TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_genesis_twin_transport_20261102.py
Original file SHA-256: 93490c0f6cc891812413934c9d5723695c4df8659608478337fe2b49bf7285c8
Inclusive original lines: 1-62
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 | """Exact original Q-twin transport; no physical source selection is assumed."""
000002 | from pathlib import Path
000003 | import sys
000004 | import sympy as s
000005 | 
000006 | sys.path.insert(0, str(Path(__file__).resolve().parents[4] / 'verification'))
000007 | from v568_bit_selector_ladder import Qc, UV
000008 | 
000009 | I = s.eye(3)
000010 | G = s.Matrix([[1, 0, 0], [0, 1, 0], [0, 2, -1]])
000011 | Sigma = s.diag(1, -1, -1)
000012 | U0, V0 = UV(Qc(0)); U2, V2 = UV(Qc(2))
000013 | if not (G*G == I and G.det() == -1):
000014 |     raise AssertionError('control at original line 13')
000015 | if not (G*U0 == U2*G and G*V0 == V2*G):
000016 |     raise AssertionError('control at original line 14')
000017 | if not (G*Sigma == Sigma*G):
000018 |     raise AssertionError('control at original line 15')
000019 | if not (G*s.Matrix([1, 0, 0]) == s.Matrix([1, 0, 0])):
000020 |     raise AssertionError('control at original line 16')
000021 | if not (G*s.ones(3, 1) == s.ones(3, 1)):
000022 |     raise AssertionError('control at original line 17')
000023 | if not (G*s.Matrix([1, 2, 0]) == s.Matrix([1, 2, 4])):
000024 |     raise AssertionError('control at original line 18')
000025 | 
000026 | # The simultaneous intertwiner space is exactly one-dimensional, not merely
000027 | # an example. Its nonzero members cannot preserve the stipulated Sigma form.
000028 | xx = s.symbols('x0:9'); X = s.Matrix(3, 3, xx)
000029 | solutions = s.linsolve(list(X*U0-U2*X)+list(X*V0-V2*X), xx)
000030 | if not (solutions == s.FiniteSet(tuple(-xx[8]*G))):
000031 |     raise AssertionError('control at original line 24')
000032 | B = G.T*Sigma*G
000033 | if not (B == s.Matrix([[1, 0, 0], [0, -5, 2], [0, 2, -1]])):
000034 |     raise AssertionError('control at original line 26')
000035 | if not (B != Sigma):
000036 |     raise AssertionError('control at original line 27')
000037 | theta = lambda A: Sigma*A.T*Sigma
000038 | theta_transport = lambda A: G*theta(G*A*G)*G
000039 | if not (s.trace(theta(V0)*V0) == 4):
000040 |     raise AssertionError('control at original line 30')
000041 | if not (s.trace(theta(V2)*V2) == 8):
000042 |     raise AssertionError('control at original line 31')
000043 | if not (s.trace(theta_transport(V2)*V2) == 4):
000044 |     raise AssertionError('control at original line 32')
000045 | if not (theta_transport(U2) == G*theta(U0)*G):
000046 |     raise AssertionError('control at original line 33')
000047 | 
000048 | M = s.Matrix([[1, 0, 0], [0, s.Rational(1, 2), s.Rational(1, 6)],
000049 |               [0, s.Rational(1, 6), s.Rational(1, 2)]])
000050 | c = s.symbols('c', real=True)
000051 | Gc = s.Matrix([[1,0,0],[0,s.Rational(1,2),s.Rational(1,2)],
000052 |                [0,(c+1)/2,(c-1)/2]])
000053 | Qplus = (Qc(c)+Sigma*Qc(c)*Sigma)/2
000054 | if not (s.simplify(Gc*M-Qplus*Gc/3) == s.zeros(3)):
000055 |     raise AssertionError('control at original line 41')
000056 | if not (Gc.det() == -s.Rational(1,2)):
000057 |     raise AssertionError('control at original line 42')
000058 | 
000059 | print('PASS: complete original pairs are GL3(Z)-conjugate; winding and grading retained.')
000060 | print('Fixed reflected word values: 4 and 8. Fully transported reflected value: 4 and 4.')
000061 | print('The original three-rate clock admits an intertwiner for both twins.')
000062 | print('No physical P1 equivalence, selected source metric, state or normalization is inferred.')