TFPT scientific source excerpt Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/check_native_spin5_functor.py Original file SHA-256: 86911d6e7634592fe9e61d232535224e9b8148308433a05a8ccf983e5a110fa2 Inclusive original lines: 201-300 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 | symmetric_lie_action(lie_element, symmetric_basis, symmetric_pairs) 000202 | ) 000203 | target_lie_actions.append(exterior_lie_action(w_lie, 5, pairs5)) 000204 | spin5_map = sp.Matrix.hstack(*spin5_columns) 000205 | source_metric = sp.diag(*[1 if a == b else 2 for a, b in symmetric_pairs]) 000206 | require(spin5_map.det() == 8, "canonical Spin5 map determinant eight", checks) 000207 | require(spin5_map.conjugate().T * spin5_map == source_metric, 000208 | "canonical Spin5 map is exactly metric preserving", checks) 000209 | require(all(is_zero(spin5_map * source - target * spin5_map) 000210 | for source, target in zip(source_lie_actions, target_lie_actions)), 000211 | "canonical map intertwines the full sp4 Lie algebra", checks) 000212 | 000213 | # This is the decisive uniqueness test: F20 alone gave dimension six on 000214 | # the ten, while full sp4 naturality leaves a single complex line. 000215 | variables10 = sp.symbols("u0:100") 000216 | unknown10 = sp.Matrix(10, 10, variables10) 000217 | equations10 = [] 000218 | for source_action, target_action in zip(source_lie_actions, target_lie_actions): 000219 | equations10 += list(unknown10 * source_action - target_action * unknown10) 000220 | coefficient10, _ = sp.linear_eq_to_matrix(equations10, variables10) 000221 | require(100 - coefficient10.rank() == 1, 000222 | "full sp4 natural intertwiner space has dimension one", checks) 000223 | 000224 | # Check the finite native F20 equivariance of the same canonical map. 000225 | source_c10 = symmetric_action(c_native, symmetric_pairs) 000226 | source_g10 = -ii * symmetric_action(g_native, symmetric_pairs) 000227 | target_c10 = exterior_action(w_c, pairs5) 000228 | target_g10 = exterior_action(w_g, pairs5) 000229 | require(is_zero(spin5_map * source_c10 - target_c10 * spin5_map) and 000230 | is_zero(spin5_map * source_g10 - target_g10 * spin5_map), 000231 | "canonical Spin5 map respects the native F20 actions", checks) 000232 | 000233 | # Hodge complement Kraus maps on an oriented orthonormal real basis of W. 000234 | # Individual matrices depend on the basis; their five-dimensional span and 000235 | # the normalized channel do not. 000236 | kraus = [] 000237 | for m in range(5): 000238 | operator = sp.zeros(10) 000239 | for column, (a, b) in enumerate(pairs5): 000240 | if m in (a, b): 000241 | continue 000242 | complement = [j for j in range(5) if j not in (m, a, b)] 000243 | sequence = [m, a, b] + complement 000244 | inversions = sum(sequence[i] > sequence[j] 000245 | for i in range(5) for j in range(i + 1, 5)) 000246 | operator[pairs5.index(tuple(complement)), column] = (-1) ** inversions 000247 | kraus.append(operator) 000248 | completeness = sum((operator.conjugate().T * operator for operator in kraus), 000249 | sp.zeros(10)) 000250 | hilbert_schmidt_gram = sp.Matrix([ 000251 | [sp.trace(left.conjugate().T * right) for right in kraus] 000252 | for left in kraus 000253 | ]) 000254 | kraus_vectors = sp.Matrix.hstack(*[ 000255 | sp.Matrix(100, 1, list(operator)) for operator in kraus 000256 | ]) 000257 | require(completeness == 3 * sp.eye(10), 000258 | "Hodge Kraus completeness sum is three I", checks) 000259 | require(hilbert_schmidt_gram == 6 * sp.eye(5) and kraus_vectors.rank() == 5, 000260 | "Hodge Kraus space has canonical dimension five", checks) 000261 | 000262 | output = { 000263 | "verdict": "CANONICAL_NATIVE_SPIN5_FUNCTOR_AND_KRAUS_SPACE", 000264 | "W5": "primitive Lambda2(V) tensor chi^(-1)", 000265 | "W5_q": encode(q5), 000266 | "W5_real_structure": "j(w)=q conjugate(w)", 000267 | "W5_F20": "sign tensor Perm5", 000268 | "W5_character": character_rows, 000269 | "F20_slot_intertwiner_dimension": 2, 000270 | "spin5_map": encode(spin5_map), 000271 | "spin5_map_determinant": str(spin5_map.det()), 000272 | "spin5_metric_identity": "F^dagger F=diag(1,2,2,2,1,2,2,1,2,1)", 000273 | "full_sp4_intertwiner_dimension": 1, 000274 | "metric_residual": "U(1) phase; real compact form leaves a sign", 000275 | "kraus_space_dimension": 5, 000276 | "kraus_hilbert_schmidt_gram": "6 I5", 000277 | "kraus_completeness": "sum C_m^dagger C_m=3 I10", 000278 | "normalized_channel": "Phi(rho)=(1/3) sum C_m rho C_m^dagger", 000279 | "checks": checks, 000280 | "scope": ( 000281 | "Full Sp4 functoriality selects a unique natural ten-intertwiner " 000282 | "line and a basis-independent Hodge Kraus space on the native " 000283 | "compact real form. F20 alone still leaves a two-dimensional " 000284 | "slot-chart Hom because sign tensor Perm5 decomposes as 1 plus 4. " 000285 | "This constructs a canonical mathematical channel; it does not " 000286 | "prove that the original physical source uses that channel." 000287 | ), 000288 | } 000289 | out = Path(__file__).with_name("native-spin5-functor-results.json") 000290 | out.write_text(json.dumps(output, indent=2, sort_keys=True) + "\n") 000291 | print(json.dumps({ 000292 | "verdict": output["verdict"], 000293 | "checks": len(checks), 000294 | "sp4_hom_dimension": output["full_sp4_intertwiner_dimension"], 000295 | "kraus_dimension": output["kraus_space_dimension"], 000296 | }, sort_keys=True)) 000297 | 000298 | 000299 | if __name__ == "__main__": 000300 | main()