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Complete evidence set behind The Anatomy of the First Jacobian Counterexample: Torus Equivariance, an Explicit 3:1 Fold, a Weight-Forcing Rigidity Theorem, and a Graded Reduction Program for Dimension Two (AGNT Labs Technical Report II v1.0, July 21 2026). Base counterexample due to L. Alpöge and Claude Fable 5 (July 20, 2026). Everything below is exact rational/symbolic arithmetic — zero floating point.
Two-agent verification. The breakthrough/ tree is the primary construction; audit/ is the author's own adversarial deformation analysis (which produced Lemma 5 and Theorem 6); audit-sol/ is an independent sibling agent's re-derivation with different algorithms and zero shared code — including the probe that found 9 apparent counter-specimens and the gauge maps proving each is a relabeling of Alpöge's map. The v0.9→v1.0 correction forced by that audit is documented in §8 of the paper; superseded/failed instruments are retained here, not hidden.
Integrity. SHA256SUMS.txt lists a checksum for every file plus the paper itself
(verify with sha256sum -c SHA256SUMS.txt from this directory).
Replication (≈15 s total, Python 3 + SymPy; the only network call is the optional HTTPS byte-audit):
cd breakthrough && python fold_anatomy.py && python forge_full.py && python forge_m45_and_foldline.py && python anatomy_and_obstruction.py && python dim2_dichotomy_and_reduction.py
cd ../audit && python audit1_reverify.py && python audit2b_weight_forcing.py && python audit3d_orbit_tangent.py && python audit3e_integrate.py
cd ../audit-sol && python audit1_core.py && python audit2_published.py && python audit5_full_gauge.py && python audit6_confirm_gauge.py
| File | Size | SHA-256 | Description |
|---|---|---|---|
| breakthrough/ — primary construction & theorems | |||
| breakthrough/fold_anatomy.py | 4.4 KB | 75e1d6ae89941f7f… | Theorem 1 (Fold): F¹⁻¹(fixed line) = axis ∪ C(s), 2:1 fold, completeness via Res_z, Gaussian fiber — 14 checks |
| breakthrough/forge_full.py | 9.7 KB | df279a0e5c96fd56… | Theorems 2–3: torus equivariance, descent a=xy b=x²z, Jac = 2(3a+b−2)², fiber degree 3; Design Forge m≤3 (staged linear/quadratic solve) + Alpöge membership |
| breakthrough/forge_results.json | 3.3 KB | b74324f072e103d3… | Forge certificates m≤3: m=1,2 excluded; m=3 unique point, c=−2 |
| breakthrough/forge_m45_and_foldline.py | 6.7 KB | b7bd4b6411573366… | Fold-line descent verification + forge m=4,5 exclusions + artifact hashing |
| breakthrough/forge_m45.json | 1.0 KB | 14154ef6f0ac3091… | m=4,5 exclusion certificates (stage-1 linear layer empty at all caps) |
| breakthrough/anatomy_and_obstruction.py | 5.4 KB | 432a416ca236e121… | Mechanisms I–III (z-affinity, Z/2 equivariance, orbit-collision) + dim-2 z-affine obstruction theorem |
| breakthrough/dim2_dichotomy_and_reduction.py | 6.9 KB | 715d0183718b01d6… | Dim-2 export: reflection-equivariant dichotomy, quotient identity, reduction equation u·Jac(H,K)²=c²K, first sweep |
| breakthrough/dim2_sweep.json | 0.8 KB | 6a4293b98d5aca49… | Reduction-equation exclusion certificates (5 nonconstant g-shapes, deg H≤4) |
| breakthrough/dc1_hunter.py | 4.9 KB | a80369ec239712e6… | Exact normal-ordered Weyl algebra A₁ engine (self-tested) + DC₁ sweep 1 |
| breakthrough/dc1_sweep1.json | 0.5 KB | ac5bcbc7300f3d25… | DC₁ sweep 1: 144 sparse two-term patterns, filtration ≤4 — zero nontrivial commuting pairs |
| breakthrough/dc1_parity_sweep.py | 2.7 KB | a64f9538a5b55edf… | DC₁ sweep 2: parity-equivariant ansatz (Mechanism II seed) |
| breakthrough/dc1_sweep2_parity.json | 0.1 KB | 16711745f5180184… | DC₁ sweep 2 certificate: 100 patterns, zero nontrivial pairs |
| breakthrough/breakthrough_hashes.json | 1.1 KB | e6936d57d5567585… | SHA-256 manifest of the breakthrough set |
| audit/ — author's adversarial deformation analysis (Lemma 5, Theorem 6) | |||
| audit/audit1_reverify.py | 5.0 KB | 6f6148cb8002c15e… | Re-verification of Theorems 1–3 from a fresh raw encoding + Gröbner quotient-dimension cross-check of the Degree Theorem (different algorithm) |
| audit/audit1.json | 1.0 KB | e3eb45b615736c4b… | Audit-1 verdicts (ALL PASS) |
| audit/audit2_weight_forcing.py | 2.3 KB | e154a3d19033f056… | Weight-forcing lemma, first staging (superseded by audit2b; retained for transparency) |
| audit/audit2b_weight_forcing.py | 1.5 KB | 98780c0b46e1ef28… | LEMMA 5 (Weight-Forcing): residual homogeneity constraint = (3−m)·w_x — slope power 3 structurally forced |
| audit/audit3_deformation.py | 6.1 KB | 362bd2a3c0a0be25… | Full-class (slope-free, 19+1 unknowns) Keller linearization at Alpöge: dim ker = 6, first trivial-span comparison |
| audit/audit3.json | 2.0 KB | b41bc19a0e9794fa… | Audit-3 kernel data |
| audit/audit3b_deformation.py | 4.5 KB | 4de95adef587fee2… | Deformation pass 2: combined pre-y/post-F2 gauge direction identified |
| audit/audit3b.json | 0.3 KB | dcb0585d63f08925… | Audit-3b verdicts |
| audit/audit3c_close_kernel.py | 5.4 KB | 76b1932077cac09b… | Deformation pass 3: all graded-gauge shear generators linearized |
| audit/audit3c.json | 0.3 KB | 43e13fd5dad5f793… | Audit-3c verdicts |
| audit/audit3c_family.py | 8.8 KB | 542acc4798e396f1… | Exploratory kernel-direction probe (superseded by 3d/3e; retained) |
| audit/audit3d_orbit_tangent.py | 4.6 KB | af4130c15846d92e… | Gauge-orbit tangent via Lie-algebra action: rank 5 inside dim-6 kernel |
| audit/audit3d.json | 0.2 KB | 1aab9934d9bb65dd… | Audit-3d verdicts |
| audit/audit3e_integrate.py | 6.4 KB | 013cc6470cf8b3b6… | THEOREM 6 decisive test: the lone non-gauge direction is SECOND-ORDER OBSTRUCTED (det J = −2 + O(s²), monomial x⁷y³z² coeff −s²/8) |
| audit/audit3e.json | 0.4 KB | 1df7083f6de182dc… | Audit-3e verdict: OBSTRUCTED — rigidity holds |
| audit/audit_all_hashes.json | 2.7 KB | 42a38a697b494f71… | SHA-256 manifest of both audit sets |
| audit-sol/ — independent sibling-agent audit (zero shared code) | |||
| audit-sol/audit1_core.py | 5.5 KB | 57bb85648c4b5729… | SOL (independent sibling agent, zero shared code): re-derivation of Theorems 1–4 + Dixmier witness by different algorithms — 18/18 |
| audit-sol/audit1_verdicts.json | 1.8 KB | 2320d77ef2fc2b0d… | Sol audit-1 verdicts |
| audit-sol/audit2_published.py | 3.7 KB | 70dee4ab6b92e167… | SOL: HTTPS byte-verification of the published Report I artifact set against SHA256SUMS (15/15) + re-verification of served objects |
| audit-sol/audit2_verdicts.json | 0.9 KB | 8d6f944f242b9cf5… | Sol audit-2 verdicts |
| audit-sol/audit3_rigidity.py | 8.0 KB | 3768653729a54c8e… | SOL adversarial probe: y-normalization freed, truly-equivariant slope class swept — 9 apparent new specimens found |
| audit-sol/audit3_results.json | 62.9 KB | e8ca08785f9cbb52… | Sol probe data (the specimens that forced the v0.9 correction) |
| audit-sol/audit4_gauge.py | 5.0 KB | 5573df109b4731a0… | SOL: diagonal-gauge test (insufficient alone — motivates full graded gauge) |
| audit-sol/audit4_verdicts.json | 2.1 KB | 007b9d8ffc46c71e… | Sol audit-4 verdicts |
| audit-sol/audit5_full_gauge.py | 5.2 KB | 08de2a80c4d24e3f… | SOL: full graded gauge group (scalings + equivariant shears) — all 5 representative specimens gauge-equivalent to Alpöge |
| audit-sol/audit5_verdicts.json | 0.4 KB | ae0e3f758e735962… | Sol audit-5 verdicts (5/5 equivalent) |
| audit-sol/audit6_confirm_gauge.py | 1.7 KB | 93b3b7a97bbe9dd7… | SOL: one gauge equivalence confirmed by DIRECT SUBSTITUTION: T∘F∘S = specimen with S=(x,y,−z), T=(−Y₁, Y₂/3, Y₃); det −2/3 proves c is not gauge-invariant |
| audit-sol/audit_hashes.json | 1.0 KB | 6347c7affe9e930b… | SHA-256 manifest of the Sol audit set |
Paper integrity. SHA-256 of the published paper:
85ad5a9bff460336bd4a6da0221ed7e9ff2c66e49a243f565500dfa0a5187a56