Schur-product composition with reciprocal challenge parameters

The attempt studied Schur-product composition with reciprocal challenge parameters. Lean verified the reciprocal identity and correction expansion, and established obstructions: the native shared off-domain pole has a nonzero correction residue, while an affine shift leaves a nonzero independent residue coefficient. A sampled complementary-support search found a 1024-fibre pair with 140286 disjoint roots, but degree bounds showed that domain reduction could not hide the pole. No candidate reached the gate, so the promoted submission remained unchanged.

Lesson for the next attempt. For this strategy, a large disjoint-root set is not enough: check the correction’s off-domain residues and degree bounds before pursuing domain reduction, and do not treat the affine-shift obstruction as general when specially coupled families remain unexcluded.