TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_claude42_general_family_ko.py Original file SHA-256: 73cc3f9892dc46c8c3e0db59c591132331b94dab90f6f0fad062d0f0c7e5e870 Inclusive original lines: 101-211 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000101 | "directed M singular values") 000102 | require(np.allclose(np.linalg.svd(s, compute_uv=False), (r, r, 0)), 000103 | "KO family singular values") 000104 | require(np.allclose(m @ m.conj().T, 000105 | np.diag((abs(a) ** 2, 0, abs(b21) ** 2))), 000106 | "naive up Gram is diagonal") 000107 | require(np.allclose(m.conj().T @ m, 000108 | np.diag((0, abs(b21) ** 2, abs(a) ** 2))), 000109 | "naive down Gram is diagonal") 000110 | 000111 | d_two = family_lift(s) @ x1 @ gamma - family_lift(s).conj().T @ x1.T @ gamma 000112 | singular_d = np.linalg.svd(d_two, compute_uv=False) 000113 | require(np.count_nonzero(singular_d > 1e-10) == 64, "full KO rank 64") 000114 | require(np.allclose(singular_d[:64], r), "full KO repeated singular value") 000115 | require(np.allclose(singular_d[64:], 0), "full KO zero singular values") 000116 | 000117 | # Exact four-sector family blocks. LR means rows L, columns R. 000118 | sd = s.conj().T 000119 | expected = { 000120 | "w1": { 000121 | (0, ("nu", "L"), ("e", "R")): -s, 000122 | (0, ("e", "L"), ("nu", "R")): -sd, 000123 | (0, ("u", "L"), ("d", "R")): s, 000124 | (0, ("d", "L"), ("u", "R")): sd, 000125 | (1, ("nu", "L"), ("e", "R")): -sd, 000126 | (1, ("e", "L"), ("nu", "R")): -s, 000127 | (1, ("u", "L"), ("d", "R")): sd, 000128 | (1, ("d", "L"), ("u", "R")): s, 000129 | }, 000130 | "w2": { 000131 | (0, ("nu", "L"), ("nu", "R")): sd, 000132 | (0, ("e", "L"), ("e", "R")): -s, 000133 | (0, ("u", "L"), ("u", "R")): -sd, 000134 | (0, ("d", "L"), ("d", "R")): s, 000135 | (1, ("nu", "L"), ("nu", "R")): s, 000136 | (1, ("e", "L"), ("e", "R")): -sd, 000137 | (1, ("u", "L"), ("u", "R")): -s, 000138 | (1, ("d", "L"), ("d", "R")): sd, 000139 | }, 000140 | } 000141 | for name, x in (("w1", x1), ("w2", x2)): 000142 | d = family_lift(s) @ x @ gamma - family_lift(s).conj().T @ x.T @ gamma 000143 | for (sector, row, col), value in expected[name].items(): 000144 | require(np.allclose(family_block(d, sector, row, col), value), 000145 | f"{name} {sector} {row} {col} family block") 000146 | 000147 | # The actual weak raising operator maps the w2 creator to w1. A family 000148 | # coefficient is a spectator of this doublet action, hence two arbitrary 000149 | # coefficients on its two components violate the fixed action. 000150 | tplus = w.T @ np.kron(eye3, c[3] @ c[4].T) @ w 000151 | require(np.array_equal(comm(tplus, x2), x1), "weak raising x2 to x1") 000152 | require(np.count_nonzero(comm(tplus, x1)) == 0, "weak highest component") 000153 | m1 = family_lift(np.diag((1, 2, 3))) 000154 | m2 = family_lift(np.diag((1, 4, 3))) 000155 | h1 = m1 @ x1 @ gamma 000156 | h2 = m2 @ x2 @ gamma 000157 | require(np.allclose(comm(tplus, h2) - h1, (m2 - m1) @ x1 @ gamma), 000158 | "component-dependent coefficient covariance residual") 000159 | require(np.linalg.norm(comm(tplus, h2) - h1) > 0, 000160 | "different component coefficients break fixed doublet") 000161 | require(np.allclose(comm(tplus, m1 @ x2 @ gamma), m1 @ x1 @ gamma), 000162 | "common coefficient preserves fixed doublet") 000163 | 000164 | ratio = b21 / a 000165 | output = { 000166 | "scope": "Actual H_F=96 KO6 completion and fixed weak-doublet action; no family-model fit", 000167 | "general_formula": { 000168 | "input": "B=M P_gamma,+", 000169 | "holomorphic": "A=M X_w gamma_F", 000170 | "D_KO": "(M+M^T)X_w gamma_F-(M^dagger+bar(M))X_w^dagger gamma_F", 000171 | "surviving_family_matrix": "S=M+M^T", 000172 | }, 000173 | "quoted_two_entry_candidate": { 000174 | "M": "a E_02+b E_21", 000175 | "a": [a.real, a.imag], 000176 | "b_rounded": [b21.real, b21.imag], 000177 | "b_over_a": [ratio.real, ratio.imag], 000178 | "common_phase_residual_from_rounded_b": abs(ratio.imag), 000179 | "directed_M_singular_values": [abs(b21), abs(a), 0.0], 000180 | "KO_S_singular_values": [r, r, 0.0], 000181 | "full_H96_D_KO_singular_values": {"value": r, "multiplicity": 64, "zero_multiplicity": 32}, 000182 | "naive_M_Mdagger_mix": "both Gram matrices are diagonal; at most a permutation, J_CP=0", 000183 | "KO_mix": "the two nonzero singular values are degenerate, so no unique CKM matrix is defined", 000184 | }, 000185 | "four_sector_pattern": { 000186 | "common_family_matrix": "S=M+M^T", 000187 | "particle_antiparticle_relation": "fixed J_F conjugation", 000188 | "quark_lepton_relation": "fixed relative minus signs", 000189 | "majorana_block": False, 000190 | }, 000191 | "weak_doublet_test": { 000192 | "raising_action": "[T_plus,X_w2]=X_w1, [T_plus,X_w1]=0", 000193 | "same_family_coefficient": "covariant", 000194 | "different_family_coefficients_on_bare_components": "nonzero covariance residual", 000195 | "scope_note": "Separate sector intertwiners or source readers may carry distinct matrices; this test only excludes relabeling the two bare components of one fixed doublet.", 000196 | }, 000197 | "source_scope": "The original primitive wedge consumer is present. This checker does not equate the Hardy moment with the whole original Hol(nabla_F*) K_f^str coefficient.", 000198 | } 000199 | OUT.write_text(json.dumps(output, indent=2, sort_keys=True) + "\n", encoding="utf-8") 000200 | print(json.dumps({ 000201 | "checks": "PASS", 000202 | "general_KO_uses_symmetric_part": True, 000203 | "KO_family_singular_values": [round(r, 12), round(r, 12), 0.0], 000204 | "full_KO_rank": 64, 000205 | "unique_CKM_from_candidate": False, 000206 | "different_bare_doublet_component_matrices_covariant": False, 000207 | }, sort_keys=True)) 000208 | 000209 | 000210 | if __name__ == "__main__": 000211 | main()