The S-unit arm has a sound two-line injectivity lemma, so g(k) <= 2 + max_d N_S(d), but Evertse's 3*7^{d+2s} gives g(k) <= 2 + 3*7^{2k+3} ~ 1029*49^k, weaker than the 1934 bound by a factor about 24.5^k, and at k=7 the quantity Evertse bounds by 7.0e14 has measured value 96 against the elementary ceiling 128.
hunts/support_d5d5ccae (Record 80 of 98 in chronological sequence)
Guiding Question
Does the two-variable S-unit equation route, with injectivity from fixed base elements, produce a bound on g(k) better than the classical 2^k, or is it provably too weak?
Method & Verification
The injectivity lemma was written in two lines, Evertse 1984 and Beukers-Schlickewei were read off the Beukers-Schlickewei paper, and S-smooth differences were counted to 10^14, reproducing Lehmer's Stormer table exactly for k=1..8.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Question filled from the HuntSpec. Handback status is not-settled; case log returns the too-weak verdict the brief allowed. Disposition is qualified rather than completed because the route is not refuted, it is starved: box-truncated counts are lower bounds only, and eight points cannot separate polynomial from exponential growth. The lemma is not claimed as new.
Date Provenance
commit 35b1318de93b2d33dea9750dc5b518c08f4bfe8a, hunts/support_d5d5ccae/RESULTS.md, author 2026-08-24T20:57:54-05:00