Penman and Wells, INTEGERS 13 (2013) A57, Theorem 21, state DeepMind Problem 42's quantity character for character and reach sup g = ln(32/5)/ln(26/5) = 1.125944426, above the AlphaEvolve value which re-counts exactly to 1.1219357375 on 309 integers, and their Q_36, a 197-element set published thirteen years earlier, already beats it at g = 1.1219505699.
hunts/r_2969b0 (Record 72 of 98 in chronological sequence)
Guiding Question
Does Penman-Wells (2013) reach a higher value of DeepMind Problem 42's quantity than the AlphaEvolve construction?
Method & Verification
Both constructions were counted by exact integer enumeration from the primary sources, the decisive inequality was decided at 120 decimal digits, and Corollary 13's four counting formulas reproduced at 64 values of j with zero mismatches.
Lineage & Relationships
None
Primary Sources (at pin 8fa46e134)
Editorial Notes
Disposition maps settled to completed. The safe statement is that the 2013 result beats the AlphaEvolve value, not that it is the current record: Staps (2015) and intervening literature were taken from the issue and not read here. The paper's abstract quantity f = ln|A+A|/ln|A-A| ranks the two sets the other way and is handled explicitly in RESULTS.md, kept out of the one-sentence headline. Question filled from the HuntSpec.
Date Provenance
commit 145f5ed9fbd26ef5fad248269d4e53d356398169, hunts/r_2969b0/RESULTS.md, author 2026-08-24T04:03:39-05:00