TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/p1_insertion_tangent.py
Original file SHA-256: 70b3d0790f40a4834644c806db90fc27402967563e6e8888a8f1192ec539ad00
Inclusive original lines: 116-176
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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000116 |     assert sp.simplify(h-2*ell*b) == sp.zeros(2)
000117 |     return {"transfer_eigenvalues": ["1/4", "1/64"],
000118 |             "calderon_projection_exact": True,
000119 |             "own_range_covariance": "I (not in the domain of finite logit induction)",
000120 |             "mixed_one_face_occupations": list(map(str, occupation.diagonal())),
000121 |             "one_face_modular_generator": list(map(str, h.diagonal())),
000122 |             "exact_recovery": "h(1-A)=2*ell*B, ell=8*log(2), B=diag(1/4,3/4)",
000123 |             "scope": "Retained conditional collar, not a physical P1 field family"}
000124 | 
000125 | 
000126 | def current_action_checks():
000127 |     roots = e8.roots()
000128 |     rootset = set(roots)
000129 |     spinors = tuple(p for p in roots if e8.grade(p) == 1)
000130 |     targets = set(p for p in roots if e8.grade(p) == 3)
000131 |     mediators = tuple(r for r in roots if e8.grade(r) == 2)
000132 |     outgoing, ranks, family_edges = Counter(), Counter(), Counter()
000133 |     values = Counter()
000134 |     sample = None
000135 |     for r in mediators:
000136 |         images = set()
000137 |         for p in spinors:
000138 |             s = e8.add(r, p)
000139 |             allowed = s in rootset
000140 |             assert allowed == (e8.dot(r, p) == -1)
000141 |             if not allowed:
000142 |                 continue
000143 |             assert s in targets
000144 |             # Actual existing three-current reader, not an inserted Yukawa matrix.
000145 |             response = e8.current_response((r, p, e8.neg(s)), (3, 2, 1))
000146 |             norm = e8.current_response((s, e8.neg(s)), (2, 1))
000147 |             coefficient = 2*response/norm
000148 |             assert coefficient == e8.epsilon(r, p)
000149 |             assert response != 0
000150 |             source_family = p[5:]
000151 |             target_conjugate_family = e8.neg(s)[5:]
000152 |             assert source_family != target_conjugate_family
000153 |             family_edges[(source_family, target_conjugate_family)] += 1
000154 |             outgoing[p] += 1
000155 |             images.add(s)
000156 |             values[str(response)] += 1
000157 |             if sample is None:
000158 |                 sample = {"r": list(map(str, r)), "p": list(map(str, p)),
000159 |                           "target": list(map(str, s)), "response_3_2_1": str(response),
000160 |                           "zero_mode_coefficient": str(coefficient)}
000161 |         ranks[len(images)] += 1
000162 |     # Check every possible same-family pairing against all existing grade-two currents.
000163 |     same_family_pairs = [(p, q) for p in spinors for q in spinors if p[5:] == q[5:]]
000164 |     for p, q in same_family_pairs:
000165 |         assert e8.neg(e8.add(p, q)) not in set(mediators)
000166 |     # One direct existing-reader zero per same-family pair, with each mediator sampled cyclically.
000167 |     for i, (p, q) in enumerate(same_family_pairs):
000168 |         assert e8.current_response((mediators[i % len(mediators)], p, q), (3, 2, 1)) == 0
000169 |     assert len(spinors) == 64 and len(mediators) == 60
000170 |     assert set(outgoing.values()) == {15} and sum(outgoing.values()) == 960
000171 |     assert ranks == {16: 60} and len(family_edges) == 12
000172 |     assert set(family_edges.values()) == {80}
000173 |     return {"spinor_current_dimension_each": 64, "grade_two_currents": 60,
000174 |             "candidate_root_pairs": len(spinors)*len(mediators),
000175 |             "nonzero_root_actions": sum(outgoing.values()),
000176 |             "outgoing_per_spinor": 15, "rank_each_root_action": 16,