TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/admissible_pair_20261028/admissible_pair_source.py
Original file SHA-256: 108640d5938126a1b610b16c0844a64e14b290a10b612af85eaf7c5af8f854be
Inclusive original lines: 201-369
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000201 |     phi_left, phi_right = partial_gains(Cs)
000202 |     require(np.array_equal(phi_left, 3 * np.eye(10)), "Phi unital gain 3I")
000203 |     require(np.array_equal(phi_right, 3 * np.eye(10)), "Phi trace preserving gain 3I")
000204 | 
000205 |     rays = old.source_rays()
000206 |     bell, raw_six, _ = old.reflection_actions(rays)
000207 |     six, _ = old.outer_mark_action(raw_six)
000208 |     mapping = old.find_bell_partition_intertwiner(bell, six)
000209 |     mark_results = []
000210 |     for mark in range(6):
000211 |         groups, kraus = old_kraus_for_mark(old, hodge, mark, bell, six, mapping)
000212 |         left, right = partial_gains(kraus)
000213 |         require(np.array_equal(left, 12 * np.eye(10)), f"mark {mark}: Psi unital gain 12I")
000214 |         require(np.array_equal(right, 12 * np.eye(10)), f"mark {mark}: Psi trace preserving gain 12I")
000215 | 
000216 |         event_overlaps = []
000217 |         for K in kraus:
000218 |             amplitudes = V.conj().T @ K.reshape(-1, order="F")
000219 |             event_overlaps.append(int(np.vdot(amplitudes, amplitudes).real))
000220 |         require(sorted(event_overlaps) == [4] * 18 + [36] * 2,
000221 |                 f"mark {mark}: exact twenty event P5 overlap distribution")
000222 |         overlap_sum = sum(event_overlaps)
000223 |         p_psi = Fraction(overlap_sum, 6 * 12 * 10)
000224 |         require(overlap_sum == 144, f"mark {mark}: total P5 numerator 144")
000225 |         require(p_psi == Fraction(1, 5), f"mark {mark}: normalized old Choi witness is one fifth")
000226 | 
000227 |         group_sums = [sum(int(np.vdot(V.conj().T @ K.reshape(-1, order="F"),
000228 |                                          V.conj().T @ K.reshape(-1, order="F")).real)
000229 |                           for K in groups[m]) for m in range(5)]
000230 |         require(sorted(group_sums) == [16, 16, 16, 48, 48],
000231 |                 f"mark {mark}: complement resolved overlap sums")
000232 | 
000233 |         unscaled_choi = sum((np.outer(K.reshape(-1, order="F"),
000234 |                                               K.reshape(-1, order="F").conj()) for K in kraus),
000235 |                             start=np.zeros((100, 100), dtype=np.complex128))
000236 |         unscaled_choi = exact_complex_integer(unscaled_choi)
000237 |         sector_weights = []
000238 |         projected_ranks = []
000239 |         kraus_vectors = np.stack([K.reshape(-1, order="F") for K in kraus], axis=1)
000240 |         for dimension, Q in sector_data:
000241 |             numerator = np.trace(Q @ unscaled_choi)
000242 |             require(numerator.imag == 0, f"mark {mark}: P{dimension} weight is real")
000243 |             sector_weights.append(Fraction(int(numerator.real), 6 * 12 * 10))
000244 |             projected_ranks.append(int(sp.Matrix(Q @ kraus_vectors).rank()))
000245 |         require(sector_weights == [Fraction(1, 5), Fraction(2, 5), Fraction(2, 5)],
000246 |                 f"mark {mark}: actual SU5 twirl weights one fifth two fifths two fifths")
000247 |         symmetric_rank = int(sp.Matrix((identity100 + swap) @ kraus_vectors).rank())
000248 |         antisymmetric_rank = int(sp.Matrix((identity100 - swap) @ kraus_vectors).rank())
000249 |         require([symmetric_rank, antisymmetric_rank] == [9, 6],
000250 |                 f"mark {mark}: old Choi support has nine symmetric and six antisymmetric directions")
000251 | 
000252 |         # The SU5 twirl is sum_d p_d (10/d)P_d.  Its population
000253 |         # entries depend only on whether two duads are equal, intersecting,
000254 |         # or disjoint.  Evaluate every one of the hundred entries.
000255 |         population_values = {"stay": set(), "intersect": set(), "disjoint": set()}
000256 |         for a, e in enumerate(hodge.PAIRS):
000257 |             for b, f in enumerate(hodge.PAIRS):
000258 |                 kind = "stay" if a == b else "disjoint" if set(e).isdisjoint(f) else "intersect"
000259 |                 coordinate = b + 10 * a
000260 |                 value = sum((weight * Fraction(10, dimension) * Fraction(int(Q[coordinate, coordinate]), 6)
000261 |                              for weight, (dimension, Q) in zip(sector_weights, sector_data)),
000262 |                             start=Fraction(0))
000263 |                 population_values[kind].add(value)
000264 |         require(population_values == {
000265 |                     "stay": {Fraction(2, 25)},
000266 |                     "intersect": {Fraction(19, 225)},
000267 |                     "disjoint": {Fraction(31, 225)},
000268 |                 }, f"mark {mark}: exact SU5 twirl population leakage")
000269 |         require(Fraction(2, 25) + 6 * Fraction(19, 225) + 3 * Fraction(31, 225) == 1,
000270 |                 f"mark {mark}: twirled population column normalization")
000271 |         full_commuting = 0
000272 |         for _name, X in full_generators:
000273 |             L = two_leg_generator(X, hodge.PAIRS, hodge.PAIR_INDEX)
000274 |             full_commuting += int(np.array_equal(L @ unscaled_choi, unscaled_choi @ L))
000275 |         sm_commuting = 0
000276 |         for _name, X in sm:
000277 |             L = two_leg_generator(X, hodge.PAIRS, hodge.PAIR_INDEX)
000278 |             sm_commuting += int(np.array_equal(L @ unscaled_choi, unscaled_choi @ L))
000279 |         require(full_commuting < 24, f"mark {mark}: old Choi matrix is not fully SU5 invariant")
000280 |         require(sm_commuting < 12, f"mark {mark}: old Choi matrix is not invariant under fixed SM subgroup")
000281 | 
000282 |         mark_results.append({
000283 |             "mark": mark,
000284 |             "p_Psi": "1/5",
000285 |             "su5_twirl_weights": {"P5": "1/5", "P45": "2/5", "P50": "2/5"},
000286 |             "projected_kraus_span_ranks": {"P5": projected_ranks[0], "P45": projected_ranks[1], "P50": projected_ranks[2]},
000287 |             "symmetric_antisymmetric_choi_support_ranks": [symmetric_rank, antisymmetric_rank],
000288 |             "su5_twirl_population_per_target": {kind: str(next(iter(values)))
000289 |                                                   for kind, values in population_values.items()},
000290 |             "su5_twirl_population_total": {
000291 |                 "stay": "2/25",
000292 |                 "intersect": "38/75",
000293 |                 "disjoint": "31/75",
000294 |             },
000295 |             "event_overlap_squared_distribution": {"4": 18, "36": 2},
000296 |             "total_overlap_numerator": overlap_sum,
000297 |             "complement_group_overlap_sums": group_sums,
000298 |             "normalized_choi_marginals": "I_10/10 on both legs",
000299 |             "old_choi_su5_generators_commuting": f"{full_commuting}/24",
000300 |             "old_choi_fixed_sm_generators_commuting": f"{sm_commuting}/12",
000301 |         })
000302 | 
000303 |     require(all(item["p_Psi"] == "1/5" for item in mark_results), "all six marks give p_Psi one fifth")
000304 |     result = {
000305 |         "verdict": [
000306 |             "P5_IS_A_RANK_FIVE_FULL_SU5_INVARIANT_TWO_LEG_PROJECTOR",
000307 |             "NORMALIZED_HODGE_CHOI_HAS_P5_PROBABILITY_ONE",
000308 |             "ACTUAL_OLD_TWENTY_EVENT_CHOI_HAS_P5_PROBABILITY_ONE_FIFTH_FOR_ALL_SIX_MARKS",
000309 |             "ACTUAL_OLD_CHOI_SU5_TWIRL_WEIGHTS_ARE_ONE_FIFTH_TWO_FIFTHS_TWO_FIFTHS",
000310 |             "SU5_TWIRL_INTRODUCES_EXACT_STAY_AND_INTERSECTION_POPULATION_LEAKAGE",
000311 |             "TWO_LEG_SU5_AND_FIXED_SM_NEUTRAL_OBSERVABLES_CAN_DISTINGUISH_PHASE_ERASURE",
000312 |             "ALL_SINGLE_LEG_OBSERVABLES_HAVE_EQUAL_MAXIMALLY_MIXED_CHOI_MARGINALS",
000313 |             "OLD_BELL10_TO_DUAD_CHART_IS_NOT_A_PHYSICAL_SU5_MODULE_IDENTIFICATION",
000314 |             "NO_PREPARATION_OR_EVENT_SELECTION_RULE_IS_DERIVED",
000315 |         ],
000316 |         "source_sha256": PINS,
000317 |         "witness": {
000318 |             "definition": "P5=(1/6) sum_m |C_m>><<C_m|",
000319 |             "space_in_fixed_chart": "Lambda^2 C^5 tensor Lambda^2 C^5, equivalently the stated dual bar10 tensor bar10 convention",
000320 |             "rank": 5,
000321 |             "projector": True,
000322 |             "su5_invariant": True,
000323 |             "su5_generators_checked": 24,
000324 |             "fixed_sm_invariant": True,
000325 |             "fixed_sm_generators_checked": 12,
000326 |         },
000327 |         "normalized_choi_witness": {
000328 |             "p_Phi": "1",
000329 |             "p_Psi_all_six_marks": "1/5",
000330 |             "derivation_Phi": "J_Phi=(1/3)VV^dagger=2P5 and rho_Phi=J_Phi/10",
000331 |             "derivation_Psi": "sum_l ||V^dagger vec(K_l)||^2=144, divided by 6*12*10",
000332 |         },
000333 |         "actual_old_su5_twirl": {
000334 |             "weights": {"P5": "1/5", "P45": "2/5", "P50": "2/5"},
000335 |             "choi_support_ranks_under_swap": {"symmetric": 9, "antisymmetric": 6},
000336 |             "projected_span_ranks": {"P5": 5, "P45": 6, "P50": 7},
000337 |             "population_per_target": {"stay": "2/25", "intersect": "19/225", "disjoint": "31/225"},
000338 |             "population_total_per_input": {"stay": "2/25", "intersect": "38/75", "disjoint": "31/75"},
000339 |             "interpretation": "twirling the noncovariant old channel preserves the P5 weight but creates non-Petersen stay and intersecting transitions",
000340 |         },
000341 |         "commutant_scope": {
000342 |             "two_leg_full_su5_commutant_restrictions_equal": False,
000343 |             "two_leg_fixed_sm_commutant_restrictions_equal": False,
000344 |             "reason": "P5 belongs to both commutants and its two normalized Choi expectations are 1 and 1/5",
000345 |             "single_leg_restrictions_equal": True,
000346 |             "single_leg_reason": "both normalized Choi marginals are I_10/10 because both channels are trace preserving and unital",
000347 |             "old_choi_itself_su5_invariant": False,
000348 |             "old_choi_itself_fixed_sm_invariant": False,
000349 |         },
000350 |         "marks": mark_results,
000351 |         "scope": {
000352 |             "operator_claim": "exact in the fixed duad chart used by the old source comparison",
000353 |             "physical_module_claim": False,
000354 |             "caveat": "the old Bell10 is Sym^2 C^4; the event label duad chart alone is not a linear SU5 intertwiner",
000355 |             "preparation_claim": False,
000356 |         },
000357 |         "checks": len(checks),
000358 |     }
000359 |     if output is not None:
000360 |         output.parent.mkdir(parents=True, exist_ok=True)
000361 |         output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n")
000362 |     return result
000363 | 
000364 | 
000365 | if __name__ == "__main__":
000366 |     parser = argparse.ArgumentParser()
000367 |     parser.add_argument("--out", type=Path)
000368 |     args = parser.parse_args()
000369 |     print(json.dumps(main(args.out), indent=2, sort_keys=True))