TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_b1_whole_source_reduction.py
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Inclusive original lines: 1-132
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000001 | """B1 continuation: exact reducing images and a whole-source counterexample.
000002 | 
000003 | Uses the existing exact intertwiner solver. Finite statements do not identify
000004 | the physical P_F or replace the circle domain by a finite Hilbert space.
000005 | """
000006 | from pathlib import Path
000007 | import json
000008 | import sys
000009 | import sympy as s
000010 | 
000011 | ROOT = Path(__file__).resolve().parents[4]
000012 | sys.path.insert(0, str(ROOT / 'experiments/theory-contracts/seam-constructive-search-20261015/operator_synthesis'))
000013 | from intertwiner_search import equation, restrict
000014 | 
000015 | checks = {}
000016 | records = []
000017 | Z = s.diag(1, -1)
000018 | S = s.Matrix([[0, 1], [1, 0]])
000019 | N = s.Matrix([[0, -1], [1, 0]])
000020 | checks['normal_sign_NZ_S'] = N*Z == S
000021 | checks['normal_sign_NS_minus_Z'] = N*S == -Z
000022 | 
000023 | for r, t in [(1, 1), (1, 2), (2, 2)]:
000024 |     n = r+t
000025 |     g = s.diag(*([1]*r+[-1]*t))
000026 |     generators = []
000027 |     for i in range(n):
000028 |         a = s.zeros(n); a[i, i] = 1
000029 |         generators.append(s.kronecker_product(Z, a))
000030 |     for i in range(n):
000031 |         for j in range(i+1, n):
000032 |             x = s.zeros(n); x[i,j] = x[j,i] = 1
000033 |             y = s.zeros(n); y[i,j] = s.I; y[j,i] = -s.I
000034 |             normal = Z if g[i,i] == g[j,j] else -S
000035 |             generators.extend([s.kronecker_product(normal,x), s.kronecker_product(normal,y)])
000036 |     dim = 2*n
000037 |     basis = s.eye(dim*dim)
000038 |     dimensions = []
000039 |     for b in generators:
000040 |         basis = restrict(basis, [equation(b,b,False)])
000041 |         dimensions.append(basis.cols)
000042 |     Gamma = s.kronecker_product(Z,g)
000043 |     candidate = s.Matrix.hstack(s.Matrix(s.eye(dim)).reshape(dim*dim,1),Gamma.reshape(dim*dim,1))
000044 |     checks[f'commutant_{r}_{t}_exact_span_I_Gamma'] = basis.cols == 2 and candidate.row_join(basis).rank() == 2
000045 |     checks[f'projector_{r}_{t}_rank_n'] = ((s.eye(dim)+Gamma)/2).rank() == n
000046 |     records.append({'grading_ranks':[r,t], 'normal_dimension':dim,
000047 |                     'generator_count':len(generators),'successive_commutant_dimensions':dimensions,
000048 |                     'final_complex_dimension':basis.cols})
000049 | 
000050 | theta = s.symbols('theta',real=True)
000051 | a,d,x,y = s.symbols('a d x y',real=True)
000052 | g = Z
000053 | pp,pm = (s.eye(2)+g)/2,(s.eye(2)-g)/2
000054 | A = s.diag(a,d)
000055 | phi = s.Matrix([[0,x+s.I*y],[x-s.I*y,0]])
000056 | B = s.kronecker_product(Z,A)-s.kronecker_product(S,phi)
000057 | E = pp.col_join(s.exp(s.I*theta)*pm)
000058 | P = (s.eye(4)+s.kronecker_product(Z,g))/2
000059 | def zero(m):
000060 |     return m.applyfunc(lambda z:s.simplify(s.expand_complex(z))) == s.zeros(*m.shape)
000061 | h = A*g-s.cos(theta)*phi-s.I*s.sin(theta)*g*phi
000062 | checks['all_phase_isometry'] = zero(E.H*E-s.eye(2))
000063 | checks['all_phase_same_image'] = zero(E*E.H-P)
000064 | checks['all_phase_reducing'] = zero(B*E-E*h)
000065 | checks['all_phase_pullback'] = zero(E.H*B*E-h)
000066 | checks['intrinsic_odd_reader'] = zero((B-s.kronecker_product(Z,s.eye(2))*B*s.kronecker_product(Z,s.eye(2)))/2+s.kronecker_product(S,phi))
000067 | 
000068 | # H = diag(log(2),-log(2)), ell=1: f=(1/5,4/5), X=(2/5)I.
000069 | H = s.diag(s.log(2),-s.log(2))
000070 | v = s.Matrix([1,1])/s.sqrt(2)
000071 | p = v*v.H
000072 | f = s.diag(s.Rational(1,5),s.Rational(4,5))
000073 | cross = s.eye(2)*s.Rational(2,5)
000074 | G = (s.eye(2)-f).row_join(cross).col_join(cross.row_join(f))
000075 | W = s.diag(v,v)
000076 | K = W.H*G*W
000077 | G_compressed_H = s.ones(2)/2
000078 | leak = (s.eye(4)-W*W.H)*G*W
000079 | defect = K-K*K
000080 | checks['original_whole_graph_is_projection'] = G*G == G
000081 | checks['one_face_reader_matches_H_compression'] = (v.H*f*v)[0] == s.Rational(1,2) and (v.H*H*v)[0] == 0
000082 | checks['one_face_does_not_reduce_H'] = H*p != p*H
000083 | checks['whole_cross_detects_loss'] = K != G_compressed_H
000084 | checks['exact_defect_factorization'] = defect == leak.H*leak
000085 | checks['nonzero_whole_defect'] = defect == s.eye(2)*s.Rational(9,100)
000086 | 
000087 | # Inspect the actual v252 field slots: quark/lepton separation survives all
000088 | # supplied Yukawa and Majorana coefficients, not the larger arbitrary-even class.
000089 | sys.path.insert(0,str(ROOT/'verification'))
000090 | import numpy as np
000091 | import v252_full_finite_triple as finite
000092 | ys = [np.array([[1,2,0],[0,3,1],[1,0,4]],complex)+j*np.eye(3) for j in range(4)]
000093 | mr = np.array([[2,1,0],[1,3,1],[0,1,4]],complex)
000094 | phi96 = finite.full_D(*ys,mr)
000095 | gamma96 = finite.grading()
000096 | q48 = [1 if name in ('u','d') else 0 for name,chirality,colour,family in finite.P]
000097 | q = np.diag(q48+q48)
000098 | omega = 2*q-np.eye(96)
000099 | checks['actual_96_quark_lepton_no_mixing'] = np.array_equal(q@phi96,phi96@q)
000100 | checks['actual_96_alternative_grading_odd'] = np.array_equal((gamma96@omega)@phi96+phi96@(gamma96@omega),np.zeros((96,96)))
000101 | checks['actual_96_alternative_distinct'] = not np.array_equal(gamma96@omega,gamma96) and not np.array_equal(gamma96@omega,-gamma96)
000102 | real_swap = finite.Kswap()
000103 | checks['actual_96_alternative_internal_KO6'] = np.array_equal(real_swap@(gamma96@omega).conjugate(),-(gamma96@omega)@real_swap)
000104 | algebra_generators = []
000105 | for lam in (1,1j):
000106 |     algebra_generators.append(finite.rep(lam,np.zeros((2,2)),np.zeros((3,3))))
000107 | for aa,bb in ((1,0),(1j,0),(0,1),(0,1j)):
000108 |     algebra_generators.append(finite.rep(0,finite.quaternion(aa,bb),np.zeros((3,3))))
000109 | for i in range(3):
000110 |     for j in range(3):
000111 |         for phase in (1,1j):
000112 |             m = np.zeros((3,3),complex); m[i,j] = phase
000113 |             algebra_generators.append(finite.rep(0,np.zeros((2,2)),m))
000114 | checks['actual_96_q_commutes_entire_SM_algebra_basis'] = all(np.array_equal(q@a,a@q) for a in algebra_generators)
000115 | checks['actual_96_alternative_grading_even_entire_SM_basis'] = all(np.array_equal((gamma96@omega)@a,a@(gamma96@omega)) for a in algebra_generators)
000116 | 
000117 | out = {'contract':'B1-WHOLE-SOURCE-REDUCTION-20261030',
000118 |        'scope':'Exact finite algebra; actual96 coefficient countertest; no physical P_F selection or new Lean proof.',
000119 |        'commutant_runs':records,'checks':{k:bool(v) for k,v in checks.items()},
000120 |        'actual_96':{'quark_rank':int(np.trace(q)), 'lepton_rank':int(96-np.trace(q)),
000121 |                     'SM_algebra_real_basis_size':len(algebra_generators),
000122 |                     'full_normal_J_tested':False,
000123 |                     'coefficient_scope':'v252 full_D and SM rep; not every even96 matrix'},
000124 |        'counterexample':{'compressed_whole_graph':str(K),'canonical_graph_of_compressed_H':str(G_compressed_H),
000125 |                          'defect':str(defect),'eigenvalues':['1/10','9/10'],
000126 |                          'single_face_equality':'For every ell>0 by f(x)+f(-x)=1; proof in B1-WHOLE-SOURCE-REDUCTION.txt'},
000127 |        'all_passed':all(checks.values())}
000128 | path = Path(__file__).with_name('B1-WHOLE-SOURCE-REDUCTION.json')
000129 | path.write_text(json.dumps(out,indent=2,ensure_ascii=False)+'\n')
000130 | print(json.dumps(out,indent=2,ensure_ascii=False))
000131 | if not out['all_passed']:
000132 |     raise SystemExit(1)