TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/craig-original-source-bridge-20261103/actual_product_pairing.py
Original file SHA-256: 6acaa9bc2c7a157a30730d7d6de75e944266afbf69b18a31c6fba654b8bd1c04
Inclusive original lines: 1-40
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 | """Evaluate the existing Spin4 x v252 branch; does not identify it with full S_adm."""
000002 | import importlib.util
000003 | import json
000004 | import sys
000005 | from pathlib import Path
000006 | import sympy as s
000007 | 
000008 | repo=Path(__file__).resolve().parents[3]
000009 | sys.path.insert(0,str(repo/'verification'))
000010 | spec=importlib.util.spec_from_file_location('original_v252',repo/'verification/v252_full_finite_triple.py')
000011 | v=importlib.util.module_from_spec(spec);spec.loader.exec_module(v)
000012 | KF=s.Matrix(v.Kswap()).applyfunc(lambda x:s.Integer(int(x)))
000013 | gF=s.Matrix(v.grading()).applyfunc(lambda x:s.Integer(int(x)))
000014 | I2=s.eye(2); I4=s.eye(4)
000015 | pauli=[s.Matrix([[0,1],[1,0]]),s.Matrix([[0,-s.I],[s.I,0]]),s.diag(1,-1)]
000016 | gam=[s.kronecker_product(pauli[0],q) for q in pauli]+[s.kronecker_product(pauli[1],I2)]
000017 | g5=gam[0]*gam[1]*gam[2]*gam[3]
000018 | C=gam[0]*gam[2]
000019 | checks={}
000020 | def zero(M):return all(s.simplify(x)==0 for x in M)
000021 | def ck(name,val):
000022 |  if not val:raise RuntimeError(name)
000023 |  checks[name]=True
000024 | 
000025 | ck('original_internal_dimension_96',KF.shape==(96,96))
000026 | ck('original_JF_square_plus',zero(KF*KF-s.eye(96)))
000027 | ck('original_JF_flips_internal_grading',zero(KF*gF+gF*KF))
000028 | ck('Spin4_J_square_minus',zero(C*C.conjugate()+I4))
000029 | ck('Spin4_J_preserves_spin_grading',zero(C*g5.conjugate()-g5*C))
000030 | ck('Spin4_conjugation_of_clifford',all(zero(C*q.conjugate()+q*C) for q in gam))
000031 | ck('spin_derivative_pairing_symmetric',all(zero((C.H*q).T-C.H*q) for q in gam))
000032 | ck('spin_mass_pairing_skew',zero((C.H*g5).T+C.H*g5))
000033 | ck('original_KF_symmetric',zero(KF.T-KF))
000034 | 
000035 | # No special Yukawa value is supplied. The full-family mass result follows
000036 | # from the original relations Phi*=Phi and KF bar(Phi)=Phi KF:
000037 | # (KF Phi)^T=bar(Phi) KF=KF Phi, hence the spin product is skew.
000038 | Gamma_diag=[int(g5[i,i]*gF[j,j]) for i in range(4) for j in range(96)]
000039 | ranks={str(e):sum(x==e for x in Gamma_diag) for e in [-1,1]}
000040 | ck('both_total_chiral_fibers_rank192',ranks=={'-1':192,'1':192})