TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/paper-source-reconstruction-20261025/microscopic_octic_composition.py
Original file SHA-256: 83fc8bb552b6118645b9f38a812dffced5278b6815f916115c7c8b2983ad47ca
Inclusive original lines: 1-166
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 | """Check the actual QWZ modes and their neutral folded Ward dictionary.
000003 | 
000004 | The all-mode statements are symbolic identities.  Floating strip calculations
000005 | are diagnostics of the existing QWZ source, not a proof of a scaling limit.
000006 | No full old suite is declared green: its transitive source pin has drifted.
000007 | """
000008 | 
000009 | from __future__ import annotations
000010 | 
000011 | import ast
000012 | import hashlib
000013 | import importlib.util
000014 | import itertools
000015 | import json
000016 | from pathlib import Path
000017 | import sys
000018 | 
000019 | import numpy as np
000020 | import sympy as sp
000021 | 
000022 | 
000023 | HERE = Path(__file__).resolve().parent
000024 | REPO = HERE.parents[2]
000025 | sys.path.insert(0, str(REPO))
000026 | sys.path.insert(0, str(REPO / "verification"))
000027 | 
000028 | 
000029 | def need(condition, message):
000030 |     if not condition:
000031 |         raise ArithmeticError(message)
000032 | 
000033 | 
000034 | def load(name, relative):
000035 |     spec = importlib.util.spec_from_file_location(name, REPO / relative)
000036 |     module = importlib.util.module_from_spec(spec)
000037 |     sys.modules[name] = module
000038 |     spec.loader.exec_module(module)
000039 |     return module
000040 | 
000041 | 
000042 | def sha(relative):
000043 |     return hashlib.sha256((REPO / relative).read_bytes()).hexdigest()
000044 | 
000045 | 
000046 | def source_nodes(relative, names):
000047 |     tree = ast.parse((REPO / relative).read_text())
000048 |     found = {}
000049 |     for node in tree.body:
000050 |         if isinstance(node, ast.FunctionDef) and node.name in names:
000051 |             found[node.name] = ast.dump(node, include_attributes=False)
000052 |         if isinstance(node, ast.Assign):
000053 |             for target in node.targets:
000054 |                 if isinstance(target, ast.Name) and target.id in names:
000055 |                     found[target.id] = ast.dump(node.value, include_attributes=False)
000056 |     need(set(found) == set(names), "source symbol absent")
000057 |     return found
000058 | 
000059 | 
000060 | def main():
000061 |     actual_path = "verification/v1033_charged_disorder.py"
000062 |     historical_path = "verification/historical_replay/v1033_original.py"
000063 |     names = {"strip_at_momentum", "SX", "SY", "SZ", "TX", "TY"}
000064 |     need(source_nodes(actual_path, names) == source_nodes(historical_path, names),
000065 |          "the actual QWZ strip or its hopping constants changed")
000066 |     source = load("paper_actual_qwz", actual_path)
000067 |     linear = load("paper_existing_linearization",
000068 |                   "experiments/theory-contracts/microscopic-energy-linearization/checker.py")
000069 |     charged = load("paper_existing_car",
000070 |                    "experiments/theory-contracts/microscopic-charged-car-limit/checker.py")
000071 |     native = load("paper_existing_octic",
000072 |                   "experiments/theory-contracts/native-octic-seam-origin-20261025/native_folded_octic_origin.py")
000073 | 
000074 |     # The first original-CAR identification, before a bosonic dictionary:
000075 |     # K = Lcal_-8/8 = sum_r c(r) :a*_(r+8) a_r:.
000076 |     r, n = sp.symbols("r n", integer=True)
000077 |     alpha = sp.Rational(1, 4)
000078 |     coefficient = lambda index: (index + alpha + 4) / 8
000079 |     need(sp.expand(coefficient(r + 8 * n) - coefficient(r)) == n,
000080 |          "CAR commutator does not give the full current-mode derivation")
000081 |     delta = sp.Matrix([(k + alpha) / 8 - sp.Rational(1, 2) for k in range(8)])
000082 |     need(sp.Matrix([coefficient(k - 8) for k in range(8)]) == delta,
000083 |          "actual sea-crossing pairs do not carry the original delta")
000084 |     need(all(-((k + sp.Rational(3, 4)) / 8 - sp.Rational(1, 2))
000085 |              == delta[7 - k] for k in range(8)),
000086 |          "orientation/counterterm convention mismatch")
000087 |     j = sp.symbols("j", integer=True)
000088 |     need(sp.expand((-j + alpha) - (sp.Rational(1, 4) - j)) == 0,
000089 |          "orientation changes the physical one-particle generator")
000090 | 
000091 |     _, orthogonal, positive, fold = native.original_transport()
000092 |     a_map = native.clean(positive.T * orthogonal.T * fold)
000093 |     b = native.clean(a_map * delta)
000094 |     i8_value = sp.expand(sum(z ** 8 for z in b)
000095 |         + 14 * sum(b[u] ** 4 * b[v] ** 4
000096 |                    for u, v in itertools.combinations(range(4), 2))
000097 |         + 168 * sp.prod(z ** 2 for z in b))
000098 |     amplitude = sp.simplify(sp.factorial(8) * sp.conjugate(i8_value)
000099 |                             / (96 * sp.sqrt(140)))
000100 |     expected = sp.sqrt(35) * (16250979 + 56071008 * sp.I) / 128
000101 |     need(sp.simplify(8 ** 8 * amplitude - expected) == 0,
000102 |          "microscopic source normalization changes the Ward amplitude")
000103 | 
000104 |     # Reuse the actual source strip and the existing analytic mode adapter.
000105 |     # The old inherited() pin is not bypassed or reported as passed.  These
000106 |     # two functions are called explicitly with this identified source, whose
000107 |     # relevant AST is checked against the preserved historical source above.
000108 |     rows = []
000109 |     row = charged.row_spinor()
000110 |     for lattice_n in (4096, 8192):
000111 |         maxima = dict(raw_generator_residual=0., projected_generator_residual=0.,
000112 |                       row_to_polarized_mode=0., wrong_sea_occupation=0.)
000113 |         for label in range(-64, 65):
000114 |             data = linear.source_strip(lattice_n, label, source)
000115 |             p, rho = data["p"], data["rho"]
000116 |             k = label - .25
000117 |             scale = lattice_n / (2 * np.pi)
000118 |             raw = np.linalg.norm((scale * data["h"] + k * np.eye(16)) @ row)
000119 |             raw_cap = np.pi * k ** 2 / lattice_n + 2 * np.pi ** 2 * abs(k) ** 3 / (3 * lattice_n ** 2)
000120 |             projected = np.linalg.norm((scale * data["h"] + k * np.eye(16)) @ data["j"])
000121 |             projected_cap = scale * (2 * rho ** 8 + abs(p) ** 3 / 6)
000122 |             distance = np.linalg.norm(data["j"] - row)
000123 |             occupation = np.vdot(row, data["negative"] @ row).real
000124 |             wrong = abs(occupation - int(label >= 1))
000125 |             need(raw <= raw_cap + 1e-10, "actual top-row generator cap failed")
000126 |             need(projected <= projected_cap + 1e-10, "polarized generator cap failed")
000127 |             need(distance <= 4 * rho + 1e-12, "same-sea mode estimate failed")
000128 |             need(wrong <= 9 * rho ** 2 + 1e-12, "actual filled-sea covariance estimate failed")
000129 |             for key, value in zip(maxima, (raw, projected, distance, wrong)):
000130 |                 maxima[key] = max(maxima[key], float(value))
000131 |         rows.append({"N": lattice_n, "labels": [-64, 64], "modes_checked": 129,
000132 |                      "maxima": maxima, "interval_arithmetic": False})
000133 | 
000134 |     report = {
000135 |         "status": "PASS_ACTUAL_QWZ_NEUTRAL_OCTIC_COMPOSITION",
000136 |         "exact": {
000137 |             "source_hopping_and_strip_equal_preserved_original_ast": True,
000138 |             "K_commutator_all_modes": "[K,h_(k,-n)]=n*h_(k,-n-1)",
000139 |             "K_vacuum_coefficients": [str(z) for z in delta],
000140 |             "QWZ_orientation_and_counterterm_identity": True,
000141 |             "charge": 0, "original_source_excitation_energy": 64,
000142 |             "ward_amplitude_folded": str(amplitude),
000143 |             "ward_amplitude_original_Lcal": str(expected),
000144 |         },
000145 |         "actual_source_diagnostics": rows,
000146 |         "source_hashes": {p: sha(p) for p in [actual_path, historical_path,
000147 |             "experiments/theory-contracts/microscopic-energy-linearization/checker.py",
000148 |             "experiments/theory-contracts/microscopic-charged-car-limit/README.md",
000149 |             "experiments/theory-contracts/native-octic-seam-origin-20261025/native_folded_octic_origin.py"]},
000150 |         "scope": {
000151 |             "fixed_original_QWZ_and_fold": True,
000152 |             "new_independent_sources": 0,
000153 |             "simultaneous_lattice_UV_limit_proved": False,
000154 |             "microscopic_full_stress_unitary_limit_proved": False,
000155 |             "P1_source_selection_proved": False,
000156 |             "all_old_source_pin_tests_passed": False,
000157 |             "complete_TFPT_proved": False,
000158 |         },
000159 |     }
000160 |     (HERE / "composition-results.json").write_text(json.dumps(report, indent=2) + "\n")
000161 |     print(report["status"])
000162 |     print("Exact original-CAR Ward identification and 258 actual source modes checked.")
000163 | 
000164 | 
000165 | if __name__ == "__main__":
000166 |     main()