The equivalences r_186989 used are correct and are now proved in full, and its arm-3 finding is right but understated: any amplification law g(k+C) >= lambda*g(k) with C and lambda>1 constant refutes Erdos #126, not just supermultiplicativity; the load-bearing new statement is that #126 is a forall-S forall-A claim while every enumeration produces exists-S exists-A, so the computational arm can only refute.
hunts/support_8ea74995 (Record 77 of 98 in chronological sequence)
Guiding Question
Are the equivalent formulations r_186989 used correct, and what is the exact implication direction of construction, composition, and pruning statements for Erdos #126?
Method & Verification
The inverse relation was proved as a Galois connection, five asymptotic equivalences were written out, the omitted-prime thread was refuted by A congruent to 1 mod p, and the amplification direction was proved by induction from g(1)=2 rather than by Fekete.
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, for the bounded question it was given to completed. Evertse and Erdos-Stewart-Tijdeman counts are literature, not verified here. The Erdos-Turan bound 3*2^(k-1) is used as published.
Date Provenance
commit 05c998ea9b23b4d11c9146023ff66972df7ab56b, hunts/support_8ea74995/RESULTS.md, author 2026-08-24T20:57:24-05:00