[aliromman]

This proof extends the explicit multivariable handoff in PR #5316 to finite local algebras with unequal characteristic-power cutoffs. It gives the exact automorphism character, full covariant tensor-stabilizer determinant image and special-linear orbit count. The complete kappa calculation is unchanged.

Proof and scope, exact checks, source pins, registered replay. Base: canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Contribution head: bef3575ddb19c44434a7e2460a353eac7c4d9387.

For A=F_q[x_1,...,x_r]/(x_i^(p^e_i)), the tangent map must preserve the height flag. With N=product_i p^e_i and h=gcd(q-1,N(p^e_i-1)/2 for all i), the stabilizer image consists exactly of triples satisfying (uvw)^((q-1)/h)=1. The GL orbit has h special-linear orbits. Modular powers compute the promised character equation without building the algebra. The supplied field characteristic and algebra-class promise are required.

CPython 3.12.14 registered normal and optimized checks pass: 5121 literal substitution maps, 188036 basis-product checks, 970 unit maps, 297 determinant triples and 64 controls across 12 contexts. Complete nonlinear automorphism domains include 48 maps for the univariate cutoff four over F4, 2880 maps for two cutoff-two variables over F4, and 2048 maps for cutoffs two and four over F2. Both modes print PASS_FROBENIUS_TENSOR_CHARACTERS; the launcher prints PASS_REGISTERED_RESEARCH_PACKAGE.

python3.12 -B scripts/research_package.py --package research/frobenius-tensor-characters

Python 3.12 and the standard library suffice. Committed-byte checks pass. The written proof covers every finite field in this promised family. The checker uses F2,F3,F4,F5,F7 and finite dimensions through 49. It does not recognize an arbitrary tensor, recover a transporter, handle arbitrary local algebras, or price a physical supplier. No selected cold replay, predecessor scientific suite, Lean, Docker or independent human/proof-kernel acceptance is claimed. Hosted status is unconfirmed at publication.

Credit Ali Romman (@aliromman) for PR #5316 and the pinned univariate proof and handoff. Credit Nick Petalas (@petalas) for PR #5252 and the finite-etale normalization and nilpotent question. The pinned sources retain David Ganz and the atlas lineage. Local filtrations, elementary matrix generators and cyclic power subgroups are classical. The scoped claim records the overlap check.

Next: recognize this promised algebra class from an input multiplication tensor and construct a verified transporter. The radical filtration and recovered height flag give a concrete starting point.

Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.