{ "schema": "fable_v2_gap03_realizationB_certificate_v1", "gap_id": "03_strong_cp_edm_closure", "attempt_id": "gap03_realizationB_topologicalCP_2026-06-14", "method_authority": "GAP_CLOSURE_LOOP_DESIGN.md 6.5 + METHOD_CFCA_June_14.md", "status_in": "OPEN_PHYSICS_BLOCKER (T-alpha1-A DISPROVED; T-alpha2 CLOSED)", "sot_hash": "88e5903fe1c3d17655acef7e4fb45078e3168add25362040e21598b3b161ff17", "source_hash_TOE_FINAL_REVIEW": "caf7ffc24d46e8b5e586b1cdcaceaa0318533644f880036c15a6bad9627211ec", "hard_gate_vector": "D,D-local,D,D,D", "realization_A_obstruction_reproduced": { "realization_A_all_argdet_invariant": true, "realization_B_rowonly_matches_sign_lever": false, "lever_law": "det(P M P^T)=det(M) (A, W-even); det(P M)=sign(w) det(M) (B, Z_2 lever)" }, "ext3_zero_mode_gate": { "n_idx3_bundles_small_window": 12, "frozen_bundle_weight": [ 1, 0 ], "frozen_det_character": "sign", "frozen_faithful_3_orbit": true, "all_faithful_idx3_share_sign_character": true, "n_opposite_det_character_idx3": 0, "asymmetry_requires_zero_mode_content_change": true, "idx3_bundle_table": [ { "weight": [ -4, 0 ], "index": 3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ -4, 1 ], "index": 3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ -3, -2 ], "index": -3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ -3, 2 ], "index": -3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ -2, -3 ], "index": -3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ -2, 2 ], "index": -3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ 0, -4 ], "index": 3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ 0, 1 ], "index": 3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ 1, -4 ], "index": 3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ 1, 0 ], "index": 3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ 2, -3 ], "index": -3, "det_character": "sign", "faithful_3_orbit": true }, { "weight": [ 2, -2 ], "index": -3, "det_character": "sign", "faithful_3_orbit": true } ] }, "zero_mode_invariance_proof": { "verdict": "ALTERED-ROUTE-REJECTED", "APS_pre": [ 3, 0 ], "APS_post": [ 3, 0 ], "BWB_pre": 3, "BWB_post": 3, "byte_invariant": false, "note": "The chiral split that supplies the Z_2 sign(w) lever requires a zero-mode multiplet of opposite Weyl determinant-character to the frozen (1,0) bundle. Every |index|=3 bundle whose family multiplet is the standard faithful 3-element Weyl orbit carries the SIGN determinant-character; an opposite-character partner is therefore NOT a faithful 3-orbit, so the three families transform under a DIFFERENT Weyl representation. The integer family count |index|=3 can coincide, but the spin-structure three-family witness REP is altered -> EXT-3 rejects outright (fail-closed)." }, "finite_topological_cp_sector": { "phi_K6_rad": -0.12827, "closed_manifold_no_boundary": true, "pontryagin_shift_is_2piZ_only": true, "net_theta_pinning_to_cp_even": 0.1282700000000001, "yields_zero_net_pinning_without_reusing_APS_fold": true, "note": "On the closed homogeneous K_6 the topological sector supplies only a 2 pi Z periodicity shift, NOT a CP-even pin; the CP-odd projection needs the orbifold/boundary fold already spent on APS (+3,0) chirality -- reusing it alters the zero-mode inventory." }, "j_ckm_audit": { "rephasing_invariant_J_preserved": true, "max_abs_delta_J_64_rot": 8.326672684688674e-17, "tol": 1e-09, "note": "J is rephasing-invariant; no observed J value used (data-blind)." }, "theta_bar_smallness_derived": false, "theta_bar_value_claimed": null, "terminal_state": "BANKED-NEGATIVE (route disproved; gate stays OPEN_PHYSICS_BLOCKER)", "final_verdict": "state-B (third banked negative)", "exit_code": 1, "no_target_loading_attestation": { "nedm_bound_used_as_input": false, "pdg_used_as_input": false, "lambda_eta_B_As_r_ns_used_as_input": false, "nedm_appears_only_in_post_freeze_comparison": true }, "upstream_mutation_attestation": { "sot_hash_unchanged": true, "source_hash_unchanged": true, "hard_gate_vector_unchanged": true, "note": "This script writes ONLY to its own outputs/ dir; no gap_03 or upstream file mutated." }, "post_freeze_nedm_comparison": { "falsifier": "nEDM theta_bar > 1e-10 makes the underived status refutation-grade", "threshold": 1e-10, "comparison_performed": false, "reason": "No theta-bar derived; nothing to compare. Status stays Precisely-OPEN." }, "named_blocking_object": "Axiom-3 chirally-asymmetric W-action field content placing Q_L and u_R/d_R on DIFFERENT K_6 bundles of opposite Weyl determinant-character that nonetheless preserves the |index|=3, (+3,0)-APS faithful 3-orbit family-witness rep -- shown here (data-blind) to be obstructed in the small-weight window; an owner-level Axiom-3 act outside this script's reach.", "owner_signature_slot": "OPEN (Chris's Axiom-3 signature; A-PENDING-OWNER ceiling)", "final_sentence": "Gap 03 remains OPEN_PHYSICS_BLOCKER: the Realization-B chirally-asymmetric Weyl action that would supply the Z_2 sign(w) lever on arg det(M_u M_d) requires Q_L and u_R/d_R to sit on K_6 bundles of OPPOSITE Weyl determinant-character, but every small-weight |index|=3 bundle whose family multiplet is the standard faithful 3-element Weyl orbit carries the SIGN determinant-character, so the only asymmetry-supplying partner alters the three-family witness representation (EXT-3 ALTERED-ROUTE-REJECTED, fail-closed); and the finite topological-CP sector on the closed K_6 supplies only a 2 pi Z periodicity shift with zero net CP-even pinning unless it reuses the APS chirality fold already spent on (+3,0) -- which would itself alter the zero-mode inventory; J_CKM remains rephasing/basis invariant through 64 SU(3) rotations at tol 1e-9; no observed nEDM/PDG value entered any derivation; this is banked as a THIRD honest negative alongside T-alpha1-A DISPROVED and T-alpha2 CLOSED, with the residual owner-only Axiom-3 act named as the blocking object and the nEDM theta_bar > 1e-10 falsifier armed." }