[aliromman]

This completes the determinant-character interface for every supplied finite-field Kronecker pencil model. It removes the global invertible-rational-slice premise and includes nonsplit regular primaries, arbitrary Jordan lengths and multiplicities, infinity, and all regular/singular mixtures. It returns exact SL labels and literal determinant-one corrections. No new kappa is claimed.

Proof, construction, exact evidence, verification, source pins, and scope. Contribution head: 29172b129a7bb4dbbb3b42ac128fa32ffec1f93b.

Each primary block has its own invertible affine chart after a slice action. The fractional transform retains its cyclic vector, so an explicit Krylov basis produces the new companion block. Exact multiset matching decides the allowed slice actions. All off-diagonal Hom spaces are included in the determinant proof. The full image is the union of the actual row/column lift cosets with the complete fixed-slice subgroup; actions with equal determinants are not silently identified.

The result closes the supplied-model regular question from Nick Petalas PR #5250 and the regular/singular coupling left by PR #5672 and PR #5683. For fixed q, image extraction from the model is deterministic polynomial time in dimension. General norm witnesses have an exact expected-polynomial randomized construction; the bounded code instead enumerates residues of degree at most three. Arbitrary-input decomposition and polynomial complexity in log(q) are not claimed.

A full closed family goes beyond diag(s,t,s+t). With a length-ell primary of common multiplicity r at every point of P1(F_q), all rational slices are singular, yet

Delta = {(x,y,z): x in (F_q*)^ell and x*y*z^(r*ell)=1}.
SL orbit count = (q-1)*gcd(q-1,ell).

F5 at length two has eight orbits; F4 at length three has nine. The determinant polynomial alone misses the extra length constraint.

python3.12 -B scripts/research_package.py --package research/finite-field-pencil-characters

Expected: PASS_COMPLETE_SUPPLIED_FINITE_FIELD_PENCIL_CHARACTERS and PASS_REGISTERED_RESEARCH_PACKAGE. Python 3.12 and the standard library suffice. Normal and optimized replay pass. The evidence has 320 coefficient-equation Hom cases, 52,807 literal solutions and 13,042 invertible stabilizers in sixteen domains. Fourteen cover all GL2 actions; two larger cases use explicitly listed subsets. Across 27 models, all 4,032 slice actions are screened, 2,194 literal lifts are checked, and all fixed cosets give 7,450 prescribed-action witnesses. All 567 determinant triples yield 239 witnesses/SL corrections and 328 exclusions. Nine mathematical and nine malformed-model controls pass, including the inherited Jordan sign example and actual damaged-source rejection.

Exact committed-byte and official export checks pass. A sealed read-only Git-free optimized replay with empty PATH passes without changing exported bytes or modes. All fifteen package files match the commit. Full-history preflight is unavailable in the shallow checkout; current source pins and bytes are checked. Hosted CI, independent human review and proof-kernel acceptance remain separate. The main planner's reported navigation regression is not repaired by this package.

The finite code uses F2/F3/F4/F5 and total dimensions at most sixteen; the written theorem has no dimension or field-size bound. Discovery of the supplied model, native realization, ownership, movement, restoration, storage, precision, repeated preparation and the full recursive invoice remain open. The selected frontier is unchanged.

Base and final canonical refresh: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority7, selected .00310045. Canonical claim. Four source files remain byte-exact, with all notices. Credit Nick Petalas PR5250 and its centralizer/canonical-form lineage, apoursh PR5672, Ali Romman PR5683, David Ganz A030/A026/A029, and classical Kronecker/companion/norm theory. New construction, proof and checks: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. Global literature priority is unclaimed.