TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_actual_weak_source_moment.py
Original file SHA-256: 7731669986a50e583c71de6066d97e8bbd4c5affc0603ca160cb02c02ddb7cd7
Inclusive original lines: 1-85
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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000001 | """Exact source moment from the actual v252 weak lift and finite Dirac.
000002 | 
000003 | Diagnostic coefficients test orientation sensitivity, not mass selection.
000004 | No original source, verification suite or physical parameters are changed.
000005 | """
000006 | import json
000007 | import sys
000008 | from pathlib import Path
000009 | 
000010 | import numpy as np
000011 | import sympy as s
000012 | 
000013 | HERE = Path(__file__).resolve().parent
000014 | sys.path.insert(0, str(HERE.parents[3] / "verification"))
000015 | import v252_full_finite_triple as v
000016 | 
000017 | 
000018 | def exact(a):
000019 |     return s.MutableSparseMatrix(a.shape[0], a.shape[1], {
000020 |         (i, j): s.Rational(str(a[i, j].real)) + s.I*s.Rational(str(a[i, j].imag))
000021 |         for i, j in zip(*np.nonzero(a))
000022 |     })
000023 | 
000024 | 
000025 | def main():
000026 |     z = np.zeros((3, 3), complex)
000027 |     sx = np.array([[0, 1], [1, 0]], complex)
000028 |     # Real gauge lift acts on the antihermitian generator before multiplying
000029 |     # by -i. Antilinearity therefore gives MINUS on the antiparticle Q block.
000030 |     T = v.rep(0, 1j*sx, z)
000031 |     K = v.Kswap()
000032 |     Q = exact(-1j*(T + K@T.conj()@K))
000033 |     gamma = exact(v.grading())
000034 |     yu = np.diag([1, 2, 3]).astype(complex)
000035 |     yd = np.diag([4, 5, 6]).astype(complex)
000036 |     perm = np.eye(3)[[2, 1, 0]]
000037 |     # Same, nonzero lepton/Majorana data in both controls; these do not
000038 |     # interact with quark flavour in this original weak representation.
000039 |     ye, yn = np.diag([2, 3, 4]), np.diag([1, 3, 5])
000040 |     mr = np.array([[2, 1, 0], [1, 3, 1], [0, 1, 4]])
000041 |     outputs = []
000042 |     checks = {"Q_selfadjoint": Q == Q.H,
000043 |               "Q_even": Q*gamma == gamma*Q}
000044 |     for label, down in (("aligned", yd), ("left_rotated_down", perm@yd)):
000045 |         D = exact(v.full_D(yu, down, ye, yn, mr))
000046 |         checks[label+"_D_odd"] = gamma*D + D*gamma == s.zeros(96)
000047 |         H0 = gamma - 4*s.I*gamma*D
000048 |         H1 = 4*Q*gamma
000049 |         checks[label+"_h_selfadjoint"] = H0 == H0.H and H1 == H1.H
000050 |         # H0+tH1 = 4h at the existing quarter mode p=1/4.
000051 |         poly = [s.eye(96)]
000052 |         moments = {}
000053 |         for n in range(1, 7):
000054 |             new = [s.zeros(96) for _ in range(len(poly)+1)]
000055 |             for k, coefficient in enumerate(poly):
000056 |                 new[k] += coefficient*H0
000057 |                 new[k+1] += coefficient*H1
000058 |             poly = new
000059 |             if n in (2, 4, 6):
000060 |                 moments[n] = [s.expand(s.trace(c)/4**n) for c in poly]
000061 |         outputs.append(moments)
000062 |     differences = {n: [s.expand(a-b) for a, b in zip(outputs[0][n], outputs[1][n])]
000063 |                    for n in (2, 4, 6)}
000064 |     checks["second_and_fourth_moments_agree"] = all(x == 0 for n in (2, 4) for x in differences[n])
000065 |     checks["sixth_moment_difference_exact"] = differences[6] == [0, 0, 5760, 0, 0, 0, 0]
000066 |     checks["same_down_singular_data"] = exact(yd).H*exact(yd) == exact(perm@yd).H*exact(perm@yd)
000067 |     result = {
000068 |         "verdict": "ACTUAL_GAUGE_COUPLED_SOURCE_RETAINS_RELATIVE_FAMILY_ORIENTATION",
000069 |         "operator": "h(t)=(I/4+tQ)gamma-i gamma D_F, Q=-i(T+J_F T J_F^-1), T=rep(0,i sigma_x,0)",
000070 |         "moments_t_coefficients": [{str(n): [str(c) for c in rows] for n, rows in out.items()} for out in outputs],
000071 |         "difference_t_coefficients": {str(n): [str(c) for c in rows] for n, rows in differences.items()},
000072 |         "cross_face_trace_difference_leading_ell6": "-244*t**2",
000073 |         "cross_face_logdet_difference_leading_ell6": "-128*t**2",
000074 |         "checks": {k: bool(vv) for k, vv in checks.items()},
000075 |         "all_checks_pass": all(checks.values()),
000076 |         "scope": "Finite p=1/4 block of the existing source. Arbitrary formal weak field t; fixed diagnostic Yukawas and nonzero fixed MR. No selected gauge background, Yukawa variation, sum over circle modes, or complete Gamma_ren coefficient is asserted."
000077 |     }
000078 |     raw = json.dumps(result, indent=2, sort_keys=True)+"\n"
000079 |     (HERE/"actual-weak-source-moment-results.json").write_text(raw)
000080 |     print(raw, end="")
000081 |     return 0 if result["all_checks_pass"] else 1
000082 | 
000083 | 
000084 | if __name__ == "__main__":
000085 |     raise SystemExit(main())