TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/source_recursion_20261028/check_old_hodge_to_a4.py
Original file SHA-256: d1278592ee955a229266efdc339c26981d8cb61c11e3404bbd52f394eea9be80
Inclusive original lines: 1-92
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | #!/usr/bin/env python3
000002 | """Exact comparison of the old five-slot Hodge table with the A4 carrier maps.
000003 | 
000004 | This is a finite convention check, not a source or dynamics model.
000005 | """
000006 | 
000007 | from itertools import combinations
000008 | import json
000009 | from pathlib import Path
000010 | 
000011 | 
000012 | def perm_sign(word):
000013 |     if len(set(word)) != len(word):
000014 |         return 0
000015 |     inversions = sum(
000016 |         word[i] > word[j]
000017 |         for i in range(len(word))
000018 |         for j in range(i + 1, len(word))
000019 |     )
000020 |     return -1 if inversions % 2 else 1
000021 | 
000022 | 
000023 | def require(condition, message):
000024 |     if not condition:
000025 |         raise RuntimeError(message)
000026 | 
000027 | 
000028 | slots = tuple(range(5))
000029 | pairs = tuple(combinations(slots, 2))
000030 | pair_index = {pair: index for index, pair in enumerate(pairs)}
000031 | 
000032 | comparisons = []
000033 | matrices = []
000034 | for omitted in slots:
000035 |     rest = tuple(i for i in slots if i != omitted)
000036 |     volume_character = perm_sign((omitted,) + rest)
000037 |     matrix = [[0 for _ in pairs] for _ in pairs]
000038 |     unordered_factorizations = set()
000039 |     for input_pair in combinations(rest, 2):
000040 |         output_pair = tuple(i for i in rest if i not in input_pair)
000041 |         old_wedge_sign = perm_sign(input_pair + output_pair)
000042 |         new_epsilon_sign = perm_sign((omitted,) + input_pair + output_pair)
000043 |         require(
000044 |             new_epsilon_sign == volume_character * old_wedge_sign,
000045 |             "old Hodge sign and new epsilon sign disagree",
000046 |         )
000047 |         matrix[pair_index[output_pair]][pair_index[input_pair]] = new_epsilon_sign
000048 |         unordered_factorizations.add(tuple(sorted((input_pair, output_pair))))
000049 |         comparisons.append(
000050 |             {
000051 |                 "omitted": omitted,
000052 |                 "input_pair": input_pair,
000053 |                 "output_pair": output_pair,
000054 |                 "old_wedge_sign": old_wedge_sign,
000055 |                 "volume_character": volume_character,
000056 |                 "new_epsilon_sign": new_epsilon_sign,
000057 |             }
000058 |         )
000059 |     require(len(unordered_factorizations) == 3, "wrong doily factorization count")
000060 |     matrices.append(matrix)
000061 | 
000062 | require(len(comparisons) == 30, "expected 30 directed Hodge entries")
000063 | require(
000064 |     sum(1 for row in matrices for entries in row for x in entries if x) == 30,
000065 |     "expected 30 nonzero matrix entries",
000066 | )
000067 | 
000068 | # Exact gain: each carrier pair excludes three of the five slots.
000069 | gain = [[0 for _ in pairs] for _ in pairs]
000070 | for matrix in matrices:
000071 |     for i in range(len(pairs)):
000072 |         for j in range(len(pairs)):
000073 |             gain[i][j] += sum(matrix[k][i] * matrix[k][j] for k in range(len(pairs)))
000074 | require(gain == [[3 if i == j else 0 for j in range(10)] for i in range(10)],
000075 |         "sum C_m^T C_m is not 3 I_10")
000076 | 
000077 | result = {
000078 |     "status": "PASS",
000079 |     "scope": "finite sign and support comparison only",
000080 |     "old_doily_unordered_lines": 15,
000081 |     "directed_matrix_entries": 30,
000082 |     "volume_character_by_omitted_slot": [
000083 |         perm_sign((m,) + tuple(i for i in slots if i != m)) for m in slots
000084 |     ],
000085 |     "identity": "epsilon(m,i,j,k,l)=chi(m)*sign((i,j,k,l))",
000086 |     "gain": "sum_m C_m^T C_m = 3 I_10",
000087 |     "comparisons": comparisons,
000088 | }
000089 | 
000090 | out = Path(__file__).with_name("old-hodge-to-a4-results.json")
000091 | out.write_text(json.dumps(result, indent=2) + "\n", encoding="utf-8")
000092 | print(json.dumps({k: v for k, v in result.items() if k != "comparisons"}, sort_keys=True))