TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/canonical-seam-fermionization-20261025/check_mobius_quarter_operator_dictionary.py
Original file SHA-256: 6c2a4e3c57aa2a5bab830b651340f9590b954bd068fdd6ac92cc89038e702912
Inclusive original lines: 1-119
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.

000001 | #!/usr/bin/env python3
000002 | """Exact reduced-longitudinal checks for the Moebius NS-cover quarters.
000003 | 
000004 | The full one-step Pin-minus monodromy is cJ with J including transverse
000005 | reflection. This checker begins after projection to the two J eigenspaces;
000006 | it does not replace the full pinor bundle action by a scalar translation.
000007 | """
000008 | 
000009 | from fractions import Fraction
000010 | 
000011 | 
000012 | def need(condition: bool, label: str) -> None:
000013 |     if not condition:
000014 |         raise AssertionError(label)
000015 |     print(f"PASS {label}")
000016 | 
000017 | 
000018 | def cover_label(epsilon: int, m: int) -> int:
000019 |     return 2 * m + epsilon
000020 | 
000021 | 
000022 | def cover_eigenvalue(n: int) -> Fraction:
000023 |     return Fraction(n, 1) + Fraction(1, 2)
000024 | 
000025 | 
000026 | def quarter_eigenvalue(epsilon: int, m: int) -> Fraction:
000027 |     a = Fraction(1, 4) if epsilon == 0 else Fraction(3, 4)
000028 |     return Fraction(m, 1) + a
000029 | 
000030 | 
000031 | def u_action(epsilon: int, m: int) -> tuple[int, int]:
000032 |     # [[0,u_base],[I,0]] in the ordered (1/4,3/4) coefficient basis.
000033 |     return (1, m) if epsilon == 0 else (0, m + 1)
000034 | 
000035 | 
000036 | def crossing_count(values: list[Fraction], shift: Fraction) -> int:
000037 |     return sum(1 for value in values if value < 0 < value + shift)
000038 | 
000039 | 
000040 | def run() -> None:
000041 |     labels = [(epsilon, m) for epsilon in (0, 1) for m in range(-8, 9)]
000042 | 
000043 |     need(
000044 |         all(
000045 |             cover_eigenvalue(cover_label(epsilon, m))
000046 |             == 2 * quarter_eigenvalue(epsilon, m)
000047 |             for epsilon, m in labels
000048 |         ),
000049 |         "B_cov = 2(B_1/4 direct-sum B_3/4)",
000050 |     )
000051 | 
000052 |     need(
000053 |         all(
000054 |             ((1 if cover_label(epsilon, m) % 2 == 0 else -1)
000055 |              == (1 if epsilon == 0 else -1))
000056 |             for epsilon, m in labels
000057 |         ),
000058 |         "half-deck eigenphases are +i on 1/4 and -i on 3/4",
000059 |     )
000060 | 
000061 |     need(
000062 |         all(
000063 |             cover_label(*u_action(epsilon, m))
000064 |             == cover_label(epsilon, m) + 1
000065 |             for epsilon, m in labels
000066 |         ),
000067 |         "u_cov has block action [[0,u_base],[I,0]]",
000068 |     )
000069 | 
000070 |     need(
000071 |         all(
000072 |             u_action(*u_action(epsilon, m)) == (epsilon, m + 1)
000073 |             for epsilon, m in labels
000074 |         ),
000075 |         "u_cov squared is diag(u_base,u_base)",
000076 |     )
000077 | 
000078 |     # Each W_epsilon maps an orthonormal Fourier basis to a disjoint parity
000079 |     # subset of the NS-cover Fourier basis.  A coefficient norm is therefore
000080 |     # preserved exactly, and the two images are orthogonal.
000081 |     coeffs = {
000082 |         (0, -2): Fraction(3, 5),
000083 |         (0, 1): Fraction(-7, 11),
000084 |         (1, -1): Fraction(5, 13),
000085 |         (1, 3): Fraction(2, 7),
000086 |     }
000087 |     source_norm = sum(value * value for value in coeffs.values())
000088 |     cover_coeffs = {
000089 |         cover_label(epsilon, m): value
000090 |         for (epsilon, m), value in coeffs.items()
000091 |     }
000092 |     target_norm = sum(value * value for value in cover_coeffs.values())
000093 |     need(
000094 |         len(cover_coeffs) == len(coeffs) and source_norm == target_norm,
000095 |         "quarter-to-cover map is isometric and sector images are orthogonal",
000096 |     )
000097 | 
000098 |     cover_values = [cover_eigenvalue(n) for n in range(-8, 9)]
000099 |     need(
000100 |         crossing_count(cover_values, Fraction(1, 1)) == 1,
000101 |         "u_cov winding one has full-cover spectral flow one",
000102 |     )
000103 |     need(
000104 |         crossing_count(cover_values, Fraction(2, 1)) == 2,
000105 |         "u_cov squared has full-cover spectral flow two",
000106 |     )
000107 | 
000108 |     for epsilon, name in ((0, "1/4"), (1, "3/4")):
000109 |         quarter_values = [quarter_eigenvalue(epsilon, m) for m in range(-8, 9)]
000110 |         need(
000111 |             crossing_count(quarter_values, Fraction(1, 1)) == 1,
000112 |             f"u_base has spectral flow one on the {name} domain",
000113 |         )
000114 | 
000115 |     print("RESULT exact Moebius quarter operator dictionary verified")
000116 | 
000117 | 
000118 | if __name__ == "__main__":
000119 |     run()