TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/mixed-current-origin-20261014/check_kms_locality_and_source_winding.py
Original file SHA-256: 7c6e4579da19d55089a95f751e72a37af250e51360ee4b02fa499df7e2fba2a7
Inclusive original lines: 35-144
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.

000035 |      'nonzero exact even-locality witness')
000036 | 
000037 | # Refined central character of the existing odd Phi, checked on source charges.
000038 | r=s.Matrix([s.Rational(1,2)]*4+[-s.Rational(1,2)]*4)
000039 | charges=[s.zeros(8,1)]
000040 | for i in range(8):
000041 |     for v in (-2,-1,1,2):
000042 |         p=s.zeros(8,1);p[i]=v;charges.append(p)
000043 | for i in range(7):
000044 |     p=s.zeros(8,1);p[i]=1;p[i+1]=1;charges.append(p)
000045 | for p in charges:
000046 |     parity=1 if int(sum(p))%2==0 else -1
000047 |     q=p if parity==1 else s.Matrix([p[(k+4)%8] for k in range(8)])+r
000048 |     need(sum(q)==sum(p),'existing Phi total charge')
000049 |     need(all(s.exp(2*s.pi*s.I*qk)==parity for qk in q),
000050 |          'target individual Cartan holonomy equals old parity')
000051 |     need(all(s.exp(2*s.pi*s.I*pk)==1 for pk in p),
000052 |          'old individual Cartan holonomy is identity')
000053 | 
000054 | # Exact truncated ORIGINAL edge spectrum, partition and parity trace.
000055 | # This is a finite control of analytic infinite products proved in the text.
000056 | x=s.symbols('x')
000057 | levels=[1,3,5,7,9,11,13,15]  # energies in units of1/4, eitherquarter.
000058 | zpoly=s.prod(1+x**e for e in levels)
000059 | spoly=s.prod(1-x**e for e in levels)
000060 | ztrace=0;strace=0
000061 | for bits in itertools.product((0,1),repeat=len(levels)):
000062 |     term=x**sum(v*e for v,e in zip(bits,levels))
000063 |     ztrace+=term;strace+=(-1)**sum(bits)*term
000064 | need(s.expand(ztrace-zpoly)==0 and s.expand(strace-spoly)==0,
000065 |      'full finite original-edge trace/product identity')
000066 | ze,zo=(zpoly+spoly)/2,(zpoly-spoly)/2
000067 | need(s.cancel((ze**2-zo**2)/(ze**2+zo**2)
000068 |               -2*zpoly*spoly/(zpoly**2+spoly**2))==0,
000069 |      'total-even two-edge central character formula')
000070 | need(s.cancel(1-2*zpoly*spoly/(zpoly**2+spoly**2)
000071 |               -(zpoly-spoly)**2/(zpoly**2+spoly**2))==0,
000072 |      'strictly positive two-edge thermal defect')
000073 | 
000074 | # Source charge-one winding parity, checked algebraically without making a
000075 | # truncated shift a supposedly unitary finite spectral-flow implementation.
000076 | u,v=s.symbols('u v')
000077 | P=s.diag(1,-1);W=s.Matrix([[0,u],[v,0]]);Pe=(s.eye(2)+P)/2
000078 | need(P*W+W*P==s.zeros(2),'odd source winding parity relation')
000079 | need(Pe*W*Pe==s.zeros(2),'left-even projection removes source W1 compression')
000080 | need(W.H*P*W*P==-W.H*W,'exact odd-winding/Cartan four-word sign')
000081 | 
000082 | thermal=[]
000083 | for alpha in (.25,.75):
000084 |     for beta in (.7,2*math.pi,8.):
000085 |         energies=np.array([e for m in range(96) for e in (m+alpha,m+1-alpha)])
000086 |         ratio=float(np.prod(np.tanh(beta*energies/2)))
000087 |         even_expect=2*ratio/(1+ratio*ratio)
000088 |         need(0<ratio<1 and 0<even_expect<1,'all-beta formulas finite controls')
000089 |         thermal.append({'alpha':alpha,'beta_source_H':beta,
000090 |             'single_edge_target_Cartan_holonomy':ratio,
000091 |             'total_even_two_edge_target_holonomy':even_expect,
000092 |             'old_Cartan_holonomy':1.})
000093 | 
000094 | # Actual original QWZ time moves an even number observable out of its region.
000095 | sys.path.insert(0,str(REPO/'verification'))
000096 | source=REPO/'verification/v1033_charged_disorder.py'
000097 | spec=importlib.util.spec_from_file_location('kms_audit_v1033',source)
000098 | mod=importlib.util.module_from_spec(spec);sys.modules[spec.name]=mod
000099 | spec.loader.exec_module(mod)
000100 | actual=[]
000101 | for sector in (1,3):
000102 |     nx,ny=8,8
000103 |     h=mod.qwz_cylinder(nx,ny,1.,sector)*nx/(2*math.pi)
000104 |     es,vs=np.linalg.eigh(h)
000105 |     t=.2
000106 |     U=(vs*np.exp(1j*t*es))@vs.conj().T
000107 |     j0=0                  # source site inside column0
000108 |     j1=2*ny              # exterior observable in adjacent column1
000109 |     f=U[:,j0]
000110 |     number_t=np.outer(f,f.conj())
000111 |     number_out=np.zeros_like(h);number_out[j1,j1]=1
000112 |     c=number_t@number_out-number_out@number_t
000113 |     cnorm=float(np.linalg.norm(c,2))
000114 |     need(cnorm>1e-4,'actual original-time fixed-region invariance fails')
000115 |     original=np.zeros_like(h);original[j0,j0]=1
000116 |     need(np.linalg.norm(original@number_out-number_out@original)<1e-14,
000117 |          'the original even local observables commute before time transport')
000118 |     # Single-mode reduced thermal state: modular flow fixes its number.
000119 |     beta=.7
000120 |     C=(vs*(1/(1+np.exp(beta*es))))@vs.conj().T
000121 |     occupation=float(C[j0,j0].real)
000122 |     need(0<occupation<1,'actual restricted finite thermal state is faithful')
000123 |     actual.append({'sector':sector,'Nx':nx,'Ny':ny,'physical_source_time':t,
000124 |         'outside_even_number_commutator_norm':cnorm,
000125 |         'local_thermal_occupation':occupation,
000126 |         'local_modular_one_mode_energy':math.log((1-occupation)/occupation)})
000127 | 
000128 | result={'date':'2026-10-23','checks_passed':True,
000129 |     'verdict':'KMS_GIVEN_EXTENSION_DOES_NOT_SUPPLY_MICROSCOPIC_LOCAL_SPINOR_MAP',
000130 |     'analytic_CAR_witness_rank':int(comm.rank()),
000131 |     'refined_charge_samples':len(charges),
000132 |     'finite_edge_fock_states':2**len(levels),
000133 |     'thermal_original_edge_controls':thermal,'actual_QWZ_time_controls':actual,
000134 |     'actual_source_sha256':hashlib.sha256(source.read_bytes()).hexdigest(),
000135 |     'global_rotations_equal_fixed_interval_modular_flow':False,
000136 |     'conditional_expectation_uniqueness_refuted':False,
000137 |     'source_W1_identified_with_primitive_P1_circle':False,
000138 |     'unitary_source_winding_Cartan_four_word_signs':{'old':1,'target':-1},
000139 |     'new_microscopic_spinor_sector':False,'all_P1_no_go':False}
000140 | (HERE/'kms-locality-and-source-winding-results.json').write_text(
000141 |     json.dumps(result,ensure_ascii=False,indent=2)+'\n')
000142 | print(json.dumps({'checks_passed':True,'actual_quarters':2,
000143 |     'fixed_interval_invariance_failed':True,'thermal_dictionary_witness':True,
000144 |     'source_W1_survives_left_even_projection':False}))