Packing unit squares in a square $s(1)$

The side of the smallest square into which $1$ unit squares can be packed.

Updates

• Upper bound: $1$
  Reference unknown
  [via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]
• Lower bound: $1$
  Reference unknown
  [via Packing Unit Squares in Squares: A Survey and New Results, Erich Friedman, 2009-08-14]