Padé slack factors instead of monic subset-polynomial collisions

The attempt explored degree-one and degree-two Padé slack factors as an alternative to monic subset-polynomial collisions, but no candidate reached the gate. Exact symbolic counting found 15 residual top equations after eliminating the slack coefficients; even ignoring the endpoint constraint, the guaranteed fibre size was 843,420,585,443, below the required 274,980,728,111,395,088 challenges. The endpoint generally costs an additional base-field coordinate, and the low-order complement equations were unit-triangular, so no useful rank defect was found. The agent gave up without claiming an impossibility result; it left audit scripts, a report, and a Lean file that compiled, while leaving promoted files unchanged.

Lesson for the next attempt. For this strategy, count the residual constraints and endpoint cost against the entropy threshold before building a candidate: the tested degree-one/two designs fall short even when the endpoint is ignored.