TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/canonical-seam-fermionization-20261025/check_same_source_affine_defect.py
Original file SHA-256: 0f51ab119938a05184a3f3e11b364dcb4ee02749487829bf65147bc86647131c
Inclusive original lines: 34-74
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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000034 |     out[0] += 1
000035 |     return tuple(out)
000036 | 
000037 | 
000038 | def eps_z(left, right):
000039 |     return -1 if sum(left[i] * right[j] for i in range(8) for j in range(i)) % 2 else 1
000040 | 
000041 | 
000042 | def eta_r(vector):
000043 |     return -1 if vector[7] * sum(vector[:7]) % 2 else 1
000044 | 
000045 | 
000046 | ONES = (1,) * 8
000047 | ZERO = (0,) * 8
000048 | E0 = (1,) + (0,) * 7
000049 | 
000050 | 
000051 | def normalize(base, half):
000052 |     """Unique n+c*s section, c in {0,1}, with 2s=(1,...,1)."""
000053 |     if half < 2:
000054 |         return tuple(base), half
000055 |     return add(base, ONES), half - 2
000056 | 
000057 | 
000058 | def add_labels(left, right):
000059 |     return normalize(add(left[0], right[0]), left[1] + right[1])
000060 | 
000061 | 
000062 | def eps_ext(left, right):
000063 |     """Associative section cocycle for E_(n+c*s)=E_n X^c.
000064 | 
000065 |     Relations: X E_n X^-1=i^Q(n) E_n and X^2=-E_(1,...,1).
000066 |     It restricts to the ordered CAR cocycle on Z8 and to the previously
000067 |     fixed even E8 cocycle on D8 union (D8+s).
000068 |     """
000069 |     n, c = left
000070 |     m, d = right
000071 |     value = (I ** (c * sum(m))) * eps_z(n, m)
000072 |     if c and d:
000073 |         value *= -eps_z(add(n, m), ONES)
000074 |     return complex(round(value.real), round(value.imag))