The question
DeepMind's alphaevolve_repository_of_problems marks Problem 42 (the sum-difference problem) world_record in status.json. Issue #5 on that repository, opened 2026-07-31 with no maintainer response, claims the record is not a record: Penman and Wells, On sets with more restricted sums than differences, INTEGERS 13 (2013) A57, Theorem 21, give an explicit family reaching ln(32/5)/ln(26/5) ~ 1.12594 in the same normalisation, above the AlphaEvolve value 1.1219. That issue discloses it was AI-produced and unreviewed. So an AI-generated challenge stands against an AI-generated record and nobody has checked either.
This hunt checks both, from the primary sources, by exact enumeration.
Scope
Writes only in hunts/r_2969b0/, plus one case-log entry in hunts/README.md. Nothing is posted upstream: what, if anything, is said to DeepMind is the owner's call. The separate C = 2 claim in the same issue is out of scope and untouched here.
Nothing in this hunt bears on RH (docs/08).
id: r_2969b0
question: Does Penman-Wells (2013) reach a higher value of DeepMind Problem 42's quantity than the AlphaEvolve construction?
frontier: AlphaEvolve construction g = 1.1219357375 (309 integers, repository notebook); challenger claim sup g = ln(32/5)/ln(26/5) = 1.125944426; Ruzsa/Granville upper bound C <= 2
proposed_attack: read both normalisations from the primary sources, instantiate the Penman-Wells family Q_j at concrete j, count |A|, |A+A|, |A-A| by enumeration, and compare exactly
dead_routes:
- trusting the notebook's prompt-text score function, which returns the reciprocal ratio and is not the quantity the problem page defines
- trusting the notebook's earlier scorer, which adds a size bonus of up to 0.01 to the ratio
required_oracles:
- exact finite-set enumeration over the integers
- the printed counts of Penman-Wells Corollary 13, recomputed rather than quoted
- the printed values g(A_15) = 1.0717 and f(X) = ln(51)/ln(47) in the same paper, used as a normalisation calibration
- 120-digit decimal comparison of the two log ratios, so the verdict does not rest on a float
kill_conditions:
- the two normalisations turn out to differ, making the comparison apples to oranges
- enumeration contradicts Corollary 13's counts at any j
- the calibration values g(A_15) and f(X) fail to reproduce, meaning we are reading a different g than the paper
- no finite Q_j exceeds the AlphaEvolve value, leaving only an unattained supremum
agents_may:
- search
- derive
- code
- attack
agents_may_not:
- declare novelty
- declare theorem status
- promote their own claim
- post anything to the upstream repository