TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/graded_boundary_functor/check_finite_typing.py
Original file SHA-256: 404cd24e04ae86ca95b981c5fc6a728930bbc2579aaefdd22e2bf2da9113f06e
Inclusive original lines: 1-74
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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000001 | """Exact actual v252 coefficient control; no physical mass selection."""
000002 | from pathlib import Path
000003 | import hashlib
000004 | import importlib.util
000005 | import json
000006 | import sys
000007 | import numpy as np
000008 | import sympy as s
000009 | 
000010 | ROOT=Path(__file__).resolve().parents[4]
000011 | SOURCE=ROOT/'verification/v252_full_finite_triple.py'
000012 | sys.path.insert(0,str(ROOT/'verification'))
000013 | spec=importlib.util.spec_from_file_location('actual_v252',SOURCE)
000014 | v=importlib.util.module_from_spec(spec)
000015 | spec.loader.exec_module(v)
000016 | 
000017 | def exact(arr):
000018 |     def entry(z):
000019 |         z=complex(z)
000020 |         if not(z.real.is_integer() and z.imag.is_integer()):
000021 |             raise ValueError('Constructor input is not a Gaussian integer')
000022 |         return s.Integer(int(z.real))+s.I*s.Integer(int(z.imag))
000023 |     return s.SparseMatrix(s.Matrix(arr.tolist()).applyfunc(entry))
000024 | 
000025 | ys=[np.diag(x).astype(complex) for x in
000026 |     ([1,2,3],[2,3,4],[3,4,5],[4,5,6])]
000027 | mr=np.array([[2,1,0],[1,3,1],[0,1,4]],complex)
000028 | phi=exact(v.full_D(*ys,mr))
000029 | g=exact(v.grading())
000030 | n=g.rows
000031 | one=s.eye(n)
000032 | Z=s.diag(1,-1)
000033 | N=s.Matrix([[0,-1],[1,0]])
000034 | S=N*Z
000035 | Gt=s.kronecker_product(Z,g)
000036 | Ic=s.I*Gt
000037 | C=s.kronecker_product(s.I*N,one)
000038 | plus,minus=(one+g)/2,(one-g)/2
000039 | E=plus.col_join(s.I*minus)
000040 | p=s.symbols('p',real=True)
000041 | B=s.kronecker_product(Z,p*one)-s.kronecker_product(S,phi)
000042 | h=p*g-s.I*g*phi
000043 | checks={
000044 |  'actual_dimension':n==96,
000045 |  'actual_phi_selfadjoint':phi.H==phi,
000046 |  'actual_phi_odd':phi*g+g*phi==s.zeros(n),
000047 |  'actual_total_B_even':Gt*B==B*Gt,
000048 |  'C_B_anticommutes':C*B==-B*C,
000049 |  'new_C_antilinear':C*Ic==-Ic*C,
000050 |  'E_isometry':E.H*E==one,
000051 |  'E_positive_total_chirality':Gt*E==E,
000052 |  'whole_original_mass_operator_intertwiner':B*E==E*h,
000053 |  'selfadjoint_h':h.H==h,
000054 |  'squared_h':h*h==p*p*one+phi*phi,
000055 | }
000056 | # The same original coefficient with arbitrary smooth scalar amplitude and
000057 | # connection, represented by independent value/first-derivative jets.
000058 | f,fp,a,ap=s.symbols('f fp a ap',real=True)
000059 | h1=-s.I*g
000060 | h0=a*g-s.I*g*f*phi
000061 | h0prime=ap*g-s.I*g*fp*phi
000062 | checks.update({
000063 |  'profile_second_derivative_coefficient':h1*h1==-one,
000064 |  'profile_first_derivative_coefficient':h1*h0+h0*h1==-2*s.I*a*one,
000065 |  'profile_zeroth_coefficient_retains_derivative':
000066 |      s.simplify(h1*h0prime+h0*h0-((a*a-s.I*ap)*one+f*f*phi*phi-fp*phi))==s.zeros(n),
000067 | })
000068 | if not all(checks.values()):
000069 |     raise RuntimeError(checks)
000070 | result={'all_pass':True,'checks':checks,'constructor_sha256':
000071 |     hashlib.sha256(SOURCE.read_bytes()).hexdigest(),
000072 |     'scope':'Full actual finite coefficient and smooth classical profile jets; not physical quantization or bosonic state selection.'}
000073 | Path(__file__).with_name('finite-results.json').write_text(json.dumps(result,indent=2)+'\n')
000074 | print(json.dumps(result))