TFPT scientific source excerpt
Original repository path: verification/v1023_derivative_filtered_wall.py
Original file SHA-256: a6850b0acc2c2cd47579b290d02aeb8b48ba32836f4141570c6daaad8f35f69a
Inclusive original lines: 1-61
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000001 | #!/usr/bin/env python3
000002 | """v1023 -- derivative-filtered physical--mirror wall certificate.
000003 | 
000004 | Exact/numerical certificate for the derivative-filtered wall coupling.
000005 | 
000006 | The certificate addresses the conflict found by the full-rank onsite wall
000007 | term: a nonzero onsite pairing lifts every physical GW zero mode.  Replacing
000008 | the physical annihilator p by D_GW p makes the mixing vanish precisely on
000009 | ker(D_GW), while keeping a uniformly separated mirror-continuation band.
000010 | The canonical bare mirror operator is not itself an invariant sector: for
000011 | every nonzero singular value it has low-band weight tending to zero only as
000012 | O(s^2).  Thus the result does not establish a gap in the bare-mirror response
000013 | and the infrared branch is quadratic (z=2), not a Weyl cone.
000014 | 
000015 | This is a finite one-particle/quasi-free theorem.  It is deliberately not
000016 | advertised as a proof of an interacting Standard-Model continuum limit.
000017 | 
000018 | Contracts: CHIRAL4D.NOMIRROR.01 [O], CHIRAL4D.MIRROR.DET16.01 [C],
000019 | and TFPT.TOE.COMPLETE.01 [O].  No marker moves.  The exact algebra is
000020 | SymPy; the finite covariance/spectrum witnesses are deterministic float64.
000021 | Python-only / Wolfram mirror deferred.  NO RH CLAIM.
000022 | """
000023 | 
000024 | from __future__ import annotations
000025 | 
000026 | import json
000027 | import math
000028 | import os
000029 | 
000030 | os.environ.setdefault("OMP_NUM_THREADS", "1")
000031 | os.environ.setdefault("MKL_NUM_THREADS", "1")
000032 | os.environ.setdefault("OPENBLAS_NUM_THREADS", "1")
000033 | os.environ.setdefault("NUMEXPR_NUM_THREADS", "1")
000034 | 
000035 | import numpy as np
000036 | import sympy as sp
000037 | 
000038 | from tfpt_constants import check as suite_check, reset, summary
000039 | 
000040 | 
000041 | TOL = 2.0e-10
000042 | 
000043 | 
000044 | def check(name: str, condition: bool, detail: str = "") -> None:
000045 |     label = name if not detail else f"{name} -- {detail}"
000046 |     suite_check(label, bool(condition))
000047 | 
000048 | 
000049 | def dagger(a: np.ndarray) -> np.ndarray:
000050 |     return a.conj().T
000051 | 
000052 | 
000053 | def wall_block(d: np.ndarray, delta: float, lam: float, g: float) -> np.ndarray:
000054 |     """Block on physical right-singular and mirror left-singular spaces."""
000055 |     n = d.shape[0]
000056 |     return np.block(
000057 |         [
000058 |             [lam * g * g * dagger(d) @ d, lam * g * dagger(d)],
000059 |             [lam * g * d, (delta + lam) * np.eye(n)],
000060 |         ]
000061 |     )