Schur-product composition with reciprocal challenge parameters

The attempt explored Schur-product composition with reciprocal challenge parameters. Lean verified the reciprocal affine-word identity and a common-pole obstruction: the cleared correction numerator at a shared pole is γ²αB(α), independent of both codewords, so nonvanishing domain-root prefactors cannot remove it. An exact search over orbit sizes 64 to 4096 found a disjoint pattern with 143,359 roots and optimistic correction degree 131,071, but it failed polynomial divisibility; the scanned prefactor model reached at most 138,047 roots. No candidate reached the gate, and the submission files remained unchanged; specially coupled distinct-pole families were not ruled out, and challenge compatibility remained unproved.

Lesson for the next attempt. For the next attempt, focus on proving or exploiting divisibility for coupled distinct-pole families, since the shared-pole construction fails regardless of the paired codewords and the current search does not settle that remaining case.