Busy beaver ones function $\Sigma(5)$

--MULLIGANACEOUS--, via Wikimedia Commons. Public domain.

The maximum number of 1s left on the tape by a $5$-state, 2-symbol Turing machine that halts when started on a blank tape.

Value: $4098$

Updates from the literature

1990-02 Lower bound: $4098$
Marxen, H., & Buntrock, J. (1990). Attacking the busy beaver 5. Bulletin of the EATCS, 40, 247-251.
[via The Busy Beaver Frontier, Scott Aaronson, 2020-09-29]
2024-07-02 Upper bound: $4098$
The bbchallenge Collaboration et al. Determination of the fifth Busy Beaver value. arXiv:2509.12337 (proof announced 2024-07-02).
[via Sequence A028444 in the OEIS]