Complete evidence set behind Machine-Verified Corollary Mining of the Jacobian Conjecture Collapse: An Explicit Degree-Three Keller Counterexample in Dimension 22 and a Certified Dixmier A₃ Witness (AGNT Labs Technical Report v1.0, July 21 2026): every certificate JSON, the explicit witness operators, and the unmodified deterministic instruments that produced and verified them. Base counterexample due to L. Alpöge and Claude Fable 5 (July 20, 2026); everything below is exact rational arithmetic — zero floating point.
Integrity. SHA256SUMS.txt lists a checksum for every file below plus the paper itself
(verify with sha256sum -c SHA256SUMS.txt from this directory). manifest.json carries the same hashes
plus environment pins and both RNG seeds. The timed-out direct-determinant attempt (phase5_symbolic_det.py) is
retained deliberately: negative instrument results are kept, not hidden.
Replication (≈50 s total, any machine with Python 3 + SymPy):
python phase1_dixmier_witness.py → phase2_normalize.py → phase3_reduce_to_degree3.py → phase4_independent_verify.py → phase5b_chain_det_proof.py → make_manifest.py
Seeds: construction 20260721, independent verification 987654321. The elimination schedule is a pure function of the input map, so all artifacts reproduce byte-identically.
Third-party spot-check without running anything: load degree3_counterexample.json in any CAS and check (a) every monomial of every Hⱼ has total degree 2 or 3; (b) the three points are distinct with identical images; (c) det J = 1 at arbitrary points.
| File | Size | SHA-256 | Description |
|---|---|---|---|
| Certificates & verified artifacts (machine-checked outputs — verbatim) | |||
| degree3_counterexample.json | 9.1 KB | 912795a13250c389… | MAIN RESULT — explicit degree-3 Keller counterexample on Q^22: all 22 components, the 3 rational collision witnesses, and the complete 18-step elimination log (Tables 2-3, Appendix A of the paper) |
| chain_det_proof.json | 4.9 KB | 57838a75e780bbaa… | Complete symbolic proof det J ≡ 1 by verified elementary factorization: 37 factor support-block determinants + 18 composition identities + base case + replay-matches-artifact assertion (§7.1) |
| dixmier_certificate.json | 2.8 KB | 13cadbcb287d3cbb… | Certified Dixmier A₃ witness: Keller property, 3-point collision, polynomiality of G, and all 36 Weyl relations (R1 9 + R3 27) verified by full symbolic expansion + random-rational second oracle (§4, Table 1) |
| dixmier_witness_operators.txt | 1.4 KB | cd120e1fdea0be19… | The explicit endomorphism φ : A₃ → A₃ — operator images φ(xᵢ), φ(∂ⱼ) in human-readable form (Appendix B) |
| normalized_map.json | 1.3 KB | 7b5f79c2f3e47d98… | Normalization G = X + H of the Alpöge map: L, H monomial profile (13 monomials, degrees 2-7), det J_G = 1, collision survival (§5.1) |
| verification_report.json | 1.6 KB | 5a49abe3c15fab88… | Independent re-verification pass output: artifacts-only, fresh seed 987654321, dual evaluation paths — 15/15 checks (§7.2) |
| manifest.json | 2.5 KB | 71670d635b694d8d… | Reproducibility manifest: environment pins, both seeds, run order, SHA-256 of every artifact (Table 5) |
| Instruments (deterministic construction & verification scripts — unmodified) | |||
| phase1_dixmier_witness.py | 6.8 KB | 6739e8c6ac90bb2d… | Instrument: constructs φ from adj(J)ᵀ/(-2) and verifies all Weyl relations dual-path; emits the Dixmier certificate (1.0 s) |
| phase2_normalize.py | 3.3 KB | e75efb359b4a8c56… | Instrument: produces and verifies the X + H normalization; profiles H to size the reduction (0.1 s) |
| phase3_reduce_to_degree3.py | 10.3 KB | d1f8612f9e5b7655… | Instrument: the 18-step verified elementary elimination engine — per-step composition identity, exact monomial cancellation, collision transport, degree-descent termination (7.0 s) |
| phase4_independent_verify.py | 6.1 KB | d4582f6420a76b48… | Instrument: independent verifier — re-parses published JSON only, fresh randomness, Schwartz-Zippel line probes, dual eval paths, independent raw re-encoding of the base map (40.6 s) |
| phase5_symbolic_det.py | 1.2 KB | 329285a7c4926f08… | Instrument: attempted DIRECT 22×22 symbolic determinant (Bareiss) — did not complete within the 600 s budget; retained for transparency (§7.1). Superseded by the factorization proof |
| phase5b_chain_det_proof.py | 7.2 KB | ff092726da6933c3… | Instrument: the chain determinant proof — deterministic replay, per-factor full-Jacobian support scan + support-block symbolic det, composition re-verification, final-map equality vs artifact (0.4 s) |
| make_manifest.py | 1.3 KB | f6fe458930f41f66… | Instrument: SHA-256 manifest generator with environment pins |
Paper integrity. SHA-256 of the published paper:
dd158dbc758f442c83020d1b99b95197d5bd2b82252773fa92894fc1110d35c2