TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/universalraum-keyD-native-instruments-20260915/native_source.py
Original file SHA-256: 380577f85d2afa8b50f91a0991769eaf8267ee5c09f327d87f17e1b4c0af1672
Inclusive original lines: 45-86
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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000045 |     return out
000046 | 
000047 | ANN5 = _jw(5)
000048 | EVEN16 = [m for m in range(32) if m.bit_count() % 2 == 0]
000049 | _CONJ = np.eye(32, dtype=np.int64)
000050 | for _a in ANN5:
000051 |     _CONJ = _CONJ @ (_a + _a.T)
000052 | BETA = [( _CONJ @ _a)[np.ix_(EVEN16, EVEN16)] for _a in ANN5 + [_a.T for _a in ANN5]]
000053 | need(len(BETA) == 10 and all(b.shape == (16, 16) for b in BETA), 'ten 16x16 spinor beta matrices')
000054 | 
000055 | # --- Native pair tensor W (verified against the pinned npz in earlier rounds)
000056 | PAIRS = list(combinations(range(64), 2))
000057 | PAIR_INDEX = {p: j for j, p in enumerate(PAIRS)}
000058 | COLORS = list(combinations(range(4), 2))
000059 | W = np.zeros((60, 2016), dtype=np.int64)
000060 | for k, beta in enumerate(BETA):
000061 |     for c, (l, r) in enumerate(COLORS):
000062 |         for j, (v, w) in enumerate(PAIRS):
000063 |             vs, vc = divmod(v, 4)
000064 |             ws, wc = divmod(w, 4)
000065 |             W[6*k + c, j] = beta[vs, ws] * (int(vc == l and wc == r) - int(vc == r and wc == l))
000066 | need(np.array_equal(W @ W.T, 8*np.eye(60, dtype=int)), 'native row Gram W W^T = 8 I_60')
000067 | need(set(map(int, np.count_nonzero(W, axis=1))) == {8}, 'eight pairs per mediator row')
000068 | 
000069 | # --- Cartan weight labels ---------------------------------------------------
000070 | CW = np.array([[1-2*((m >> j) & 1) for j in range(3)]
000071 |                for m in range(8) if m.bit_count() % 2 == 0], dtype=np.int64)
000072 | FW = np.array([[1-2*((m >> j) & 1) for j in range(5)] + list(c)
000073 |                for m in EVEN16 for c in CW], dtype=np.int64)
000074 | BW = []
000075 | for k in range(10):
000076 |     v = [0]*5
000077 |     v[k % 5] = -2 if k < 5 else 2
000078 |     for a, b in COLORS:
000079 |         BW.append(v + list(CW[a] + CW[b]))
000080 | BW = np.array(BW, dtype=np.int64)
000081 | need(FW.shape == (64, 8) and BW.shape == (60, 8), 'weight label shapes')
000082 | _lookup = {PAIRS[c]: (int(r), int(W[r, c])) for r, c in zip(*np.nonzero(W))}
000083 | need(len(_lookup) == 480, 'one mediator channel per supported pair')
000084 | need(all(np.array_equal(FW[i] + FW[j], BW[A])
000085 |          for (i, j), (A, _v) in _lookup.items()), 'Cartan charge conservation at all 480 vertices')
000086 |