TFPT scientific source excerpt Original repository path: experiments/theory-contracts/mixed-current-origin-20261014/check_odd_refielding.py Original file SHA-256: cdf152af1b8ad56a2a0ce46a847324e523cc779d2b65f7f6f35f25acd1781b5e Inclusive original lines: 1-132 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. 000001 | """Exact controls for the old-rho, parity-conditioned odd-sector re-fielding. 000002 | 000003 | This is a source/time-compatible representation candidate, not a P1 local 000004 | field construction. Its locality failure is part of the controlled result. 000005 | """ 000006 | from fractions import Fraction as F 000007 | from collections import defaultdict 000008 | from pathlib import Path 000009 | import json 000010 | import sympy as S 000011 | 000012 | 000013 | def need(value, label): 000014 | if not value: 000015 | raise ValueError(label) 000016 | 000017 | 000018 | def theta_charge(alpha, half, cutoff=128): 000019 | state={(0,0,F(0)):1} 000020 | for k in range(8): 000021 | delta=(F(k)+alpha)/8-F(1,2) 000022 | base=F(1,2) if delta<0 else F(-1,2) 000023 | baseline=16*base*base+32*delta*base if half else 0 000024 | options=[] 000025 | for m in range(-4,5): 000026 | q=F(m)+F(1,2) if half else F(m) 000027 | e=16*q*q+32*delta*q-baseline 000028 | if 0<=e<=cutoff: 000029 | need(e.denominator==1,'integral quarter-energy exponent') 000030 | options.append((int(e),m%2,q)) 000031 | nxt=defaultdict(int) 000032 | for (energy,parity,charge),count in state.items(): 000033 | for e,p,q in options: 000034 | if energy+e<=cutoff: 000035 | nxt[energy+e,(parity+p)%2,charge+q]+=count 000036 | state=dict(nxt) 000037 | return state 000038 | 000039 | 000040 | P=S.zeros(8) 000041 | for k in range(8):P[k,(k+4)%8]=1 000042 | r=S.Matrix([S.Rational(1,2)]*4+[-S.Rational(1,2)]*4) 000043 | R=S.zeros(8) 000044 | for k in range(8):R[k,(k-1)%8]=1 000045 | A=P*R 000046 | unit0=S.eye(8)[:,0] 000047 | lam=P*unit0+r 000048 | need(R*P==P*R and R*r+unit0==lam,'same primitive winding map on both parities') 000049 | need(lam.dot(lam)==2 and sum(lam)==1,'primitive winding spinor root and unit total charge') 000050 | need(A**8==S.eye(8),'primitive winding permutation order8') 000051 | need(sum((A**j*lam for j in range(8)),S.zeros(8,1))==S.ones(8,1), 000052 | 'eight primitive steps retain integer charge carry') 000053 | checks=[] 000054 | for alpha in [S.Rational(1,4),S.Rational(3,4)]: 000055 | delta=S.Matrix([(k+alpha)/8-S.Rational(1,2) for k in range(8)]) 000056 | need(P*P==S.eye(8) and P*r==-r,'rho involution') 000057 | need(P*delta==delta+r,'full energy linear coefficient') 000058 | need(r.dot(r)/2+delta.dot(r)==0,'full energy constant') 000059 | need(sum(r)==0,'total charge preserved') 000060 | symbols=S.Matrix(S.symbols('p0:8')) 000061 | K=lambda v:v.dot(v)/2+delta.dot(v) 000062 | transformed=A*symbols+lam 000063 | need(S.expand(K(transformed)-K(symbols)-(sum(symbols)+alpha)/8)==0, 000064 | 'primitive W1 exact source Ward energy increment') 000065 | a=theta_charge(F(int(alpha.p),int(alpha.q)),False) 000066 | b=theta_charge(F(int(alpha.p),int(alpha.q)),True) 000067 | need(a==b,'all exact parity/energy/total-charge coefficients through128') 000068 | checks.append({'alpha':str(alpha),'all_energy_Q_parity_coefficients_equal_through_quarter_units':128, 000069 | 'coefficient_keys':len(a)}) 000070 | 000071 | # The changed current's failure of original microscopic locality has a 000072 | # bounded exact three-mode CAR witness. Modes0,1 local;mode2 remote. 000073 | def annihilator(k): 000074 | out=S.zeros(8) 000075 | for bits in range(8): 000076 | if bits&(1<>3)&1) for m in basis]) 000101 | root=S.zeros(16) 000102 | for m in basis: 000103 | if m&(1<<4) and not m&(1<<3): 000104 | sign=(-1)**((m&((1<<4)-1)).bit_count()) 000105 | t=m^(1<<4) 000106 | sign*=(-1)**((t&((1<<3)-1)).bit_count()) 000107 | t|=1<<3 000108 | root[index[t],index[m]]=sign 000109 | anchor_comm=chi*root-root*chi 000110 | need(anchor_comm.rank()==4,'finite anchor sign is not invariant under D5 root E45') 000111 | need(S.trace(anchor_comm.T*anchor_comm)==16,'finite anchor commutator HS square') 000112 | 000113 | result={'date':'2026-10-22','result':'EXACT_TIME_Q_COMPATIBLE_ODD_REFIELDING_BUT_NOT_ORIGINAL_LOCAL_NET', 000114 | 'rho_involution_Q_and_energy_preserved':True, 000115 | 'theta_controls':checks, 000116 | 'proof_of_all_energy_equality':'rho(p)=Pp+r,Pr=-r,Pdelta=delta+r,r²/2+delta.r=0', 000117 | 'even_sector_unchanged':True, 000118 | 'primitive_W1_target_action':'q -> A q+lambda, A=P R=R^5, lambda=(1/2)^5(-1/2)^3', 000119 | 'primitive_W1_charge_increment':1, 000120 | 'primitive_W1_K_increment':'(Q+alpha)/8', 000121 | 'primitive_W1_eighth_power':'q -> q+(1)^8; charge increases8', 000122 | 'primitive_W1_is_local_spinor_field':False, 000123 | 'odd_Cartan_beta_pullback':'H_beta becomes1-H_beta for beta=e0-e4', 000124 | 'proper_locality_obstruction':'For mean-zero localized beta-current and Pbeta=-beta,Wprime=Pi_even W+Pi_odd W*. For an odd remote CAR unitary B,[Wprime,B]=parity B(W-W*),nonzero.', 000125 | 'exact_finite_CAR_commutator_norm':2, 000126 | 'finite_Arf_anchor_sign_D5_root_commutator_rank':4, 000127 | 'finite_Arf_anchor_sign_D5_root_commutator_HS_squared':16, 000128 | 'finite_Arf_scope':'Excludes literal D5-equivariant identification of the existing anchor-bit sign with a uniform central NS/R boundary label; no refutation of the finite Arf theorem or all geometric Pfaffian maps.', 000129 | 'microscopic_P1_spinor_origin_derived':False, 000130 | 'new_energy_or_source_copy_chosen':False} 000131 | Path(__file__).with_name('odd-refielding-results.json').write_text(json.dumps(result,indent=2)+'\n') 000132 | print(json.dumps(result,indent=2))