TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_b1_graded_charge_transport.py
Original file SHA-256: 5ddadb584e44a922c029e8e2095def3611329ce1af5ce1223029cde2fb8d6875
Inclusive original lines: 1-68
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 | """Decisive invariant for the existing actual v252 real-gauge dictionary.
000002 | 
000003 | Compare the specified grading/charge tuples, not all conceivable physical
000004 | carrier maps. No anomaly-free condition is substituted for source derivation.
000005 | """
000006 | from pathlib import Path
000007 | import json
000008 | import sys
000009 | import numpy as np
000010 | import sympy as s
000011 | 
000012 | ROOT=Path(__file__).resolve().parents[4]
000013 | sys.path.insert(0,str(ROOT/'verification'))
000014 | import v252_full_finite_triple as finite
000015 | K=finite.Kswap()
000016 | # Infinitesimal original connected unimodular lift:
000017 | # lambda=exp(it/2), m=exp(-it/6)I3, q=I2.
000018 | # Evaluate its derivative multiplied by 6, using Gaussian integers.
000019 | left6=finite.rep(3j,np.zeros((2,2)), -1j*np.eye(3)).imag
000020 | Y6=left6-K@left6@K
000021 | assert np.all(Y6==np.round(Y6))
000022 | charges6=[int(x) for x in np.diag(Y6)]
000023 | g=s.diag(*[int(x) for x in np.diag(finite.grading())])
000024 | q48=[int(name in ('u','d')) for name,ch,colour,family in finite.P]
000025 | q=s.diag(*(q48+q48))
000026 | gp=g*(2*q-s.eye(96))
000027 | Y=s.diag(*[s.Rational(x,6) for x in charges6])
000028 | def trace_power(grading,k):
000029 |     return sum(grading[i,i]*Y[i,i]**k for i in range(96))
000030 | def spectrum(grading):
000031 |     counts={}
000032 |     for i in range(96):
000033 |         key=f'grade={grading[i,i]},Y={Y[i,i]}'
000034 |         counts[key]=counts.get(key,0)+1
000035 |     return counts
000036 | actual=trace_power(g,3)
000037 | alternative=trace_power(gp,3)
000038 | sign_class=[]
000039 | for sq,sl in ((1,1),(1,-1),(-1,1),(-1,-1)):
000040 |     grading=g*(sq*q+sl*(s.eye(96)-q))
000041 |     sign_class.append({'quark_sign':sq,'lepton_sign':sl,
000042 |                        'trace3':str(trace_power(grading,3)),
000043 |                        'trace5':str(trace_power(grading,5)),
000044 |                        'same_joint_multiplicities_as_original':spectrum(grading)==spectrum(g)})
000045 | expected_particle=[]
000046 | for name,ch,colour,family in finite.P:
000047 |     expected_particle.append(({'nu':-3,'e':-3,'u':1,'d':1} if ch=='L' else {'nu':0,'e':-6,'u':4,'d':-2})[name])
000048 | checks={
000049 |     'original_real_gauge_charge_diagonal':s.Matrix([[int(x) for x in row] for row in Y6])==6*Y,
000050 |     'original_real_gauge_matches_actual_SM_field_charges':charges6==expected_particle+[-x for x in expected_particle],
000051 |     'original_total_cubic_graded_trace_zero':actual==0,
000052 |     'quark_cubic_trace_minus_9_over_2':s.trace(q*g*Y**3)==-s.Rational(9,2),
000053 |     'lepton_cubic_trace_plus_9_over_2':s.trace((s.eye(96)-q)*g*Y**3)==s.Rational(9,2),
000054 |     'alternative_cubic_graded_trace_minus_9':alternative==-9,
000055 |     'no_unitary_simultaneously_intertwines_specified_grading_and_charge':actual!=alternative,
000056 |     'joint_graded_charge_multiplicities_different':spectrum(g)!=spectrum(gp),
000057 |     'original_fifth_graded_trace_10_over_3':trace_power(g,5)==s.Rational(10,3),
000058 |     'only_original_sign_choice_preserves_fixed_joint_dictionary':sum(x['same_joint_multiplicities_as_original'] for x in sign_class)==1 and sign_class[0]['same_joint_multiplicities_as_original'],
000059 | }
000060 | result={'contract':'B1-GRADED-CHARGE-TRANSPORT-20261030','checks':checks,
000061 |         'original_cubic_graded_trace':str(actual),'alternative_cubic_graded_trace':str(alternative),
000062 |         'original_joint_multiplicities':spectrum(g),'alternative_joint_multiplicities':spectrum(gp),
000063 |         'complete_four_sector_sign_class':sign_class,
000064 |         'scope':'No unitary U with U*Y U=Y and U*gamma U=gamma(2q-I). Applies to the specified graded charge tuple only. Does not exclude alternate source maps with another transported intrinsic grading, extra sectors or inflow. Does not derive physical P_F.',
000065 |         'all_passed':all(checks.values())}
000066 | Path(__file__).with_name('B1-GRADED-CHARGE-TRANSPORT.json').write_text(json.dumps(result,indent=2)+'\n')
000067 | print(json.dumps(result,indent=2))
000068 | assert result['all_passed']