TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_original_color_density_descent.py
Original file SHA-256: 1a01188cdff0ee922eb82ab4eee70795585b72d94a83a0c49266db020fb2eb07
Inclusive original lines: 1-84
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 | """R073: actual color-selector action on the original infinite-Maya currents."""
000002 | from pathlib import Path
000003 | import sys, json
000004 | from fractions import Fraction
000005 | import sympy as s
000006 | 
000007 | HERE = Path(__file__).resolve().parent
000008 | REPO = HERE.parents[3]
000009 | sys.path.insert(0, str(REPO/'experiments/theory-contracts/joint-native-algebra-selection-20261016'))
000010 | import check_original_current_schur_kernel as original
000011 | 
000012 | data = json.loads((REPO/'experiments/theory-contracts/v16-operator-pullback-20261014/fold-results.json').read_text())
000013 | M = s.Matrix([[s.Rational(x) for x in row] for row in data['explicit_Weyl_matrix']])
000014 | target = s.Matrix([1,1,-2,0,0,0,0,0])
000015 | w = list(map(int, M.T*target))
000016 | checks = []
000017 | 
000018 | 
000019 | def need(ok, msg):
000020 |     if not bool(ok):
000021 |         raise AssertionError(msg)
000022 |     checks.append(msg)
000023 | 
000024 | 
000025 | def color(lam):
000026 |     # All changed beads are above -depth. The infinite identical sea cancels.
000027 |     depth = sum(lam)+3
000028 |     occ = {(lam[i-1] if i <= len(lam) else 0)-i for i in range(1, depth+1)}
000029 |     vac = set(range(-depth, 0))
000030 |     return (sum(w[r%8] for r in occ-vac)-sum(w[r%8] for r in vac-occ))%3
000031 | 
000032 | 
000033 | need(w == [1,-1,0,-1,-1,-1,0,-1], 'actual center transported by unchanged M')
000034 | D = [sum((w[j]-w[(j-r)%8])%3 != 0 for j in range(8)) for r in range(8)]
000035 | L = [sum((w[j]-w[(j-r)%8])%3 != 0 for j in range(r)) for r in range(8)]
000036 | need(D == [0,6,4,6,2,6,4,6], 'all eight full-residue counts')
000037 | need(L == [0,1,1,3,1,3,3,5], 'all eight prefix counts')
000038 | need([j for j,x in enumerate(w) if x%3 == 1] == [0], 'unique residue1 gives all-mode witness')
000039 | rows = []
000040 | for m in range(1,25):
000041 |     terms = original.add_ribbons((), m)
000042 |     charged = sum(abs(coefficient)**2 for lam,coefficient in terms if color(lam))
000043 |     neutral = sum(abs(coefficient)**2 for lam,coefficient in terms if not color(lam))
000044 |     predicted = (m//8)*D[m%8]+L[m%8]
000045 |     need(charged == predicted and charged+neutral == m, f'original infinite-Maya J_-{m} full vector color count')
000046 |     rows.append({'m':m,'charged_norm2':charged,'neutral_norm2':neutral,'total_norm2':m})
000047 | need(rows[0]['charged_norm2'] == 1 and rows[0]['neutral_norm2'] == 0, 'whole J1J-1 word norm1, factorwise color projections0')
000048 | need(Fraction(rows[0]['charged_norm2'],4) == Fraction(1,4), 'cos(theta) infinitesimal leakage exactly1/4')
000049 | need([k for k in range(8) if all((w[j]-w[(j+k)%8])%3 == 0 for j in range(8))] == [0], 'only period8 scalar density shift preserves all colors')
000050 | 
000051 | # Independent actual arc-matrix commutant system, computed modulo z^2+z+1.
000052 | z = s.symbols('z')
000053 | roots = [(1+s.I)/s.sqrt(2)]
000054 | F = s.Matrix(8,8,lambda r,k:s.expand_complex(roots[0]**(r*k))/s.sqrt(8))
000055 | Z = (F*s.diag(*[z**(x%3) for x in w])*F.conjugate().T).applyfunc(s.expand)
000056 | Z = Z.applyfunc(lambda x:s.rem(x,z*z+z+1,z))
000057 | g = s.symbols('g0:8')
000058 | comm = s.diag(*g)*Z-Z*s.diag(*g)
000059 | equations=[]
000060 | for x in comm:
000061 |     equations.extend([s.expand(x).coeff(z,0),s.expand(x).coeff(z,1)])
000062 | A,_ = s.linear_eq_to_matrix(equations,g)
000063 | need(A.rank() == 7 and A.nullspace() == [s.ones(8,1)], 'actual color arc matrix forces all diagonal arc phases equal')
000064 | Za = Z.subs(z,(-1+s.I*s.sqrt(3))/2).applyfunc(s.simplify)
000065 | P = s.zeros(8); P[0,0]=1
000066 | Q = s.zeros(8); Q[1,1]=1
000067 | leak = (Za*P*Za.conjugate().T*Q-Q*Za*P*Za.conjugate().T).applyfunc(s.simplify)
000068 | norm = s.simplify(s.trace(leak.conjugate().T*leak))
000069 | need(s.simplify(Za[1,0]*s.conjugate(Za[1,0])) == s.Rational(3,64), 'original color action connects two different cover arcs')
000070 | need(norm == s.Rational(183,2048), 'exterior locality witness has nonzero exact norm183/2048')
000071 | 
000072 | # q-current transfers only between modes with the same actual residue/color.
000073 | q = M.T*s.Matrix([0,1,-1,0,0,0,0,0])
000074 | need((q.T*q)[0] == 2, 'actual q current retained at level2')
000075 | need(all(w[(r+8*n)%8] == w[r%8] for r in range(8) for n in [-1,0,1]), 'whole q-current mode rule preserves actual center')
000076 | result={'result':'R073','passed':len(checks),'w':w,'D':D,'L':L,
000077 |         'whole_formula':'ell_(8k+s)=k*D_s+L_s; ell_m=0 iff8 dividesm',
000078 |         'continuous_admissible_scalar_profiles':'Fourier support in8Z',
000079 |         'cos_leakage_norm2':'1/4','arc_commutant_rank':7,
000080 |         'exterior_commutator_norm2':'183/2048',
000081 |         'coordinate_support_class':'O=F^-1(K) modulo nullsets for color-invariant CAR support',
000082 |         'modes':rows,'checks':checks}
000083 | (HERE/'ORIGINAL-COLOR-DENSITY-DESCENT.json').write_text(json.dumps(result,indent=2)+'\n')
000084 | print(json.dumps({'result':'R073','passed':len(checks),'actual_Maya_modes':24,'arc_commutant_rank':7}))