_approx: 149
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-7
  type: lower_bound
  value:
    latex: '115'
    decimal_approx: 115
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-8
  type: lower_bound
  value:
    latex: '134'
    decimal_approx: 134
    alt_display: null
  date: '2015'
  primary_source: exoo-tatarevic-2015
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-14
  type: lower_bound
  value:
    latex: '67'
    decimal_approx: 67
    alt_display: null
  date: '2016'
  primary_source: kolodyazhny-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-15
  type: lower_bound
  value:
    latex: '74'
    decimal_approx: 74
    alt_display: null
  date: '2016'
  primary_source: kolodyazhny-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-9
  type: lower_bound
  value:
    latex: '133'
    decimal_approx: 133
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-11
  type: lower_bound
  value:
    latex: '183'
    decimal_approx: 183
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-12
  type: lower_bound
  value:
    latex: '203'
    decimal_approx: 203
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-13
  type: lower_bound
  value:
    latex: '233'
    decimal_approx: 233
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-14
  type: lower_bound
  value:
    latex: '267'
    decimal_approx: 267
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-9
  type: lower_bound
  value:
    latex: '183'
    decimal_approx: 183
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-10
  type: lower_bound
  value:
    latex: '204'
    decimal_approx: 204
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-12
  type: lower_bound
  value:
    latex: '294'
    decimal_approx: 294
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-13
  type: lower_bound
  value:
    latex: '347'
    decimal_approx: 347
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-9
  type: lower_bound
  value:
    latex: '252'
    decimal_approx: 252
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-10
  type: lower_bound
  value:
    latex: '292'
    decimal_approx: 292
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-9
  type: lower_bound
  value:
    latex: '329'
    decimal_approx: 329
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-10
  type: lower_bound
  value:
    latex: '343'
    decimal_approx: 343
    alt_display: null
  date: '2016'
  primary_source: kuznetsov-2016
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-16-2
  type: lower_bound
  value:
    latex: '200'
    decimal_approx: 200
    alt_display: null
  date: 2016-10
  primary_source: abas-2016
  secondary_source: wikipedia-degree-diameter
- constant: van-der-waerden-5-5
  type: lower_bound
  value:
    latex: '98742'
    decimal_approx: 98742
    alt_display: 98,742
  date: '2017-06-21'
  primary_source: heule-2017
  secondary_source: wikipedia-van-der-waerden
- constant: degree-diameter-3-8
  type: lower_bound
  value:
    latex: '360'
    decimal_approx: 360
    alt_display: null
  date: '2018'
  primary_source: jianxiang-chen-2018
  secondary_source: wikipedia-degree-diameter
- constant: disk-covering-13
  type: upper_bound
  value:
    latex: '{\approx}0.346'
    decimal_approx: 0.346
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-14
  type: upper_bound
  value:
    latex: '{\approx}0.331'
    decimal_approx: 0.331
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-15
  type: upper_bound
  value:
    latex: '{\approx}0.318'
    decimal_approx: 0.318
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-16
  type: upper_bound
  value:
    latex: '{\approx}0.308'
    decimal_approx: 0.308
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-17
  type: upper_bound
  value:
    latex: '{\approx}0.299'
    decimal_approx: 0.299
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-18
  type: upper_bound
  value:
    latex: '{\approx}0.290'
    decimal_approx: 0.29
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-19
  type: upper_bound
  value:
    latex: \frac{\sqrt{13}}{13}
    decimal_approx: 0.2773501
    alt_display: "\u22480.2773501"
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-20
  type: upper_bound
  value:
    latex: '{\approx}0.271'
    decimal_approx: 0.271
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-21
  type: upper_bound
  value:
    latex: '{\approx}0.263'
    decimal_approx: 0.263
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-22
  type: upper_bound
  value:
    latex: '{\approx}0.253'
    decimal_approx: 0.253
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-23
  type: upper_bound
  value:
    latex: '{\approx}0.25'
    decimal_approx: 0.25
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-24
  type: upper_bound
  value:
    latex: '{\approx}0.245'
    decimal_approx: 0.245
    alt_display: null
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: disk-covering-25
  type: upper_bound
  value:
    latex: \frac{1}{\sqrt{6}+\sqrt{3}}
    decimal_approx: 0.2391463
    alt_display: "\u22480.2391463"
  date: '2018'
  primary_source: tan-2018
  secondary_source: friedman-circles-covering-circles
- constant: ramsey-5-5
  type: upper_bound
  value:
    latex: '48'
    decimal_approx: 48
    alt_display: null
  date: '2018'
  primary_source: angeltveit-mckay-2018
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: van-der-waerden-5-7
  type: lower_bound
  value:
    latex: '2941520'
    decimal_approx: 2941520
    alt_display: 2,941,520
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-5-8
  type: lower_bound
  value:
    latex: '16718220'
    decimal_approx: 16718220
    alt_display: 16,718,220
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-5-11
  type: lower_bound
  value:
    latex: '3621901591'
    decimal_approx: 3621901591
    alt_display: 3,621,901,591
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-6-7
  type: lower_bound
  value:
    latex: '20590634'
    decimal_approx: 20590634
    alt_display: 20,590,634
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-6-8
  type: lower_bound
  value:
    latex: '117027534'
    decimal_approx: 117027534
    alt_display: 117,027,534
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-6-9
  type: lower_bound
  value:
    latex: '557942064'
    decimal_approx: 557942064
    alt_display: 557,942,064
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-6-10
  type: lower_bound
  value:
    latex: '3798864791'
    decimal_approx: 3798864791
    alt_display: 3,798,864,791
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: van-der-waerden-6-11
  type: lower_bound
  value:
    latex: '39840917502'
    decimal_approx: 39840917502
    alt_display: 39,840,917,502
  date: 2018-03
  primary_source: blankenship-c-t-2018
  secondary_source: null
- constant: minimal-superpermutation-7
  type: upper_bound
  value:
    latex: '5907'
    decimal_approx: 5907
    alt_display: null
  date: '2019-02-01'
  primary_source: coanda-2019
  secondary_source: egan-superpermutations
- constant: minimal-superpermutation-7
  type: upper_bound
  value:
    latex: '5906'
    decimal_approx: 5906
    alt_display: null
  date: '2019-02-27'
  primary_source: houston-egan-2019
  secondary_source: egan-superpermutations
- constant: van-der-waerden-4-6
  type: lower_bound
  value:
    latex: '157210'
    decimal_approx: 157210
    alt_display: 157,210
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-7
  type: lower_bound
  value:
    latex: '2284752'
    decimal_approx: 2284752
    alt_display: 2,284,752
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-8
  type: lower_bound
  value:
    latex: '12288156'
    decimal_approx: 12288156
    alt_display: 12,288,156
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-9
  type: lower_bound
  value:
    latex: '139847086'
    decimal_approx: 139847086
    alt_display: 139,847,086
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-10
  type: lower_bound
  value:
    latex: '1189640579'
    decimal_approx: 1189640579
    alt_display: 1,189,640,579
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-4-11
  type: lower_bound
  value:
    latex: '3464368084'
    decimal_approx: 3464368084
    alt_display: 3,464,368,084
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-6
  type: lower_bound
  value:
    latex: '786741'
    decimal_approx: 786741
    alt_display: 786,741
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-7
  type: lower_bound
  value:
    latex: '15993258'
    decimal_approx: 15993258
    alt_display: 15,993,258
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-8
  type: lower_bound
  value:
    latex: '86017086'
    decimal_approx: 86017086
    alt_display: 86,017,086
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-9
  type: lower_bound
  value:
    latex: '978929596'
    decimal_approx: 978929596
    alt_display: 978,929,596
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-10
  type: lower_bound
  value:
    latex: '8327484047'
    decimal_approx: 8327484047
    alt_display: 8,327,484,047
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-5-11
  type: lower_bound
  value:
    latex: '38108048914'
    decimal_approx: 38108048914
    alt_display: 38,108,048,914
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-6
  type: lower_bound
  value:
    latex: '1555550'
    decimal_approx: 1555550
    alt_display: 1,555,550
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-7
  type: lower_bound
  value:
    latex: '111952800'
    decimal_approx: 111952800
    alt_display: 111,952,800
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-8
  type: lower_bound
  value:
    latex: '602119596'
    decimal_approx: 602119596
    alt_display: 602,119,596
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-9
  type: lower_bound
  value:
    latex: '6852507166'
    decimal_approx: 6852507166
    alt_display: 6,852,507,166
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-10
  type: lower_bound
  value:
    latex: '58292388323'
    decimal_approx: 58292388323
    alt_display: 58,292,388,323
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: van-der-waerden-6-11
  type: lower_bound
  value:
    latex: '419188538044'
    decimal_approx: 419188538044
    alt_display: 419,188,538,044
  date: '2019-05-22'
  primary_source: monroe-2019
  secondary_source: wikipedia-van-der-waerden
- constant: debruijn-newman
  type: upper_bound
  value:
    latex: \le 0.22
    decimal_approx: 0.22
    alt_display: null
  date: '2019-08-26'
  primary_source: polymath-2019
  secondary_source: wikipedia-debruijn-newman
- constant: ramsey-4-15
  type: lower_bound
  value:
    latex: '158'
    decimal_approx: 158
    alt_display: null
  date: '2020'
  primary_source: tatarevic-2020
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-11
  type: lower_bound
  value:
    latex: '262'
    decimal_approx: 262
    alt_display: null
  date: '2020'
  primary_source: tatarevic-2020
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-8
  type: lower_bound
  value:
    latex: '219'
    decimal_approx: 219
    alt_display: null
  date: '2020'
  primary_source: tatarevic-2020
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-6
  type: upper_bound
  value:
    latex: '40'
    decimal_approx: 40
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-7
  type: upper_bound
  value:
    latex: '58'
    decimal_approx: 58
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-8
  type: upper_bound
  value:
    latex: '79'
    decimal_approx: 79
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-9
  type: upper_bound
  value:
    latex: '105'
    decimal_approx: 105
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-10
  type: upper_bound
  value:
    latex: '135'
    decimal_approx: 135
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-11
  type: upper_bound
  value:
    latex: '170'
    decimal_approx: 170
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-12
  type: upper_bound
  value:
    latex: '210'
    decimal_approx: 210
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-13
  type: upper_bound
  value:
    latex: '256'
    decimal_approx: 256
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-14
  type: upper_bound
  value:
    latex: '307'
    decimal_approx: 307
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-4-15
  type: upper_bound
  value:
    latex: '364'
    decimal_approx: 364
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-5
  type: upper_bound
  value:
    latex: '46'
    decimal_approx: 46
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-6
  type: upper_bound
  value:
    latex: '85'
    decimal_approx: 85
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-7
  type: upper_bound
  value:
    latex: '133'
    decimal_approx: 133
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-8
  type: upper_bound
  value:
    latex: '193'
    decimal_approx: 193
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-9
  type: upper_bound
  value:
    latex: '282'
    decimal_approx: 282
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-10
  type: upper_bound
  value:
    latex: '381'
    decimal_approx: 381
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-11
  type: upper_bound
  value:
    latex: '511'
    decimal_approx: 511
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-12
  type: upper_bound
  value:
    latex: '672'
    decimal_approx: 672
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-13
  type: upper_bound
  value:
    latex: '860'
    decimal_approx: 860
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-14
  type: upper_bound
  value:
    latex: '1081'
    decimal_approx: 1081
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-5-15
  type: upper_bound
  value:
    latex: '1341'
    decimal_approx: 1341
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-6
  type: upper_bound
  value:
    latex: '160'
    decimal_approx: 160
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-7
  type: upper_bound
  value:
    latex: '270'
    decimal_approx: 270
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-8
  type: upper_bound
  value:
    latex: '423'
    decimal_approx: 423
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-9
  type: upper_bound
  value:
    latex: '651'
    decimal_approx: 651
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-10
  type: upper_bound
  value:
    latex: '944'
    decimal_approx: 944
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-11
  type: upper_bound
  value:
    latex: '1346'
    decimal_approx: 1346
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-12
  type: upper_bound
  value:
    latex: '1855'
    decimal_approx: 1855
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-13
  type: upper_bound
  value:
    latex: '2499'
    decimal_approx: 2499
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-14
  type: upper_bound
  value:
    latex: '3301'
    decimal_approx: 3301
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-6-15
  type: upper_bound
  value:
    latex: '4305'
    decimal_approx: 4305
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-7
  type: upper_bound
  value:
    latex: '492'
    decimal_approx: 492
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-8
  type: upper_bound
  value:
    latex: '832'
    decimal_approx: 832
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-9
  type: upper_bound
  value:
    latex: '1368'
    decimal_approx: 1368
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-10
  type: upper_bound
  value:
    latex: '2119'
    decimal_approx: 2119
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-11
  type: upper_bound
  value:
    latex: '3197'
    decimal_approx: 3197
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-12
  type: upper_bound
  value:
    latex: '4665'
    decimal_approx: 4665
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-13
  type: upper_bound
  value:
    latex: '6653'
    decimal_approx: 6653
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-14
  type: upper_bound
  value:
    latex: '9260'
    decimal_approx: 9260
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-7-15
  type: upper_bound
  value:
    latex: '12635'
    decimal_approx: 12635
    alt_display: 12,635
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-8
  type: upper_bound
  value:
    latex: '1518'
    decimal_approx: 1518
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-9
  type: upper_bound
  value:
    latex: '2662'
    decimal_approx: 2662
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-10
  type: upper_bound
  value:
    latex: '4402'
    decimal_approx: 4402
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-11
  type: upper_bound
  value:
    latex: '7040'
    decimal_approx: 7040
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-8-12
  type: upper_bound
  value:
    latex: '10836'
    decimal_approx: 10836
    alt_display: 10,836
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-9
  type: upper_bound
  value:
    latex: '4956'
    decimal_approx: 4956
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-10
  type: upper_bound
  value:
    latex: '8675'
    decimal_approx: 8675
    alt_display: null
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-9-11
  type: upper_bound
  value:
    latex: '14631'
    decimal_approx: 14631
    alt_display: 14,631
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-10-10
  type: upper_bound
  value:
    latex: '16064'
    decimal_approx: 16064
    alt_display: 16,064
  date: '2020'
  primary_source: angeltveit-mckay-2019-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: debruijn-newman
  type: lower_bound
  value:
    latex: \ge 0
    decimal_approx: 0.0
    alt_display: null
  date: '2020-04-06'
  primary_source: rodgers-tao-2018
  secondary_source: wikipedia-debruijn-newman
- constant: degree-diameter-13-3
  type: lower_bound
  value:
    latex: '856'
    decimal_approx: 856
    alt_display: null
  date: '2021'
  primary_source: pelakhaty-2021
  secondary_source: wikipedia-degree-diameter
- constant: debruijn-newman
  type: upper_bound
  value:
    latex: \le 0.2
    decimal_approx: 0.2
    alt_display: null
  date: '2021-01-22'
  primary_source: platt-trudgian-2020
  secondary_source: wikipedia-debruijn-newman
- constant: ramsey-5-6
  type: lower_bound
  value:
    latex: '59'
    decimal_approx: 59
    alt_display: null
  date: '2023'
  primary_source: exoo-2023
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: ramsey-3-10
  type: upper_bound
  value:
    latex: '41'
    decimal_approx: 41
    alt_display: null
  date: '2024'
  primary_source: angeltveit-2024
  secondary_source: ejc-ds1-small-ramsey-numbers
- constant: degree-diameter-6-8
  type: lower_bound
  value:
    latex: '76891'
    decimal_approx: 76891
    alt_display: 76,891
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-6
  type: lower_bound
  value:
    latex: '12264'
    decimal_approx: 12264
    alt_display: 12,264
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-7-7
  type: lower_bound
  value:
    latex: '53020'
    decimal_approx: 53020
    alt_display: 53,020
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-8-5
  type: lower_bound
  value:
    latex: '5115'
    decimal_approx: 5115
    alt_display: null
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-9-4
  type: lower_bound
  value:
    latex: '1640'
    decimal_approx: 1640
    alt_display: null
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-4
  type: lower_bound
  value:
    latex: '2331'
    decimal_approx: 2331
    alt_display: null
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-10-5
  type: lower_bound
  value:
    latex: '13203'
    decimal_approx: 13203
    alt_display: 13,203
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-11-5
  type: lower_bound
  value:
    latex: '19620'
    decimal_approx: 19620
    alt_display: 19,620
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-12-5
  type: lower_bound
  value:
    latex: '29621'
    decimal_approx: 29621
    alt_display: 29,621
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-13-5
  type: lower_bound
  value:
    latex: '40488'
    decimal_approx: 40488
    alt_display: 40,488
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-14-5
  type: lower_bound
  value:
    latex: '58095'
    decimal_approx: 58095
    alt_display: 58,095
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
- constant: degree-diameter-15-5
  type: lower_bound
  value:
    latex: '77520'
    decimal_approx: 77520
    alt_display: 77,520
  date: '2024-06-27'
  primary_source: comellasgraphs
  secondary_source: wikipedia-degree-diameter
