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DONE / RELEASED — PR #5661, exact head 5d72227. The supplied-decomposition premise is removed for split Frobenius products over explicit finite fields. The package recovers primitive factors, local height types, all three factor maps, complete SL labels and determinant-one transporters. No algebra promise or invertible slice is required. The proof gives deterministic polynomial time in dimension for each fixed q. The recognizer agrees with a separate coefficient-index orbit generator on all 72,353 two-dimensional tensors over F2/F3/F4. There are 62 additional presentations, 798 basis products, 62 SL transporters and 325 controls, including a nontrivial component-order sign. Registered Python 3.12.14 normal/optimized replay, exact committed bytes, export integrity, and a read-only Git-free optimized replay pass. All 12 package files match their committed objects; the export has one additional integrity manifest. Source corruption is rejected. Published PR body and GitHub-rendered HTML match the reviewed draft. The shallow checkout prevents a full-history preflight claim; the immediate base and retained-source commit are verified ancestors. Nonsplit residue fields and a physical supplier remain open. No new kappa, selected-frontier change, independent human review or proof-kernel acceptance is claimed. Hosted CI is separate. Credit apoursh PR5656/5502, Ali Romman PR5637/5459/5540, Nick Petalas PR5252 and David Ganz's atlas lineage. Substantial OpenAI Codex assistance. This scope is released. Original claimCLAIM — remove the supplied decomposition from split Frobenius tensor recognition. I take the released next task in PR #5656, exact head b5e6e7c. Starting from an arbitrary square tensor over an explicit finite field, I will recover the nucleus, primitive idempotents, regular module generators and local height types, then return all three checked factor maps. The target class is a finite product of split Frobenius-truncated local algebras. I will also bind the recovered decomposition to the existing product character formula; nonsplit residue fields remain outside this task. The changed premise is discovery of the decomposition, instead of receiving it as a certificate. The finite verifier will compare complete small tensor domains against a separate orbit generator, exercise nilpotent products over extension fields, and reject nonregular modules and wrong residue fields. I will state a deterministic complexity bound for fixed q. This is a tensor-interface result; no physical supplier, free arithmetic or new kappa is assumed. Base df0137e, priority revision 7, selected conditional kappa .00310045. Fresh complete open-PR and Discussion pagination and all 7,676 main README/TASK/ledger notes were checked. The product-character scope is marked released. Credit apoursh PR5656/5502, Ali Romman PR5637/5459, Nick Petalas PR5252, David Ganz and the retained atlas lineage. Prepared for Ali Romman with substantial OpenAI Codex assistance. Expiry: 2026-10-26T05:21:52.849008+00:00 |
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DONE / RELEASED — supplied-decomposition nonsplit Frobenius-product determinant characters. Public artifact: PR #5663, exact head Evidence: six complete tiny matrix domains (40,487 matrices), 150 complete small nilpotent substitutions, independent F81 arithmetic/norm checks, 512 determinant triples and malformed-certificate/type controls. Registered normal/optimized replay, committed-source/history verification and official export checks pass; both final-head commands reproduce the complete RESULT in a read-only Git-free export, and all five source-corruption controls reject before import. Bounds and unrun obligations are explicit in the PR. Hosted CI was in progress at publication. This is a scoped proof plus finite evidence, not independent human or proof-kernel acceptance. The claim is released. Arbitrary nonsplit recognition and coefficient-field discovery remain with Ali Romman’s complementary claim; this package assumes the decomposition and common explicit residue presentations. Other follow-ups and source credit are in README/TASK.json. Prepared by apoursh with substantial OpenAI Codex assistance; Apache-2.0. Original advance claim and overlap coverageCLAIM — supplied-decomposition determinant characters for Frobenius products with nontrivial residue fields. I take the second open question in PR5656 and the nonsplit-character boundary retained by PR5661. For A = product_j F_(q^d_j)[x_i]/(x_i^(p^h_ji)) as an F_q-algebra, I will derive the norm, coefficient-Frobenius and equal-component permutation contributions to the automorphism determinant image, then the covariant tensor-stabilizer image and supplied-map orbit labels. The decomposition and coefficient-field presentations are supplied. This is complementary to @aliromman's completed split-product recognition; arbitrary nonsplit tensor recognition and coefficient-field discovery are outside this claim. Success/stop test: a self-contained proof with explicit determinant witnesses, a bounded exact checker against literal ground-field matrices, extension-field/nilpotent and component-matching controls, and registered normal/optimized plus Git-free replay. No physical supplier or new kappa is claimed. Compare: PR5658 routing already bounds field-level prefixes/suffixes but its remaining physical-cost task needs a named caller; this named algebraic gap has a complete bounded acceptance test. Base canonical main Credit Nick Petalas PR5252, Ali Romman PR5459/5637/5661, apoursh PR5502/5656, David Ganz and the retained atlas lineage. Prepared by apoursh with substantial OpenAI Codex assistance; Apache-2.0. |
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DONE / RELEASED — PR #5664, exact head 8f7773e. Arbitrary square tensors can now be recognized as finite residue-field Frobenius products, with discovered primitive factors, coefficient fields, local heights and all three literal factor maps. The proof is polynomial in dimension for fixed base field, with no enumeration of q^d residue elements. The character theorem, labels and special-linear transporters remain with apoursh's complementary supplied-decomposition scope; no competing result is claimed here. All 72,353 small tensors agree with a separate orbit generator. The package also checks 52 presentations, 1,392 basis products and 272 controls, including degree-three residues, nonsplit nilpotents and nonregular modules. Registered Python 3.12.14 normal/optimized, exact committed-byte/export, read-only Git-free optimized and source-corruption checks pass. All 13 package files match the commit; the export includes one additional integrity manifest. Published body and GitHub-rendered HTML match the reviewed draft. The checkout is shallow; full-history preflight, hosted CI, independent human and proof-kernel acceptance are not claimed. This resolves the nonsplit recognition/discovery scope. It supplies no paid native caller and no new kappa; the selected frontier is unchanged. The next integration should use these recovered field tables in the separate character interface after coordinating its field-isomorphism and basis contract. Credit PR5661/5637/5502/5656, Nick Petalas PR5252, apoursh, Ali Romman, David Ganz and the retained atlas lineage. Substantial OpenAI Codex assistance. No new scope is reserved. Claim and scope historyCLAIM / scope narrowed — arbitrary nonsplit tensor recognition and coefficient-field discovery only. The submission refresh found apoursh's supplied-character claim, posted seconds before this claim. It explicitly excludes arbitrary nonsplit tensor recognition and coefficient-field discovery. I retain those complementary outputs and remove the overlapping character-image, label and transporter outputs from this package. No competing character theorem or extra result is claimed. The recognizer recovers every primitive local factor, its finite coefficient field and height list, then gives all three literal tensor factor maps. The proof uses the q^d fixed algebra and module tops of dimension d, with polynomial base-field operations and no q^d element enumeration. Complete small tensor comparisons passed; the narrowed verifier is being rerun with additional degree-three residue fixtures. Source and publication checks remain pending. No new kappa or physical supplier is claimed. The original two-hour expiry remains. Original claim and scope historyCLAIM — recognize Frobenius products with nonsplit residue fields. The split-product scope in PR5661 is complete and released. I now change its residue-field premise. The target class is a finite product of L_j[x_i]/(x_i^(p^h_i)), where each L_j is any finite extension of the supplied base field K. The input remains an arbitrary square K-tensor. I will recover the local residue degrees, coefficient fields and height types by K-linear algebra, and return literal factor maps to models with explicit coefficient-field tables. A separate proof and checker will derive the covariant stabilizer determinant image, including residue Frobenius signs and identical-component swaps. The key candidate is the canonical coefficient field ker(Frob_(q^d)-I) in a local component with residue degree d, followed by a height test using spans over that recovered field. The module top must have K-dimension d, not one. This should avoid enumerating q^d field elements and preserve polynomial time in tensor dimension for fixed K. I will test all small tensors against a separate orbit generator, nonsplit nilpotent products, and false field/height/sign controls. A canonical field-isomorphism algorithm or cross-presentation SL transporter is not silently assumed. No paid supplier or new kappa is claimed. This follows the explicit nonsplit limitation of PR5656/5661 and the finite-etale precedent PR5252. Base df0137e, priority 7, selected .00310045. Refreshed coverage: 350 open PRs, 4,965 Discussion records, and all 7,676 tracked main notes. No active matching claim was found; arbitrary diffs and unpublished work remain outside that coverage. Budget 120 minutes. Expiry 2026-10-26T05:41:29.424651+00:00. Credit apoursh, Nick Petalas, Ali Romman, David Ganz and the retained tensor lineage. Ali Romman with substantial OpenAI Codex assistance. |
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DONE / RELEASED — PR #5668, exact head Registered normal/optimized replay, committed-byte/source-history checks and a read-only Git-free export pass. Evidence includes 112 field identifications, six raw-recognition fixtures, all 512 F9 determinant triples (128 accepted, 384 rejected), component-permutation/reference-change controls and rejected false base-semilinear maps. All ten mutated source inputs reject before import. Hosted CI was in progress at publication; independent human/proof-kernel acceptance is not claimed. The integration scope is released. Further expansion needs a named physical consumer and a complete cost bill, or specified large-residue arithmetic requirements. Exact proof, bounds, sources and next questions are linked in the PR. Credit Ali Romman PR5664/5661/5637/5459, apoursh PR5663/5656/5502, Nick Petalas PR5252 and David Ganz/retained atlas lineage. Prepared by apoursh with substantial OpenAI Codex assistance; Apache-2.0. Original advance claim and overlap coverageCLAIM — connect nonsplit recognition to fixed-reference SL labels and transporters. I take the released integration question in PR5664 ( Success/stop test: prove choice-independent labels relative to that reference, check literal three-factor and covariant identities on nonsplit/repeated/mixed fixtures, demonstrate a wrong raw-label comparison, reject invalid maps and base-semilinear substitutions, and pass authenticated normal/optimized plus Git-free replay. The bridge itself avoids q^d element enumeration; the retained character constructor has separate table/norm-search costs, so no polynomial claim for the entire executable. No new kappa. Base canonical main |
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DONE / RELEASED — PR #5656, exact head
b5e6e7c45f606d639d102570f9fab257e1d0d393.The supplied-decomposition split-product result is complete: exact automorphism and covariant stabilizer determinant images, component matching by full height type, canonical component-order signs, complete SL labels, and constructive determinant-one transporters. The theorem covers finite fields; the executable covers prime fields. F3[x]/x^9 has two SL orbits, whereas two identical copies have one because the permitted block swap contributes −1.
Proof, checker, source pins and next questions. Registered normal/optimized checks, source-history and committed-byte checks, export integrity, and paired read-only Git-free replays pass. Finite evidence includes 40,487 matrices, 2,372 normalized autotopisms, 4,874 local substitutions, covariant coefficient checks and 12 certificate rejection controls.
No arbitrary-product recognition, nonsplit residue fields, paid native supplier, new kappa, independent human review or proof-kernel acceptance is claimed. Hosted CI is separate; the PR records the already reported shared upstream planning-link defect. The scope is released.
The smallest next task is primitive-idempotent recovery plus local height recognition from an arbitrary tensor, to remove the supplied-decomposition premise. This needs a complete decomposition algorithm and complexity proof. Credit Ali Romman (#5637/#5459), apoursh (#5502), Nick Petalas (#5252), David Ganz and the retained atlas lineage. New work by apoursh with substantial OpenAI Codex assistance; Apache-2.0.
Original advance claim and overlap coverage
CLAIM — split products of Frobenius-truncated local algebras
Following Ali Romman's released PR #5637 handoff (head 86389e5), I am taking the supplied-decomposition product case: component matching, the automorphism determinant subgroup, and the covariant multiplication-tensor stabilizer image, with explicit small witnesses and rejection controls. Local character input: PR #5459 at bef3575; component height invariants: PR #5502; finite-etale normalization: PR #5252. Predecessor attribution will be retained.
Base df0137e, priority revision 7. This changes the formal-interface-lemma card to a written algebraic interface proof plus exact finite verification; no Lean formalization, arbitrary-product recognition, larger residue fields, physical supplier, or kappa improvement is claimed. The intended certificate has a supplied product model and checked factor maps. Block permutations must match isomorphism types, not just dimensions.
Overlap checked: current main guidance, live newest handoffs including #5637, and bounded all-state PR searches for product/Frobenius/component terms. Sparse local notes, unpublished work and arbitrary historical diffs are outside coverage. About one hour of work; this advisory claim expires at 2026-10-26 05:00 UTC. Work is currently local only; I will replace this status with the public artifact and any remaining gap.
apoursh, with substantial OpenAI Codex assistance. Apache-2.0; no general literature-priority claim.
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