TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_color_spin_source_interface.py
Original file SHA-256: 4796b8e1da63eed03269f5ed9e3396a5f3c71e7dee1c98f5b4c1f0c1feac7ee0
Inclusive original lines: 1-95
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 | """R070: exact original color action on the retained folded CAR charge frame.
000002 | 
000003 | This checks a necessary interface condition, not physical fermionization,
000004 | source selection, local spacetime, or an alternative fitted frame.
000005 | """
000006 | import itertools
000007 | import json
000008 | from pathlib import Path
000009 | 
000010 | import sympy as s
000011 | 
000012 | HERE = Path(__file__).resolve().parent
000013 | ROOT = HERE.parents[3]
000014 | FOLD = ROOT / "experiments/theory-contracts/v16-operator-pullback-20261014/fold-results.json"
000015 | 
000016 | 
000017 | def main():
000018 |     m = s.Matrix(json.loads(FOLD.read_text())["explicit_Weyl_matrix"])
000019 |     eye = s.eye(8)
000020 |     axes = [eye[:, i] for i in range(8)]
000021 |     a, b = axes[0] - axes[1], axes[1] - axes[2]
000022 |     w = axes[0] + axes[1] - 2 * axes[2]
000023 |     colors = [a, -a, b, -b, a + b, -a - b]
000024 |     wf = m.T * w
000025 |     tests = []
000026 | 
000027 |     def need(label, condition):
000028 |         if not bool(condition):
000029 |             raise AssertionError(label)
000030 |         tests.append(label)
000031 | 
000032 |     need("original M is orthogonal", m.T * m == eye)
000033 |     need("original color charge in source frame", list(wf) == [1, -1, 0, -1, -1, -1, 0, -1])
000034 |     need("integer color charge on every NS integer charge", all(x.q == 1 for x in wf))
000035 |     need("integer color charge on half-spinor E8 coset", sum(wf) / 2 == -2)
000036 |     mapped = [m.T * q for q in colors]
000037 |     integer = [all(x.q == 1 for x in q) for q in mapped]
000038 |     need("exactly two of six original color roots belong to CAR D8", sum(integer) == 2)
000039 |     need("retained color A1 is the actual first simple root", integer == [True, True, False, False, False, False])
000040 |     need("first root exact preimage", list(mapped[0]) == [0, 0, 1, 0, 0, 0, -1, 0])
000041 | 
000042 |     for k, q in enumerate(mapped):
000043 |         need(f"color root {k} has norm two", q.dot(q) == 2)
000044 |         if integer[k]:
000045 |             need(f"color root {k} has even integer charge", sum(q) % 2 == 0)
000046 |         else:
000047 |             need(f"color root {k} is the retained E8 half coset", all(x.q == 2 for x in q))
000048 |             for j in range(8):
000049 |                 need(f"color root {k} has nontrivial full monodromy with CAR generator {j}", (q[j] % 1) == s.Rational(1, 2))
000050 | 
000051 |     # On integer charges N=Z8 the original color character has order exactly3.
000052 |     # On D8 it is also onto; e0+e2 has even sum and color charge1.
000053 |     d8_witness = axes[0] + axes[2]
000054 |     need("color map onto Z3 on Z8", wf.dot(axes[0]) == 1)
000055 |     need("color map onto Z3 on D8", sum(d8_witness) % 2 == 0 and wf.dot(d8_witness) == 1)
000056 |     odd_neutral = axes[2]
000057 |     need("actual source has an odd neutral charge", wf.dot(odd_neutral) == 0 and odd_neutral.dot(odd_neutral) == 1)
000058 |     need("odd neutral charge lies outside E8", sum(odd_neutral) % 2 == 1)
000059 | 
000060 |     # Independent complete norm-two root control of the same original matrix.
000061 |     roots = []
000062 |     for i, j in itertools.combinations(range(8), 2):
000063 |         for x, y in itertools.product([-1, 1], repeat=2):
000064 |             roots.append(x * axes[i] + y * axes[j])
000065 |     for signs in itertools.product([-1, 1], repeat=8):
000066 |         if signs.count(-1) % 2 == 0:
000067 |             roots.append(s.Matrix(signs) / 2)
000068 |     rootset = {tuple(q) for q in roots}
000069 |     need("complete retained E8 shell", len(rootset) == 240)
000070 |     need("M preserves every original E8 root", {tuple(m * q) for q in roots} == rootset)
000071 |     need("original color roots lie in complete shell", all(tuple(q) in rootset for q in colors))
000072 | 
000073 |     out = {
000074 |         "result": "R070",
000075 |         "status": "SCOPED_INTERFACE_DECIDED_PHYSICAL_F1_OPEN",
000076 |         "input": str(FOLD.relative_to(ROOT)),
000077 |         "color_charge_in_original_fold_frame": [str(x) for x in wf],
000078 |         "color_root_preimages": [[str(x) for x in q] for q in mapped],
000079 |         "color_roots_in_unchanged_even_CAR_lattice": sum(integer),
000080 |         "color_roots_requiring_NS_R_sector_change": len(colors) - sum(integer),
000081 |         "monodromy_of_each_missing_root_with_each_odd_vector_generator": "-1",
000082 |         "common_neutral_even_lattice_index_in_E8": 6,
000083 |         "common_neutral_even_lattice_determinant": 36,
000084 |         "bosonic_and_fermionic_neutral_neighbors_determinants": [9, 9],
000085 |         "neighbor_index_over_common_even_lattice": 2,
000086 |         "scope": "Original fixed M and color Cartan. Center action extends to NS CAR, full color root action does not preserve its charge lattice. Four-module parent is retained; no new physical field map, local sector endpoint, state/measure/time, 96-matter identification, 3+1 or gravity is derived.",
000087 |         "checks_passed": len(tests),
000088 |         "checks": tests,
000089 |     }
000090 |     (HERE / "COLOR-SPIN-SOURCE-INTERFACE.json").write_text(json.dumps(out, indent=2) + "\n")
000091 |     print(json.dumps({k: out[k] for k in ["status", "color_charge_in_original_fold_frame", "color_roots_in_unchanged_even_CAR_lattice", "color_roots_requiring_NS_R_sector_change", "checks_passed"]}))
000092 | 
000093 | 
000094 | if __name__ == "__main__":
000095 |     main()