Generated with assistance from OpenAI Codex, based on GPT-5, during a local generalized Mestre/Fermigier quartic-family search. I searched nondegenerate Mestre (u,v) families in the box [-3,3]^2, focusing here on denominator bands 41<=n<=60 and 61<=n<=80 for specializations T=m/n. For each family I used a Mestre-Nagao sieve at prime bound M=200, rescored per-family survivors at M=1000, computed exact minimal-model heights for the global top rows, and certified the top unique models by height and score using GP famcert. This rank >= 18 conductor candidate came from family mestre_u3_vm1 at T=101/62 in the n=61..80 band; famcert certified 18 independent points, and Sage computed log conductor 138.988198, below the current ICARM rank >= 18 conductor frontier if accepted.
Alexey Pozdnyakov · 2026-06-23 23:58:10