TFPT scientific source excerpt Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_sewing_20261028/clock/check_native_six_ovoid_clock_bundle.py Original file SHA-256: 003259b0ecb7d3b47007a0b36b3b5e16c826d9efae2927acfa1c2206548af4b3 Inclusive original lines: 201-314 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. 000201 | } 000202 | require(s5_order_census == { 000203 | "1": 1, "2": 25, "3": 20, "4": 30, "5": 24, "6": 20 000204 | }, "order census of the 120-element group") 000205 | require(pJ == tuple(range(6)), "J acts projectively trivially on fibers") 000206 | require(len({p[0] for p in group_s5}) == 6, 000207 | "C,G,sigma group is transitive on six fibers") 000208 | 000209 | # Prove the named identification, rather than infer it from the census: 000210 | # find an explicit relabeling under which the computed permutation group 000211 | # is exactly PGL(2,5) on P^1(F5). The classical faithful degree-six 000212 | # action gives PGL(2,5) ~= S5. 000213 | pgl2 = pgl2_five_group() 000214 | pgl2_relabel = next((r for r in itertools.permutations(range(6)) 000215 | if {conjugate_permutation(p, r) for p in group_s5} 000216 | == pgl2), None) 000217 | require(pgl2_relabel is not None, 000218 | "computed 120-group is conjugate to PGL(2,5) in S6") 000219 | 000220 | # Each form canonically determines the five Hodge/Clifford currents. 000221 | # They are the six point-ovoids of the Pauli doily, not the raw spread 000222 | # labels of v783; those are related by v783's point-line duality. 000223 | ovoids = {} 000224 | nontrivial = [name for name in sorted(pauli) if name != "II"] 000225 | for omega_name in forms: 000226 | omega = pauli[omega_name] 000227 | currents = [ 000228 | name for name in nontrivial 000229 | if is_zero(pauli[name].T * omega - omega * pauli[name]) 000230 | ] 000231 | require(len(currents) == 5, "each alternating form selects five currents") 000232 | require(all(is_zero(pauli[a] * pauli[b] + pauli[b] * pauli[a]) 000233 | for i, a in enumerate(currents) for b in currents[i+1:]), 000234 | "each selected five-current set pairwise anticommutes") 000235 | ovoids[omega_name] = currents 000236 | require(ovoids["IY"] == ["XI", "YX", "YY", "YZ", "ZI"], 000237 | "IY fiber is the identified Hodge K5") 000238 | require(len({tuple(v) for v in ovoids.values()}) == 6, 000239 | "six current ovoids are distinct") 000240 | require(all(sum(name in v for v in ovoids.values()) == 2 000241 | for name in nontrivial), 000242 | "every nontrivial Pauli lies in two ovoids") 000243 | require(all(len(set(ovoids[a]) & set(ovoids[b])) == 1 000244 | for i, a in enumerate(forms) for b in forms[i+1:]), 000245 | "each pair of ovoids intersects in one Pauli") 000246 | 000247 | # Direct covariance of both the form and its five-current fiber. 000248 | for op_name, op in (("C", C), ("G", G), ("sigma", sigma), 000249 | ("alpha", alpha), ("J", J)): 000250 | image_map = actions[op_name]["images"] 000251 | for omega_name in forms: 000252 | target = image_map[omega_name] 000253 | transported = set() 000254 | for current in ovoids[omega_name]: 000255 | image = (op * pauli[current] * op.conjugate().T).applyfunc(canonical) 000256 | hit = next(name for name in nontrivial 000257 | if any(is_zero(image - phase * pauli[name]) 000258 | for phase in phase_set)) 000259 | transported.add(hit) 000260 | require(transported == set(ovoids[target]), 000261 | "full five-current fibers transport covariantly") 000262 | 000263 | result = { 000264 | "verdict": "NATIVE_SIX_FIBER_CLOCK_BUNDLE_EXACT", 000265 | "fiber_labels": forms, 000266 | "fiber_ovoids": ovoids, 000267 | "actions": actions, 000268 | "permutation_group_orders": { 000269 | "F20_C_G": len(group_f20), 000270 | "F20_plus_sigma": len(group_s5), 000271 | "F20_plus_sigma_plus_alpha": len(group_s6), 000272 | }, 000273 | "S5_element_order_census": s5_order_census, 000274 | "S5_identification_certificate": { 000275 | "model": "PGL(2,5) on P^1(F5), classically isomorphic to S5", 000276 | "fiber_to_projective_line_relabeling": list(pgl2_relabel), 000277 | "exact_group_equality_after_relabeling": True, 000278 | }, 000279 | "trace_typing": { 000280 | "native_sigma_complex_C4": 1, 000281 | "native_sigma_realification_R8": 2, 000282 | }, 000283 | "transitive_with_sigma": True, 000284 | "named_group_identifications": { 000285 | "F20_C_G": "F20 stabilizer of the marked IY fiber", 000286 | "F20_plus_sigma": "transitive S5 action on six fibers", 000287 | "F20_plus_sigma_plus_alpha": "S6 action on six fibers", 000288 | "J": "projectively trivial on fibers", 000289 | }, 000290 | "matrix_relations": { 000291 | "C5": "I", 000292 | "G4": "I", 000293 | "G_C_Ginv": "C^2", 000294 | "sigma3": "I", 000295 | "alpha2": "iI", 000296 | "alpha_sigma_alpha_inv": "sigma^-1", 000297 | }, 000298 | "source_scope": [ 000299 | "C and G are the selected native F20 word pair already exactly intertwined with v419", 000300 | "sigma is the frozen v783 native family clock", 000301 | "alpha is the reviewed scalar-square theta lift", 000302 | "the bundle removes the false requirement of one sigma-fixed symplectic form", 000303 | "selection of this conjugate native F20 as the physical v419 subgroup remains a source marking premise", 000304 | "no P1/P2 state, time, or source instrument follows from the finite bundle alone", 000305 | ], 000306 | } 000307 | payload = json.dumps(result, indent=2, sort_keys=True) + "\n" 000308 | RESULT.write_text(payload) 000309 | print(payload, end="") 000310 | print("RESULT_SHA256", hashlib.sha256(payload.encode()).hexdigest()) 000311 | 000312 | 000313 | if __name__ == "__main__": 000314 | main()