Erdos #126 reduces in four elementary lines to a unit-equation solution count: g(k) <= 2 + N(k+1) where N(r) bounds solutions of x+y=1 in a rank-r subgroup of Q*, so N(r)=exp(o(r)) implies the conjecture, and the known N(r) <= 2^{8r+8} is the same exponential wall the 1934 theorem sits at.
hunts/support_f3ab3e34 (Record 82 of 98 in chronological sequence)
Guiding Question
Ignoring the earlier brief's three lanes, what proof program does Erdos #126 admit from the statement, and which first unproved step is strongest?
Method & Verification
The injectivity map c |-> ((a1+c)/D, -(a2+c)/D) into X+Y=1 was written out and machine-checked on a witness as exact rationals, then four chains were ranked by the strength of their first unproved step.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
No HuntSpec.question field; question filled from the bounded question in MISSION.md. Handback status is not-settled; case log says not settled, and the program is named. Disposition is qualified because the reduction is a program, not a settlement, and is not claimed as new. Literature rows come from search summaries and arXiv:2602.07545 because erdosproblems.com/126 returned HTTP 403; treat them as cited, not verified at source.
Date Provenance
commit 9307652f6d6dc8a660f2a3a4f0e6aaece79a0fc5, hunts/support_f3ab3e34/RESULTS.md, author 2026-08-24T20:58:22-05:00