TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/check_mobius_zero_mode_rp.py
Original file SHA-256: 9554a64c350e9b444c52093f328e0688c29ab968e5adbc934f1e562747c62b70
Inclusive original lines: 1-101
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 | #!/usr/bin/env python3
000002 | """Exact zero-transverse-mode reflection-positivity test.
000003 | 
000004 | This is not a model construction.  It restricts the stated flat Moebius
000005 | Dirac Green operator to the invariant transverse zero branch from Theorem
000006 | 8.2 of arXiv:2610.03745v1.
000007 | """
000008 | 
000009 | from __future__ import annotations
000010 | 
000011 | import argparse
000012 | import hashlib
000013 | import json
000014 | from pathlib import Path
000015 | 
000016 | import sympy as sp
000017 | 
000018 | 
000019 | def encode(x: sp.Expr) -> str:
000020 |     return str(sp.simplify(x))
000021 | 
000022 | 
000023 | def main() -> None:
000024 |     parser = argparse.ArgumentParser()
000025 |     parser.add_argument("--output", type=Path, required=True)
000026 |     args = parser.parse_args()
000027 | 
000028 |     rows = []
000029 |     for label, q in (("plus_i", sp.I), ("minus_i", -sp.I)):
000030 |         # Green kernel of partial_x on q-twisted functions.  On (-1,0) and
000031 |         # (0,1) it is constant.  The jump is one and G(s+1)=q G(s).
000032 |         g_minus = sp.simplify(1 / (q - 1))
000033 |         g_plus = sp.simplify(q / (q - 1))
000034 |         occupation = sp.simplify(-g_minus)
000035 | 
000036 |         assert sp.simplify(g_plus - g_minus) == 1
000037 |         assert sp.simplify(g_plus - q * g_minus) == 0
000038 |         assert sp.im(g_minus) != 0
000039 |         assert sp.im(occupation) != 0
000040 | 
000041 |         # The same functional is the normalized one-mode trace with the
000042 |         # temporal insertion z=-q^{-1}.
000043 |         z = sp.simplify(-1 / q)
000044 |         c = sp.Matrix([[0, 1], [0, 0]])
000045 |         cdag = c.T
000046 |         number = cdag * c
000047 |         rho_num = sp.diag(1, z)
000048 |         omega_number = sp.simplify(sp.trace(rho_num * number) /
000049 |                                    sp.trace(rho_num))
000050 |         assert number * number == number
000051 |         assert sp.simplify(omega_number - occupation) == 0
000052 | 
000053 |         # Every unit-modulus phase in the standard charge-exchanging,
000054 |         # order-reversing fermionic reflection cancels on c^* c.  Thus its
000055 |         # reflected square has the same non-real value omega(N^2)=omega(N).
000056 |         reflected_number_norm = omega_number
000057 | 
000058 |         rows.append({
000059 |             "sector": label,
000060 |             "q": encode(q),
000061 |             "green_0_minus": encode(g_minus),
000062 |             "green_0_plus": encode(g_plus),
000063 |             "twisted_trace_insertion_z": encode(z),
000064 |             "occupation": encode(occupation),
000065 |             "occupation_real": bool(sp.im(occupation) == 0),
000066 |             "neutral_number_reflected_norm": encode(reflected_number_norm),
000067 |             "neutral_number_norm_real": bool(sp.im(reflected_number_norm) == 0),
000068 |             "standard_linear_reflection_target_q": encode(1 / q),
000069 |             "fixed_sector_under_standard_linear_reflection": bool(
000070 |                 sp.simplify(1 / q - q) == 0),
000071 |         })
000072 | 
000073 |     ratio = sp.simplify(
000074 |         sp.sympify(rows[0]["green_0_minus"]) /
000075 |         sp.sympify(rows[1]["green_0_minus"])
000076 |     )
000077 |     assert ratio == sp.I
000078 | 
000079 |     result = {
000080 |         "claim": "fixed Pin-minus zero branch fails full CAR OS positivity",
000081 |         "convention": (
000082 |             "Euclidean skew Dirac is slashD=iD; on f0 it is b*partial_x. "
000083 |             "The Clifford b cancels in the reflected scalar kernel."
000084 |         ),
000085 |         "half_interval": "0 < x < 1/2",
000086 |         "sectors": rows,
000087 |         "ratio_of_two_standard_reflected_constants": encode(ratio),
000088 |         "conclusion": (
000089 |             "The standard linear Clifford reflection exchanges q and q^-1. "
000090 |             "A constant field phase may rotate a charged one-particle rank-one "
000091 |             "form, but cancels on the neutral number word; its reflected norm "
000092 |             "is non-real in both quarter sectors."
000093 |         ),
000094 |     }
000095 |     body = json.dumps(result, indent=2, sort_keys=True) + "\n"
000096 |     args.output.write_text(body, encoding="utf-8")
000097 |     print(hashlib.sha256(body.encode("utf-8")).hexdigest())
000098 | 
000099 | 
000100 | if __name__ == "__main__":
000101 |     main()