Ranging over all k-subsets of the first nine primes for k <= 5 does not beat the first k primes, so r_186989's flagged door with genuine trade shape is slack; the sweep produced a proved normalization (admissible sets are exactly the S-smooth dilates of primitive ones) and a refutation of the residue lemma |A| <= p-1 for p not in S, which is false for every odd p.
hunts/support_60982bf6 (Record 75 of 98 in chronological sequence)
Guiding Question
Does ranging over choices of S, instead of freezing the first k primes, beat r_186989's table, and which structural lemmas does that computation discover or falsify?
Method & Verification
A solver that builds edges from S-smooth sums rather than scanning O(N^2) pairs ran exhaustively over all binom(9,k) subsets for k <= 5 (381 searches), and the residue lemma was killed by trial-division witnesses at p = 3, 5, 7 including A={1,3,7,13}, S={2,5,7} from r_186989's own table.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
No HuntSpec.question field; question filled from the bounded question in MISSION.md. Disposition maps settled, as a support answer to completed. 'First k primes are not beaten' is exhaustive over the stated subsets and boxes only, and is a claim about a maximum, which this machinery cannot refute. The height conjecture is not leaned on.
Date Provenance
commit f1c41069f9cb8f0df9167edb40613154a0427a3c, hunts/support_60982bf6/RESULTS.md, author 2026-08-24T20:56:42-05:00