[aliromman]

This supplies the missing raw-input extraction for finite-field matrix-pencil characters: from any two rectangular coefficient matrices, it returns all left and right minimal-index blocks, every regular primary including infinity, and exact row and column maps. It needs no invertible base-field slice. This is an enabling algorithm and proof; no new kappa is claimed.

Proof, algorithm, exact result, verification, source pins, and validation limits. Exact contribution head: e34ae992744db135b9d4e378bfe26fd31fb82ad7.

The maps satisfy A Q = R A0 and B Q = R B0; both are invertible and the slice map is the identity. The class includes zero-index blocks, dependent slices, zero rows or columns, repeated irreducible primaries, extension fields and regular pencils with no invertible rational slice. Shortest polynomial null chains and linear projection equations split singular blocks. A stabilized preimage sequence isolates infinity; exact Berlekamp factorization and maximal cyclic summands finish the regular residue. For each fixed finite field, the algorithm is polynomial in the dimensions. No polynomial bound in log(q), numerical stability or fast canonical-form record is claimed.

This closes the explicit raw-decomposition obligation left by Nick Petalas PR #5250, apoursh PR #5672, PR #5683, and the completed supplied-model interface PR #5689. Their determinant and special-linear formulas are separate work and are not reimplemented here. David Ganz's tensor-atlas lineage supplies the motivation. Kronecker decomposition, primary module theory, Wong sequences and Berlekamp factorization remain classical predecessor work; their primary-source references and the proof of this implementation are in the linked proof.

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

Expected: PASS_RAW_PENCIL_DECOMPOSITION and PASS_REGISTERED_RESEARCH_PACKAGE. Python3.12 and the standard library suffice. A separate elementary-GL orbit oracle covers all 80,545 raw pencils in the five domains: 2x2 over F2/F3/F4 and 2x3/3x2 over F2. It finds 114 strict orbits and checks extracted types in both directions. Every input also has both literal map equations checked. The replay includes 1,776 polynomial divisor/product cases, 96 larger constructed pencils, 22,812 constructed coefficient equations, 12 no-invertible-slice examples and 183 failure controls.

Normal and optimized replays pass, including registered Python3.12.14. An actually damaged retained source is rejected. The sealed Git-free optimized replay passes with empty PATH, with ten exported files unchanged in bytes and read-only modes. Exact committed-byte and official final export checks pass. The full-history preflight is omitted in the shallow checkout; immediate source ancestry and exact local/remote source bytes are checked. Hosted CI, independent human review and proof-kernel acceptance remain separate. The executable has ordinary finite-memory and Python recursion limits; the written algorithm has no dimension bound.

The byte-exact field arithmetic is retained from PR #5664 source, with its notice. The new extraction, implementation proof and checks are by Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. Global literature priority is unclaimed.

Base and final canonical refresh: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority7, selected .00310045. Canonical claim. The fresh complete overlap inventory found no competing raw-extraction reservation. The selected main-transform bottleneck remains. Native realization, ownership, storage, precision, preparation, routes, restoration and the full recursive invoice are open; this algebraic result assigns none of them zero cost.