Erdos #126 is not settleable at scout cost and the scout died on a preregistered kill condition (suggestive finite data, no iterable lemma, no exp(o(k)) reduction); two things survive: f(n-1) <= f0(n) <= f(n), so the Formal Conjectures Finset Nat statement is faithful for the limit and wrong for pinned finite values, and a rigorous composition law would refute the conjecture rather than prove it, since g(1)=2 plus supermultiplicativity gives g(k) >= 2^k by Fekete.
hunts/r_186989 (Record 71 of 98 in chronological sequence)
Guiding Question
Does bounded reconnaissance on Erdos 126 find an iterable lemma, an exp(o(k)) reduction, or a rigorous composition law strong enough to promote the pair-sum prime-support problem to a funded lane?
Method & Verification
The problem was inverted to g(k) before any search, then exact branch-and-bound clique search on the S-smooth pair-sum graph produced lower bounds g(k) >= 2, 4, 5, 6, 8, 10, 11 for k = 1..7, with the positivity inequality and the Fekete direction written as short proofs.
Lineage & Relationships
support_517b887f ↗, support_60982bf6 ↗, support_7ddfee4b ↗, support_8ea74995 ↗, support_95bb5cb7 ↗, support_baf4cde6 ↗, support_d5d5ccae ↗, support_eccd5f5e ↗, support_f3ab3e34 ↗
Primary Sources (at pin 8fa46e134)
Editorial Notes
Handback status is not-settled; case log says not settled, scout killed on a preregistered kill condition. Disposition is qualified rather than completed because the conjecture is untouched and the table is lower bounds only. Evidence grade is ordinary mathematical derivation for the two survivors; the g(k) table is measured and is not an upper bound. Later support hunts refute the omitted-prime thread and the 'optima live below 50' reading; those corrections are recorded on the support rows and are not silently edited into this headline. Question filled from the HuntSpec. Hunt number in the brief was #90, already taken by amtopa_ceiling; the case log records this as Hunt #91.
Date Provenance
commit 322c7a76e4b9e9217525af2cc2364ede2847b195, hunts/r_186989/RESULTS.md, author 2026-08-24T21:29:51-05:00