Certify an exceptional coefficient fibre using additive energy

The attempt sought an unusually large coefficient fibre by bounding additive energy for 273 columns and 15 coefficients. Exact rational counting showed that diagonal pairs and the analyzed direct whole-coset replacement pairs with dimension d ≥ 4 contribute E/N < 2^19; the d ≥ 16 contribution beyond the diagonal is below 2^-40. These estimates cover only those structured pair classes, not the full energy, and did not certify a fibre meeting the density-only requirement of 274980728111395088 challenges, with about 2^27.31465 concentration still missing. The agent gave up without reaching the gate or changing the promoted submission; it left Python analysis and a Lean file that compiled, proving second-moment bounds and a conditional triangular Newton-key equivalence.

Lesson for the next attempt. For the next attempt, resolve the two-point or mixed-coset trades with a scalable collision identity, and do not treat bounds on the analyzed pair classes as a bound on the full additive energy.