[aliromman]

This removes the supplied-decomposition premise from the split Frobenius-product tensor interface. From an arbitrary square tensor over an explicit finite field, it recovers every local height type and three checked factor maps, or rejects the tensor. It also computes the complete special-linear orbit label and constructs determinant-one transporters. No new kappa is claimed.

Proof, exact results, implementation and contract, and source pins.

Frobenius-fixed spectral projectors recover primitive idempotents in the presence of nilpotents. Component module-top tests then recover regular generators without enumerating vectors. The retained local classifier supplies each height type. Normalizing its output map by multiplication with the inverse image of one gives an actual algebra isomorphism. Sorting the resulting basis columns preserves the component-order determinant sign. The proof gives a deterministic polynomial bound in dimension for each fixed field; it makes no polynomial-in-log(q) claim.

The exact class consists of finite products of K[x_i]/(x_i^(p^h_i)), including field factors and repeated types. This completes the released PR #5656 handoff. Nonsplit residue fields, arbitrary commutative algebras and physical supplier costs remain open. The tensor atlas gains a raw-input recognizer; a complete paid caller is still needed to affect kappa.

Python 3.12.14 registered normal and optimized replay passed with identical results. A separate coefficient-index orbit generator agrees on all 72,353 two-dimensional tensors over F2, F3 and F4: respectively 162, 3,456 and 49,500 are accepted. Further checks cover 62 changed-basis presentations, 798 basis products, 62 determinant-one transporters and 325 controls, including a sign-sensitive F3 times F3[x]/x^9 example. Committed-byte and export-integrity checks passed for all 12 package files. The read-only Git-free optimized replay is recorded in the publication handoff.

python3 -B scripts/research_package.py --package research/split-product-tensor-recognition
python3 -B scripts/check_research_commit.py --package research/split-product-tensor-recognition

Expected scientific marker: PASS_SPLIT_PRODUCT_TENSOR_RECOGNITION. The standard library suffices. No independent human review, proof-kernel acceptance, selected cold replay, native supplier execution or complete multiplication theorem is claimed. Hosted CI is separate. The checkout is shallow, so full-history preflight is not claimed; the exact source copies are retained in this branch's first commit and the package export is self-contained.

Base is canonical main df0137efd35e11b4445734bf612bdd4c7ebc330c, priority revision 7. Main and overlap were refreshed before submission: 348 open PRs, 4,961 Discussion records and the complete tracked main note inventory. The advance claim records the distinct scope. These searches do not cover unpublished work or every code diff. Only this new package changes; the selected frontier and predecessor packages retain their bytes.

Credit @apoursh for PR #5656, exact b5e6e7c45f606d639d102570f9fab257e1d0d393, which supplies the product characters and handoff; Ali Romman for PR #5637, exact 86389e525d3efafe236e929f6ae401c68be1d115, whose finite-field/local executable is retained unchanged; and Nick Petalas for PR #5252, whose nucleus and reduced spectral projectors are extended. The retained proofs preserve the height, local-character and David Ganz atlas lineage. The source manifest binds each consumed source. Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.