TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/charged_source_alternatives_20261027/check_modular_sewing.py
Original file SHA-256: 9fec3ac832649d79b13fe5d84f198f15e8b1a8a570aab1be6aa3185f59049d87
Inclusive original lines: 1-66
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000001 | """Exact decision test on the existing D5+A3 discriminant modules.
000002 | 
000003 | This tests chiral cycle-exchange closure, not a physical P1 sewing law.
000004 | """
000005 | import itertools
000006 | import json
000007 | import sympy as s
000008 | 
000009 | 
000010 | def require(condition, message):
000011 |     if not condition:
000012 |         raise RuntimeError(message)
000013 | 
000014 | 
000015 | labels = list(itertools.product(range(4), repeat=2))
000016 | idx = {a: i for i, a in enumerate(labels)}
000017 | S = s.Matrix(16, 16, lambda i, j: s.I ** (-(5*labels[i][0]*labels[j][0]
000018 |                                            + 3*labels[i][1]*labels[j][1]) % 4) / 4)
000019 | T = s.diag(*[s.exp(s.pi*s.I*s.Rational(5*a*a+3*b*b, 4)).expand(complex=True)
000020 |              for a, b in labels])
000021 | C = s.zeros(16)
000022 | for a in labels:
000023 |     C[idx[a], idx[(-a[0] % 4, -a[1] % 4)]] = 1
000024 | require(S.conjugate().T*S == s.eye(16), 'unitary finite Fourier action')
000025 | require(S*S == C, 'S squared is charge conjugation')
000026 | require(s.simplify(T.conjugate().T*T) == s.eye(16), 'unitary twists')
000027 | 
000028 | supports = {
000029 |     'U_D5_A3': [(0, 0)],
000030 |     'D8': [(0, 0), (2, 2)],
000031 |     'E8_plus': [(a, a) for a in range(4)],
000032 |     'E8_minus': [(a, (-a) % 4) for a in range(4)],
000033 | }
000034 | out = {}
000035 | for name, H in supports.items():
000036 |     v = s.Matrix([int(a in H) for a in labels])
000037 |     perp = [a for a in labels if all((5*a[0]*h[0]+3*a[1]*h[1]) % 4 == 0 for h in H)]
000038 |     expected = s.Rational(len(H), 4)*s.Matrix([int(a in perp) for a in labels])
000039 |     require(S*v == expected, 'Fourier support identity '+name)
000040 |     require(T*v == v, 'local bosonic support '+name)
000041 |     fixed = S*v == v
000042 |     require(fixed == (len(H) == 4), 'closure classification '+name)
000043 |     out[name] = {
000044 |         'support': H,
000045 |         'support_size': len(H),
000046 |         'orthogonal_support_size': len(perp),
000047 |         'vacuum_coefficient_after_S': str((S*v)[0]),
000048 |         'single_chiral_vacuum_fixed': fixed,
000049 |         'contains_marked_h_1_1': (1, 1) in H,
000050 |     }
000051 | 
000052 | # A complete scalar paired amplitude can be modular invariant without a
000053 | # one-dimensional chiral block: M=I pairs every module with its conjugate.
000054 | M = s.eye(16)
000055 | require(S.conjugate().T*M*S == M, 'paired S covariance')
000056 | require(s.simplify(T.conjugate().T*M*T) == M, 'paired T covariance')
000057 | require(M.rank() == 16 and M[0, 0] == 1, 'paired amplitude is not chiral rank one')
000058 | 
000059 | print(json.dumps({
000060 |     'verdict': 'CHIRAL_VACUUM_CYCLE_EXCHANGE_SELECTS_TWO_E8_EXTENSIONS',
000061 |     'formula': 'S v_H = (|H|/4) v_H_perp',
000062 |     'extensions': out,
000063 |     'paired_scalar_control': {'rank': 16, 'vacuum_multiplicity': 1,
000064 |                              'S_and_T_invariant': True},
000065 |     'scope': 'existing unitary connected same-conformal extension class; no P1 origin of chiral cycle exchange, no physical countermodel',
000066 | }, indent=2, sort_keys=True))