[aliromman]

This enabling construction completes special-linear recognition for raw finite-field matrix pencils. From any two m-by-n coefficient matrices over one common finite field, with m,n>0, it returns a complete SL_m x SL_n x SL_2 orbit label, a fixed representative, and an explicit determinant-one transporter. It covers singular blocks, zero indices, all regular primary degrees/lengths/multiplicities, infinity, zero pencils and absence of an invertible rational slice. Complete kappa is unchanged.

Proof, implementation, source pins, exact evidence, validation and limits.

PR #5692 supplies raw strict decomposition; PR #5689 supplies complete fixed-slice determinant characters. This closes their remaining raw-to-SL boundary. It enumerates special-linear slice actions and keeps every actual row/column basis and permutation determinant. The least strict-type/coset pair is a complete orbit label. Literal stabilizer corrections give maps to one fixed representative and between equivalent raw inputs. The retained bounded character program is only a comparison oracle and is not patched.

The decision is deterministic and polynomial in dimension for fixed field. Exact uniform-sampling norm witnesses implement the general-degree construction that the predecessor left outside its bounded executable. Each nonzero norm target has success probability at least 1/q, so map preparation has expected polynomial cost for fixed field. Every norm and final map is checked exactly. Randomness changes runtime and witness choice; it does not change labels or correctness. No deterministic worst-case witness bound or complexity polynomial in log(q) is claimed.

python3.12 -B scripts/research_package.py --package research/raw-pencil-sl-transport

Expected markers:

PASS_RAW_PENCIL_SL_SMALL
PASS_RAW_PENCIL_SL_EXTENSION
PASS_RAW_PENCIL_SL_FIXTURES
PASS_RAW_PENCIL_SL_NORMS
PASS_RAW_PENCIL_SL_CHARACTERS
PASS_REGISTERED_RESEARCH_PACKAGE

Python 3.12 and the standard library suffice; the exhaustive phases use at most four process workers.

Independent elementary-transvection orbits cover all 81,244 raw pencils in eleven F2/F3/F4 domains, with 76 SL orbits across those domains. Every input's label and literal determinant-one map is checked. Larger F2/F3/F4/F9 fixtures include degree four, length four, index six, multiplicity four, dimension seventeen and regular no-invertible-slice families. There are 23 larger raw-to-raw transports, 29 malformed/inequivalent/singular-map controls, 112 norm targets through degree eight, 336 length-one/two/four determinant lifts, three invalid norm controls, and all 180 determinant triples in fifteen supplied-model comparison orbits. The evidence records the corrected negative-control expectation.

Normal Python 3.14.7, final registered Python 3.12.14 and optimized read-only Git-free replay pass. The latter uses an empty executable path, rejects an actual changed source before execution and preserves all 21 export files. All 20 committed package files pass official export/check. The shallow checkout prevents full-history preflight; exact bytes and immediate retained-source ancestry are checked. The shared main CI navigation test currently blocks hosted package replays; existing repairs are PR #5659 and PR #5703. No hosted pass is claimed.

This is an algebraic admissibility tool for two-slice tensor-atlas mechanisms. Field isomorphisms and more-than-two-slice tensors are outside scope. A native producer/consumer, physical routes, dirty restoration, storage, precision, repeated preparation and the complete recursive invoice remain unknown. No physical supplier, practical multiplication speedup, independent human review or proof-kernel acceptance follows. All costs are positive; no new kappa is inferred from the classification.

Base and refreshed main: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority 7, selected conditional kappa .00310045. Consumed heads: e34ae992744db135b9d4e378bfe26fd31fb82ad7 and 29172b129a7bb4dbbb3b42ac128fa32ffec1f93b. Source retention: ee3536dbba8cf627b6e65459d38cc14c86436e79; scientific code: 3afe93780f111c6368badd47394ce761d4421317; contribution head: 7ad7cf04b4b3ff1d0193e4d8f552eb63b842d0c5.

Credit the two consumed predecessors, Nick Petalas (@petalas), PR #5250, @apoursh, PR #5672, Ali Romman (@aliromman), PR #5683, David Ganz's tensor atlas credit and the classical Kronecker/module/centralizer/norm lineage retained in the linked proof and sources. All eleven source files and notices remain byte-exact. Global literature priority is unclaimed.

Ali Romman with substantial OpenAI Codex assistance; no subagents. This uses the same assistant family as the consumed packages, with a separately written finite-orbit oracle. Apache-2.0. Scoped claim.