""" strongcp_realizationB.py ======================== Gap 03 / Strong-CP -- theta-bar smallness, Realization-B route (the chirally-asymmetric Weyl action) and the finite topological-CP sector, on K_6 = SU(3)/T^2, executed under the GAP_CLOSURE_LOOP_DESIGN sub-loop 6.5 and CFCA (METHOD_CFCA_June_14.md). WHAT THIS SCRIPT DOES (data-blind; no observed value on the input side): (1) Reproduces the banked Realization-A obstruction structurally: theta_QCD * Tr(G ^ G~) is a class function on su(3), hence W-EVEN; arg det(M_u M_d) is W-EVEN because det(P M P^T) = det(M). So the Z_2 sign(w) lever does NOT exist when Q_L, u_R, d_R share one K_6 representation (Realization A, STRUCTURALLY DISPROVED 2026-06-10). (2) Constructs Realization-B structurally: the only way to obtain the Z_2 sign(w) lever on the Yukawa-overlap determinant is the ROW-ONLY Weyl action M -> P_w M, giving det(P_w M) = sign(w) det(M). This is realizable ONLY if Q_L and u_R/d_R carry zero-mode Weyl representations whose DETERMINANT-CHARACTERS differ by the sign character of S_3 -- i.e. Q_L and u_R/d_R must sit on DIFFERENT internal K_6 bundles whose zero-mode W-reps are inequivalent of opposite det-character. (This is exactly the field-content change the banked obstruction named, and the Axiom-3 act reserved to Chris.) (3) THE EXT-3 ZERO-MODE GATE (the load-bearing check). The family count is the spin-c Borel-Weil-Bott (BWB) index of the bundle on K_6 = SU(3)/T^2; the frozen value is |index| = 3 (APS chirality (n_L, n_R) = (+3, 0)). This script computes the BWB index as an explicit function of the bundle weight (p, q) via the Weyl character formula, and -- crucially -- the DETERMINANT-CHARACTER of the zero-mode Weyl representation each candidate bundle carries. It then asks whether ANY chiral split (different weights for Q_L vs u_R/d_R) can simultaneously (a) supply the opposite-det-character asymmetry that the Z_2 lever needs, and (b) keep BOTH bundles' |index| = 3 with the same (+3, 0) one-sided APS chirality content. (4) Runs the theta-bar transform consequence and the J_CKM = 3.0e-5 basis-invariance audit (64 random SU(3) rotations, seed 0) through the same pipeline the banked Realization-A run used, for whichever Realization-B candidate the EXT-3 gate admits. (5) Emits outputs/gap03_realizationB_certificate.json + the zero_mode_invariance_proof block, and exits with the honest terminal code. EXIT CODES (per GAP_CLOSURE_LOOP_DESIGN 6.5 SPEC): 0 -> state A (DERIVATION-CANDIDATE-PENDING-OWNER): theta-bar < 1e-10, J_CKM preserved at tol 1e-9, zero-mode byte-invariant, no target-loading, no upstream mutation. NOT "closed" -- pending Chris's Axiom-3 signature. 1 -> state B (BANKED NEGATIVE): the chiral asymmetry that the Z_2 lever requires necessarily alters the zero-mode content (or the finite topological CP sector yields zero net theta-pinning). A third honest negative alongside T-alpha1-A DISPROVED and T-alpha2 CLOSED. 2 -> state C/D: cannot construct without an unauthorized Axiom-3 mutation; Precisely-OPEN with named blocking object + falsifier. DISCIPLINE (non-negotiable, METHOD_CFCA_June_14.md / loop GUARD 1-4): - NO observed value (theta-bar nEDM bound, PDG, Lambda, eta_B, A_s, r, n_s) EVER enters on the input side. nEDM appears ONLY in a labeled post-freeze comparison block (never used to derive). - SoT hash 88e5903..., source hash caf7ff... must be unchanged. - No promotional word (proves/closed/exact/derived/unconditional) without its licensing computation in the same passage. Frozen pins (verbatim): see frozen_inputs.yaml of gap_03. Author authority: GAP_CLOSURE_LOOP_DESIGN.md 6.5 + METHOD_CFCA_June_14.md. """ from __future__ import annotations import json import math from itertools import permutations from pathlib import Path import numpy as np # ---------------------------------------------------------------------- # Paths / frozen pins (read-only; never mutated) # ---------------------------------------------------------------------- HERE = Path(__file__).resolve().parent OUT_DIR = HERE / "outputs" OUT_DIR.mkdir(parents=True, exist_ok=True) SOT_HASH = "88e5903fe1c3d17655acef7e4fb45078e3168add25362040e21598b3b161ff17" SOURCE_HASH = "caf7ffc24d46e8b5e586b1cdcaceaa0318533644f880036c15a6bad9627211ec" HARD_GATE = "D,D-local,D,D,D" # Frozen geometry (from gap_03/frozen_inputs.yaml; the spin-c bundle weight # (p,q) = (1,0) and the frozen-row family witness BWB |index| = 3, APS (+3,0)). FROZEN_SPIN_C_WEIGHT = (1, 0) # geometry.spin_c_structure.bundle_weight FROZEN_BWB_ABS_INDEX = 3 # |index| = 3 (three families) FROZEN_APS_NL_NR = (3, 0) # one-sided APS index (n_L, n_R) NEDM_FORBIDDEN_INPUT_FLAG = True # theta-bar nEDM bound NEVER an input # The nEDM bound is recorded ONLY for the post-freeze comparison block. # It is NOT used anywhere in any derivation. (loop GUARD 2.) NEDM_THETABAR_FALSIFIER = 1e-10 # post-freeze comparison threshold only # ====================================================================== # PART 1 -- su(3) / SU(3)/T^2 Borel-Weil-Bott machinery (numpy-only) # ====================================================================== # Fundamental weights in the orthogonal e_i basis (sum-zero su(3) weights): W1 = np.array([2.0 / 3, -1.0 / 3, -1.0 / 3]) # omega_1 W2 = np.array([1.0 / 3, 1.0 / 3, -2.0 / 3]) # omega_2 RHO = W1 + W2 # rho = (1, 0, -1) in e-basis POS_ROOTS = [np.array([1.0, -1, 0]), np.array([0.0, 1, -1]), np.array([1.0, 0, -1])] # Weyl group S_3 acting by permuting the 3 e-coordinates; length l(w). _LEN = {(0, 1, 2): 0, (1, 0, 2): 1, (0, 2, 1): 1, (2, 1, 0): 1, (2, 0, 1): 2, (1, 2, 0): 2} def to_e(p, q): """Convert a (p, q) fundamental-weight label to e-basis coordinates.""" return p * W1 + q * W2 def _weyl_dim(mu_e): """Weyl dimension formula for the dominant su(3) weight mu_e.""" mr = mu_e + RHO num = den = 1.0 for a in POS_ROOTS: num *= float(np.dot(mr, a)) den *= float(np.dot(RHO, a)) return num / den def bwb_index(p, q): """ Spin-c Borel-Weil-Bott index (Euler characteristic) of the line bundle L_{(p,q)} on K_6 = SU(3)/T^2. BWB: shift lambda by rho; if lambda+rho lies on a Weyl wall (singular) the index is 0; else a unique Weyl element w makes it strictly dominant, cohomology sits in degree l(w), and chi = (-1)^{l(w)} dim V_mu. Returns the signed integer index. """ lr = to_e(p, q) + RHO for perm in permutations(range(3)): v = np.array([lr[perm[i]] for i in range(3)]) if v[0] > v[1] + 1e-9 and v[1] > v[2] + 1e-9: # strictly dominant return int(round(((-1) ** _LEN[perm]) * _weyl_dim(v - RHO))) return 0 # singular def zero_mode_weight_multiplet(p, q): """ Return the explicit set of weights of the zero-mode multiplet of L_{(p,q)} (the dominant irrep V_mu whose dimension = |index|), as e-basis vectors, together with whether they form a single faithful S_3 orbit of 3 DISTINCT weights. """ lr = to_e(p, q) + RHO for perm in permutations(range(3)): v = np.array([lr[perm[i]] for i in range(3)]) if v[0] > v[1] + 1e-9 and v[1] > v[2] + 1e-9: mu = v - RHO # For |index|=3 the relevant multiplet is the 3-dim irrep; its # extreme weight orbit under S_3 is the family multiplet that the # Weyl action permutes. Build the S_3 orbit of mu. orbit = [] for q2 in permutations(range(3)): w = tuple(round(mu[q2[i]], 6) for i in range(3)) if w not in orbit: orbit.append(w) faithful_3 = (len(orbit) == 3) return orbit, faithful_3, mu return [], False, None def zero_mode_det_character(p, q): """ The DETERMINANT-CHARACTER of the Weyl representation carried by the zero-mode family multiplet of L_{(p,q)}. For a multiplet that is a single faithful 3-element Weyl orbit, S_3 acts by the 3-dim PERMUTATION representation; its determinant as a map S_3 -> {+1, -1} is exactly the SIGN character (det of the permutation matrix). For a non-faithful orbit (a repeated/degenerate weight) the det-character degenerates -- which is a DIFFERENT zero-mode content. Returns: ('sign', faithful) or ('degenerate', faithful). """ _, faithful_3, _ = zero_mode_weight_multiplet(p, q) if faithful_3: return "sign", True return "degenerate", False # ====================================================================== # PART 2 -- Realization-A reproduction (the banked obstruction) # ====================================================================== def realization_A_obstruction(): """ Reproduce, structurally, why Realization A is W-even (banked DISPROOF). Uses representative quark mass matrices with the frozen arg-det phase structure (NOT observed values -- generic complex matrices with the frozen determinant-phase relation). The point is the TRANSFORMATION law, which is matrix-independent: det(P M P^T) = det(M) for any permutation P. """ rng = np.random.default_rng(0) # Generic (non-observational) complex 3x3 matrices; only the transform # law is load-bearing, not the numbers. M_u = rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)) M_d = rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)) arg0 = float(np.angle(np.linalg.det(M_u) * np.linalg.det(M_d))) results_A, results_B = [], [] for perm in [(0, 1, 2), (1, 0, 2), (0, 2, 1), (2, 1, 0), (2, 0, 1), (1, 2, 0)]: P = np.zeros((3, 3)) for i in range(3): P[perm[i], i] = 1.0 sgn = int(round(np.linalg.det(P))) # Realization A: joint row+col -> det invariant aA = float(np.angle(np.linalg.det(P @ M_u @ P.T) * np.linalg.det(P @ M_d @ P.T))) results_A.append(abs(((aA - arg0 + math.pi) % (2 * math.pi)) - math.pi) < 1e-9) # Realization B: row-only -> det picks up sign(w) (the Z_2 lever) aB = float(np.angle(np.linalg.det(P @ M_u) * np.linalg.det(P @ M_d))) expected = 0.0 if sgn == 1 else math.pi results_B.append( abs(((aB - arg0 - expected + math.pi) % (2 * math.pi)) - math.pi) < 1e-9 ) return { "realization_A_all_argdet_invariant": bool(all(results_A)), "realization_B_rowonly_matches_sign_lever": bool(all(results_B)), "lever_law": "det(P M P^T)=det(M) (A, W-even); det(P M)=sign(w) det(M) (B, Z_2 lever)", } # ====================================================================== # PART 3 -- The EXT-3 zero-mode gate: can the asymmetry coexist with # byte-invariant family content? # ====================================================================== def ext3_zero_mode_gate(): """ The decisive structural test. Realization B needs Q_L and u_R/d_R on bundles whose zero-mode Weyl representations have OPPOSITE determinant-character, so that the row-only (chirally-asymmetric) Weyl action gives the Z_2 sign(w) lever on the overlap determinant WITHOUT it cancelling between left and right factors. But (PART 1) every |index|=3 bundle whose zero-mode multiplet is a faithful 3-element Weyl orbit carries the SAME det-character = the SIGN character of S_3. So Q_L's and u_R/d_R's det-characters are EQUAL -> they cancel in the overlap -> W-EVEN. No lever. (This is the banked Realization-A result, re-derived bundle-theoretically.) The ONLY escape is to put at least one of Q_L / u_R / d_R on a bundle whose zero-mode multiplet is NOT a faithful 3-orbit (a degenerate / non-orbit multiplet of opposite det-character). We enumerate the small weights, find every |index|=3 bundle, classify its det-character and APS-compatible chirality, and check whether any admissible opposite- det-character partner EXISTS that keeps |index|=3 and (+3,0) chirality. """ # Enumerate small-weight bundles with |index| = 3 idx3_bundles = [] for p in range(-6, 7): for q in range(-6, 7): if abs(bwb_index(p, q)) == FROZEN_BWB_ABS_INDEX: detchar, faithful = zero_mode_det_character(p, q) idx3_bundles.append({ "weight": (p, q), "index": bwb_index(p, q), "det_character": detchar, "faithful_3_orbit": faithful, }) # Frozen bundle det-character (the (1,0) bundle the corpus uses) frozen_detchar, frozen_faithful = zero_mode_det_character(*FROZEN_SPIN_C_WEIGHT) # Is there ANY |index|=3 bundle with det-character OPPOSITE to the # frozen one (i.e. NOT 'sign'), that still has |index|=3 -- the only way # to supply the asymmetry WITHOUT cancellation? opposite_detchar_idx3 = [ b for b in idx3_bundles if b["det_character"] != frozen_detchar ] # An opposite-det-character |index|=3 bundle that is NOT a faithful # 3-orbit necessarily reorganizes the zero-mode rep content -- the # three families no longer transform as the standard permutation # multiplet. That is an ALTERATION of the SM zero-mode content under # any honest reading of "byte-invariant family witness" (the families # transform under a different Weyl representation -> the spin-structure # witness rep changes), even though the integer |index| can coincide. asymmetry_requires_content_change = (len(opposite_detchar_idx3) == 0) or all( (not b["faithful_3_orbit"]) for b in opposite_detchar_idx3 ) return { "n_idx3_bundles_small_window": len(idx3_bundles), "frozen_bundle_weight": list(FROZEN_SPIN_C_WEIGHT), "frozen_det_character": frozen_detchar, "frozen_faithful_3_orbit": frozen_faithful, "all_faithful_idx3_share_sign_character": all( b["det_character"] == "sign" for b in idx3_bundles if b["faithful_3_orbit"] ), "n_opposite_det_character_idx3": len(opposite_detchar_idx3), "asymmetry_requires_zero_mode_content_change": bool( asymmetry_requires_content_change ), "idx3_bundle_table": idx3_bundles, } def zero_mode_invariance_proof(gate): """ Build the EXT-3 zero-mode-invariance proof block (the W2 deliverable). APS index: the chirality / mirror content is the orbifold APS index (n_L, n_R) = (+3, 0). A chiral split that gives Q_L and u_R/d_R DIFFERENT internal K_6 bundles either (i) keeps both on faithful 3-orbit |index|=3 bundles -> NO opposite det-character -> NO Z_2 lever (Realization A again, theta-bar NOT pinned), or (ii) uses an opposite det-character bundle -> that bundle's zero-mode multiplet is NOT the standard faithful permutation 3-orbit -> the family Weyl-rep content (the spin-structure three-family witness rep) is ALTERED. Either branch fails the closure: (i) does not pin theta-bar; (ii) alters the zero-mode content -> EXT-3 REJECTS outright. """ aps_pre = list(FROZEN_APS_NL_NR) bwb_pre = FROZEN_BWB_ABS_INDEX if gate["asymmetry_requires_zero_mode_content_change"]: # Branch (ii): the only asymmetry-supplying bundles change the rep # content. The integer |index| may still read 3, but the Weyl # representation the three families carry is not byte-invariant. verdict = "ALTERED-ROUTE-REJECTED" aps_post = aps_pre # the integer can coincide ... bwb_post = bwb_pre # ... but the rep content does not. 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)." ) else: verdict = "INVARIANT" aps_post = aps_pre bwb_post = bwb_pre byte_invariant = True note = ( "An opposite-det-character |index|=3 bundle with a faithful 3-orbit " "family multiplet exists; the chiral split preserves the family " "Weyl-rep content byte-for-byte." ) return { "verdict": verdict, "APS_pre": aps_pre, "APS_post": aps_post, "BWB_pre": bwb_pre, "BWB_post": bwb_post, "byte_invariant": byte_invariant, "note": note, } # ====================================================================== # PART 4 -- finite topological-CP sector (route 3) data-blind check # ====================================================================== def finite_topological_cp_sector(): """ Route 3: a finite topological CP sector pinning theta_QCD into a CP-even sector WITHOUT the Weyl-class-function obstruction. Structural check: theta_QCD couples to Tr(G ^ G~), whose integral over a CLOSED internal factor is 2 pi * (an integer Pontryagin number). A finite topological sector can shift theta_QCD by 2 pi Z (a periodicity identification) but cannot PIN a CP-even value unless there is a boundary/orbifold CP-odd projection. On K_6 = SU(3)/T^2 (a CLOSED homogeneous space, no boundary) the spin-c holonomy phase Phi_K6 = -0.12827 rad is a fixed continuous topological datum -- NOT a member of the discrete CP-even set {0, pi}. A finite topological CP sector that pinned theta_QCD to {0, pi} would have to set Phi_K6's CP-odd contribution to a discrete value; the closed-manifold Pontryagin integral provides only a 2 pi Z shift, which yields ZERO net theta- pinning toward {0, pi}. The CP-odd projection requires the SAME boundary/orbifold data as the APS chirality fold -- and that fold is already spent fixing chirality (+3, 0); reusing it to also project theta_QCD CP-even would alter the (n_L, n_R) inventory. """ phi_k6 = -0.12827 discrete_cp_even = [0.0, math.pi] # net pinning available from a closed-manifold topological sector: pin_to_cp_even = min( abs(((phi_k6 - t + math.pi) % (2 * math.pi)) - math.pi) for t in discrete_cp_even ) return { "phi_K6_rad": phi_k6, "closed_manifold_no_boundary": True, "pontryagin_shift_is_2piZ_only": True, "net_theta_pinning_to_cp_even": float(pin_to_cp_even), "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." ), } # ====================================================================== # PART 5 -- J_CKM basis-invariance audit (preserved through the route) # ====================================================================== def j_ckm_audit(): """ Confirm J_CKM is rephasing/basis invariant through 64 random SU(3) rotations (seed 0), matching the banked Realization-A audit at tol 1e-9. Uses generic (non-observational) representative matrices: only the invariance of the rephasing-invariant Jarlskog is being checked, never an observed J value. """ rng = np.random.default_rng(0) M_u = rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)) M_d = rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)) def jarlskog(Mu, Md): Hu = Mu @ Mu.conj().T Hd = Md @ Md.conj().T _, Uu = np.linalg.eigh(Hu) _, Ud = np.linalg.eigh(Hd) V = Uu.conj().T @ Ud return float(np.imag(V[0, 1] * V[1, 2] * np.conj(V[0, 2]) * np.conj(V[1, 1]))) j0 = jarlskog(M_u, M_d) max_delta = 0.0 for _ in range(64): UL = np.linalg.qr(rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)))[0] UuR = np.linalg.qr(rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)))[0] UdR = np.linalg.qr(rng.normal(size=(3, 3)) + 1j * rng.normal(size=(3, 3)))[0] jw = jarlskog(UL @ M_u @ UuR.conj().T, UL @ M_d @ UdR.conj().T) max_delta = max(max_delta, abs(jw - j0)) return { "rephasing_invariant_J_preserved": bool(max_delta < 1e-9), "max_abs_delta_J_64_rot": float(max_delta), "tol": 1e-9, "note": "J is rephasing-invariant; no observed J value used (data-blind).", } # ====================================================================== # MAIN # ====================================================================== def main() -> int: obstruction = realization_A_obstruction() gate = ext3_zero_mode_gate() zmi = zero_mode_invariance_proof(gate) topo = finite_topological_cp_sector() jck = j_ckm_audit() # ---- Decide the honest terminal ----------------------------------- # State A requires: theta-bar < 1e-10 derived WITHOUT tuning AND # zero-mode byte-invariant. The EXT-3 gate determines admissibility. route2_admissible = (zmi["verdict"] == "INVARIANT") route3_pins = (topo["net_theta_pinning_to_cp_even"] < 1e-10) and ( not topo["yields_zero_net_pinning_without_reusing_APS_fold"] ) if route2_admissible: # Would need the actual theta-bar value; only reachable if a # zero-mode-invariant asymmetry bundle existed. It does not in the # small window (see gate). Kept as the documented A-branch logic. terminal_state = "DERIVATION-CANDIDATE-PENDING-OWNER" exit_code = 0 final_verdict = "state-A (PENDING owner Axiom-3 signature)" elif route3_pins: terminal_state = "DERIVATION-CANDIDATE-PENDING-OWNER" exit_code = 0 final_verdict = "state-A via topological-CP (PENDING owner)" else: # Both routes fail the EXT-3 / pinning test data-blind: # - Route 2 (Realization B): the asymmetry-supplying bundle alters # the zero-mode Weyl-rep content -> EXT-3 ALTERED-ROUTE-REJECTED. # - Route 3 (topological CP): zero net theta-pinning on the closed # K_6 without reusing the APS chirality fold. # This is a THIRD honest negative, banked alongside T-alpha1-A # DISPROVED and T-alpha2 CLOSED. The gate itself stays # OPEN_PHYSICS_BLOCKER (the route is disproved; Chris may still # author an Axiom-3 field content that is outside this script's # data-blind reach). terminal_state = "BANKED-NEGATIVE (route disproved; gate stays OPEN_PHYSICS_BLOCKER)" exit_code = 1 final_verdict = "state-B (third banked negative)" certificate = { "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": SOT_HASH, "source_hash_TOE_FINAL_REVIEW": SOURCE_HASH, "hard_gate_vector": HARD_GATE, "realization_A_obstruction_reproduced": obstruction, "ext3_zero_mode_gate": gate, "zero_mode_invariance_proof": zmi, "finite_topological_cp_sector": topo, "j_ckm_audit": jck, # theta-bar is NOT claimed small: the route that would pin it fails # the zero-mode gate data-blind. No theta-bar number is asserted as # "derived small" (loop GUARD 1). "theta_bar_smallness_derived": False, "theta_bar_value_claimed": None, "terminal_state": terminal_state, "final_verdict": final_verdict, "exit_code": exit_code, "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 comparison block (nEDM appears ONLY here, never upstream) "post_freeze_nedm_comparison": { "falsifier": "nEDM theta_bar > 1e-10 makes the underived status refutation-grade", "threshold": NEDM_THETABAR_FALSIFIER, "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." ), } out_path = OUT_DIR / "gap03_realizationB_certificate.json" out_path.write_text(json.dumps(certificate, indent=2), encoding="utf-8") # also write the dedicated zero-mode proof (W2 deliverable schema) (OUT_DIR / "zero_mode_invariance_proof.json").write_text( json.dumps(zmi, indent=2), encoding="utf-8" ) print("strongcp_realizationB.py") print(f" Realization-A W-even reproduced: " f"{obstruction['realization_A_all_argdet_invariant']}") print(f" |index|=3 bundles in window: {gate['n_idx3_bundles_small_window']}") print(f" all faithful idx3 share sign-character: " f"{gate['all_faithful_idx3_share_sign_character']}") print(f" asymmetry requires content change: " f"{gate['asymmetry_requires_zero_mode_content_change']}") print(f" EXT-3 zero-mode verdict: {zmi['verdict']}") print(f" topological-CP net pinning: " f"{topo['net_theta_pinning_to_cp_even']:.5f} rad (>1e-10 => no pin)") print(f" J_CKM 64-rot invariant: " f"{jck['rephasing_invariant_J_preserved']} (max dJ={jck['max_abs_delta_J_64_rot']:.2e})") print(f" TERMINAL: {terminal_state}") print(f" WROTE {out_path}") return exit_code if __name__ == "__main__": raise SystemExit(main())