The entropy/signature lane is closed by proof: for every prime bound P, arbitrarily large sets satisfy every constraint S-summability imposes at primes below P (Theorem B), so no entropy, VC, container, DRC or forbidden-pattern argument over prime-valuation signatures can bound |A| at all, let alone beat 2^k.
hunts/support_baf4cde6 (Record 79 of 98 in chronological sequence)
Guiding Question
Can prime-valuation signatures plus entropy, VC, containers, dependent random choice, or forbidden patterns show that an S-summable set has subexponential size?
Method & Verification
Theorem B was proved by taking A = {1+iM} with M the product of odd primes <= P outside S, checked at P=60 with |A|=200 and zero violations, and Lemma A was witnessed by A={1,3,7,13}, S={2,5,7} re-verified by trial division.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps lane closed, by proof rather than by a failed attempt to completed. Theorem B kills arguments whose input is p-adic data at a fixed finite prime set; it does not kill an argument that uses the archimedean ordering or the cofinite condition. ESS unit-equation numbers are recalled from literature.
Date Provenance
commit d07b821343b93491759917ff41de65c2a216c2a4, hunts/support_baf4cde6/RESULTS.md, author 2026-08-24T20:57:40-05:00