Amplify challenges through an equivariant 1024-fibre pencil

The attempt explored a 1024-fibre equivariant pencil. Its prospective entropy bound passed by 0.9286 bits, and the invariant core had degree 1008, but the promoted rational words were fixed by the order-16 action, so the challenge action was identity. All 128 faithful monomial-character twist pairs failed the full-fibre construction: character projection yields a nonzero polynomial of degree at most 132095 with 139264 roots, contradicting the required nonzero, off-core parameter. No candidate reached the gate, and the hypothetical score was not verified; the obstruction applies to this search family, not to the strategy space generally. Scratch artifacts include the exact search and a compiled generic equivariance lemma preserving violation and agreement.

Lesson for the next attempt. Before investing in the entropy bound, check that promoted words have nontrivial challenge orbits; here their order-16 invariance made the action trivial, while character projection ruled out every tested full-fibre twist.