TFPT scientific source excerpt Original repository path: experiments/theory-contracts/charged-sector-readout-clock-20261013/checker.py Original file SHA-256: bf949d11034c1d17322971b58c712c0bef01bb6a3d0e6aa63aeca6d7d41b45d6 Inclusive original lines: 42-117 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. 000042 | def run(): 000043 | here=Path(__file__).parent 000044 | manifest=json.loads((here/'source_manifest.json').read_text()) 000045 | for entry in manifest['sources']: 000046 | if hashlib.sha256((ROOT/entry['path']).read_bytes()).hexdigest()!=entry['sha256']: 000047 | raise RuntimeError('Source changed: '+entry['path']) 000048 | native=_native_neutral_branch() 000049 | P=native['P5']; I=s.eye(8) 000050 | roots=[s.Matrix(r)/2 for r in sorted(native['retained'])] 000051 | chevalley=_actual_current_source()['chevalley'] 000052 | all_roots={root for root in chevalley.roots if chevalley.ridx[root] in native['closure']} 000053 | clock=json.loads((ROOT/'experiments/theory-contracts/compiler-integral-triality-20260918/certificate.json').read_text()) 000054 | C=s.Matrix(clock['clock_matrices']['C']['vector']) 000055 | J=s.Matrix(clock['clock_matrices']['J']['vector']) 000056 | checks=[] 000057 | def check(name, value): 000058 | checks.append({'name':name,'ok':bool(value)}) 000059 | check('original 48 marked roots and full 240 closure',len(roots)==48 and len(all_roots)==240) 000060 | check('original P5 orthogonal rank five',P==s.diag(1,1,1,1,1,0,0,0) and P*P==P and P.trace()==5) 000061 | check('every retained charge has D5 norm5/4 A3 norm3/4 and total2', 000062 | all((b.T*P*b)[0]==s.Rational(5,4) and (b.T*(I-P)*b)[0]==s.Rational(3,4) and (b.T*b)[0]==2 for b in roots)) 000063 | check('old neutral response contains no D5 component',P*native['R_matrix']==s.zeros(8)) 000064 | z,w1,w2=s.symbols('z w1 w2') 000065 | # Actual current Ward contraction, not an imposed fractional pair function. 000066 | current=1/(z-w1)-1/(z-w2) 000067 | check('Wick sector-stress insertion gives normalized Ward kernel', 000068 | s.factor(s.Rational(5,8)*current**2-s.Rational(5,8)*(w1-w2)**2/((z-w1)**2*(z-w2)**2))==0) 000069 | coeffs={str(a):partition_coefficients(a,12) for a in [s.Rational(5,4),s.Rational(3,4),s.Integer(2)]} 000070 | check('oscillator partitions generate carrier exponent5/4 through degree12', 000071 | coeffs['5/4']==[s.rf(s.Rational(5,4),n)/s.factorial(n) for n in range(13)]) 000072 | check('convolution restores full local exponent2 through degree12', 000073 | [sum(coeffs['5/4'][k]*coeffs['3/4'][n-k] for k in range(n+1)) for n in range(13)]==coeffs['2']==list(map(s.Integer,range(1,14)))) 000074 | u,q=s.symbols('u q',positive=True) 000075 | a=s.Rational(5,4) 000076 | G=((1-u)/(1-u*q))**a 000077 | check('normalized carrier response at q1',G.subs(q,1)==1) 000078 | check('zero-grade probability retains nonzero normalization',G.subs(q,0)==(1-u)**a) 000079 | # Use positive u in (0,1); fourth powers remove fractional-power simplification ambiguity. 000080 | check('reference-ratio matches target analytic factor on physical branch', 000081 | s.factor((G/G.subs(q,0))**4-(1-u*q)**-5)==0) 000082 | check('mean energy grade differs in carrier and full readout', 000083 | s.simplify(s.diff(G,q).subs(q,1)-s.Rational(5,4)*u/(1-u))==0) 000084 | clock_results={} 000085 | for name,g,rank,norm in [('C',C,4,s.Rational(23,8)),('J',J,2,s.Integer(2))]: 000086 | d=g.T*P*g-P 000087 | check(name+' is orthogonal and preserves original closed root set',g.T*g==I and {tuple(g*s.Matrix(r)) for r in all_roots}==all_roots) 000088 | check(name+' does not preserve the fixed carrier projector',d.rank()==rank and s.trace(d*d)==norm) 000089 | check(name+' transports marked response covariantly',all(s.simplify(((g*b).T*(g*P*g.T)*(g*b))[0]-(b.T*P*b)[0])==0 for b in roots)) 000090 | clock_results[name]={'difference_rank':d.rank(),'difference_squared_norm':str(s.trace(d*d)), 000091 | 'retained_carrier_norms_after_action':dict(Counter(str(((g*b).T*P*(g*b))[0]) for b in roots))} 000092 | columns=[] 000093 | for i in range(8): 000094 | for j in range(i,8): 000095 | B=s.zeros(8); B[i,j]=B[j,i]=1 000096 | columns.append(s.Matrix([x for g in (C,J) for x in g.T*B*g-B])) 000097 | rank=modular_rank(s.Matrix.hstack(*columns)) 000098 | # Rank mod101 gives the lower bound35 over Q. Identity gives upper bound35. 000099 | check('actual common clock invariant symmetric space one dimensional',rank==35 and all(g.T*I*g==I for g in(C,J))) 000100 | avg=s.Rational(5,8)*I 000101 | check('unique invariant trace5 quadratic coefficient is5/8I',avg.trace()==5 and all(g.T*avg*g==avg for g in(C,J))) 000102 | spin=s.ones(8,1)/2 000103 | check('explicit spinor clock changes carrier charge norm', (spin.T*P*spin)[0]==s.Rational(5,4) and ((C*spin).T*P*C*spin)[0]==1) 000104 | # At fixed u>0, scaled common flow produces q^(5/8), not a carrier exponent5/4. 000105 | check('scaled total and carrier flows have unequal second cumulants', 000106 | (s.Rational(5,8)**2*2-s.Rational(5,4))==-s.Rational(15,32)) 000107 | result={'verdict':'PARTIAL','mathematical_verdict':'MARKED_RESPONSE_CONSTRUCTED_CLOCK_IDENTIFICATION_REJECTED', 000108 | 'passed':sum(x['ok'] for x in checks),'total':len(checks),'checks':checks, 000109 | 'clock_results':clock_results,'clock_symmetric_constraint_rank':rank, 000110 | 'carrier_coefficients_0_to_5':list(map(str,coeffs['5/4'][:6])), 000111 | 'joint_response':'((1-u)/(1-u*q5))^(5/4) * ((1-u)/(1-u*q3))^(3/4)', 000112 | 'common_time_H_delta':'exp(-t*(1-delta.dot(beta)))*((1-u)/(1-u*exp(-t)))^2', 000113 | 'scope':'Chosen native E8 lattice-VOA vacuum, marked D5/A3 splitting, regularized charged vector; oscillator conformal grade, not particle number.', 000114 | 'physical_gates_closed':[], 'complete_TFPT_solution':False} 000115 | (here/'results.json').write_text(json.dumps(result,indent=2)+'\n') 000116 | print(json.dumps(result,indent=2)) 000117 | if result['passed']!=result['total']: raise SystemExit(1)