TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_doily_record_orientation.py
Original file SHA-256: 4deb52b5132693a1ddd99cefb49c301b6cacfef62d26a0412cec932b4dfe0d5e
Inclusive original lines: 1-106
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 | #!/usr/bin/env python3
000002 | """R064: native E8 record action, typed Sym2 lift and ordered response.
000003 | Reconstructs original source. No physical state, clock or geometry selected.
000004 | """
000005 | from pathlib import Path
000006 | import sys,json,hashlib,itertools as it
000007 | import numpy as np
000008 | import sympy as sp
000009 | ROOT=Path(__file__).resolve().parents[4]
000010 | SOURCE=ROOT/'experiments/theory-contracts/compiler-correlated-event-clock-20260919/source_channel.py'
000011 | sys.path.insert(0,str(SOURCE.parent))
000012 | import source_channel as s
000013 | checks=[]
000014 | def require(name,test):
000015 |     ok=bool(test);checks.append(dict(name=name,passed=ok))
000016 |     if not ok:raise RuntimeError(name)
000017 | def exact(m):
000018 |     return sp.Matrix([[sp.Rational(float(v.real))+sp.I*sp.Rational(float(v.imag)) for v in row] for row in m])
000019 | require('unchanged original source SHA',hashlib.sha256(SOURCE.read_bytes()).hexdigest()=='3852fabaf10c143fe20238b67406df6396f85c931dfd4834fe91a2d7ef900593')
000020 | zs=s.source_rays();clock,_,_=s.reflection_actions(zs)
000021 | P=s.PAULIS;labels=s.V4;non=[j for j,x in enumerate(labels) if any(x)]
000022 | Rs=[np.eye(4)-np.outer(z,z.conj())/2 for z in zs]
000023 | F=np.column_stack([p.reshape(-1)/2 for p in s.SYMMETRIC_PAULIS])
000024 | require('actual Bell10 embedding isometry',np.array_equal(F.conj().T@F,np.eye(10)))
000025 | require('actual Bell10 lies in symmetric tensors',all(np.array_equal(F[:,j].reshape(4,4).T,F[:,j].reshape(4,4)) for j in range(10)))
000026 | require('actual original U is Sym2 r in this embedding',all(np.array_equal(U,F.conj().T@np.kron(R,R)@F) for U,R in zip(clock,Rs)))
000027 | perms=[];sgns=[];groups={};routing=[]
000028 | for ri,R in enumerate(Rs):
000029 |     perm={};sign={}
000030 |     for a in non:
000031 |         b,ph=s.phase_match(R@P[a]@R.conj().T,P,1)
000032 |         perm[a]=b;sign[a]=int(round(ph.real))
000033 |     L=tuple(a for a in non if perm[a]==a);groups.setdefault(L,[]).append(ri)
000034 |     for a in non:
000035 |         if a in L:continue
000036 |         qs=[q for q in L if s.symp(labels[a],labels[q])==0]
000037 |         if len(qs)!=1:raise RuntimeError('unique compatible point')
000038 |         q=qs[0];hit=tuple(x^y for x,y in zip(labels[a],labels[q]))
000039 |         routing.append((labels[perm[a]]==hit,perm[a]!=q,perm[a] not in L))
000040 |     perms.append(perm);sgns.append(sign)
000041 | require('native context grouping fifteen groups of four',len(groups)==15 and all(len(v)==4 for v in groups.values()))
000042 | require('all 720 external ray-point actions are p to p+q not p to q',len(routing)==720 and all(all(z) for z in routing))
000043 | require('all sixty unsigned actions involutive',all(all(p[p[a]]==a for a in non) for p in perms))
000044 | require('each context action fixes three and swaps six pairs',all(sum(p[a]==a for a in non)==3 for p in perms))
000045 | A=np.array([[int(a!=b and s.symp(labels[a],labels[b])==0) for a in non] for b in non])
000046 | T=np.zeros((15,15),dtype=int);S=np.zeros((15,15),dtype=int)
000047 | for j,a in enumerate(non):
000048 |     for p,sgn in zip(perms,sgns):
000049 |         i=non.index(p[a]);T[i,j]+=1;S[i,j]+=sgn[a]
000050 | require('unsigned label count is 12I+8A',np.array_equal(T,12*np.eye(15,dtype=int)+8*A))
000051 | require('unsigned label count symmetric stochastic after division60',np.array_equal(T,T.T) and np.array_equal(T.sum(axis=0),np.full(15,60)))
000052 | require('signed fundamental Pauli mean is 12I/60',np.array_equal(S,12*np.eye(15,dtype=int)))
000053 | Q={};J={}
000054 | for a in non:
000055 |     pp=(np.eye(4)+P[a])/2
000056 |     Q[a]=F.conj().T@np.kron(pp,pp)@F
000057 |     J[a]=F.conj().T@(np.kron(P[a],np.eye(4))+np.kron(np.eye(4),P[a]))@F
000058 | require('fifteen actual plus-sector tensor lifts are rank3 projections',all(np.array_equal(q@q,q) and np.trace(q)==3 for q in Q.values()))
000059 | require('all actual J have spectrum plus2x3 zero4 minus2x3',all(np.allclose(np.linalg.eigvalsh(j),[-2]*3+[0]*4+[2]*3,atol=1e-14,rtol=0) for j in J.values()))
000060 | require('all 900 actual Sym2 record-J intertwiners exact binary arithmetic',all(np.array_equal(U@J[a]@U.conj().T,sgns[i][a]*J[perms[i][a]]) for i,U in enumerate(clock) for a in non))
000061 | require('all 900 sector lifts transport with retained sign',all(np.array_equal(U@Q[a]@U.conj().T,F.conj().T@np.kron((np.eye(4)+sgns[i][a]*P[perms[i][a]])/2,(np.eye(4)+sgns[i][a]*P[perms[i][a]])/2)@F) for i,U in enumerate(clock) for a in non))
000062 | # Source matrices and lifted probes contain only small Gaussian dyadic rationals.
000063 | require('all matrices used in bulk identities are small Gaussian half-integers',all(np.array_equal(2*m.real,np.round(2*m.real)) and np.array_equal(2*m.imag,np.round(2*m.imag)) and np.max(abs(m))<=2 for m in [F]+clock+Rs+list(J.values())+list(Q.values())))
000064 | # Analytic proof plus exact symbolic named witnesses, independent of eigensolver tolerances.
000065 | Fe=exact(F);r=exact(Rs[0]);v=exact(Rs[13]);I4=sp.eye(4)
000066 | require('named rays original ordering',np.array_equal(zs[0],[-2,0,0,0]) and np.array_equal(zs[13],[-1,-1,-1,-1]))
000067 | require('named reflection r and s exact',r==sp.diag(-1,1,1,1) and v==I4-sp.ones(4)/2)
000068 | Ur=Fe.conjugate().T*sp.kronecker_product(r,r)*Fe
000069 | Us=Fe.conjugate().T*sp.kronecker_product(v,v)*Fe
000070 | require('named actual clock matrices exact',Ur==exact(clock[0]) and Us==exact(clock[13]))
000071 | require('probe labels actual IZ and XI',np.array_equal(P[1],np.kron(np.eye(2),np.diag([1,-1]))) and np.array_equal(P[8],np.kron([[0,1],[1,0]],np.eye(2))))
000072 | rho=exact(Q[1])/3;E=exact(Q[8]);V=Us*Ur;W=Ur*Us
000073 | p_rs=sp.trace(E*V*rho*V.conjugate().T);p_sr=sp.trace(E*W*rho*W.conjugate().T)
000074 | require('exact actual ordered conditional responses 1/3 and1',p_rs==sp.Rational(1,3) and p_sr==1)
000075 | AA=sp.eye(4)[:,[0,2]];BB=sp.Matrix([[1,0],[0,1],[1,0],[0,1]])/sp.sqrt(2)
000076 | M1=BB.T*v*r*AA;M2=BB.T*r*v*AA;K1=M1.conjugate().T*M1;K2=M2.conjugate().T*M2
000077 | require('independent compressed fundamental amplitudes have squared singular values 1/0 and1/1',K1*K1==K1 and sp.trace(K1)==1 and K2==sp.eye(2))
000078 | require('independent symmetric tensor trace reproduces both actual order responses',((sp.trace(K1))**2+sp.trace(K1*K1))/6==p_rs and ((sp.trace(K2))**2+sp.trace(K2*K2))/6==p_sr)
000079 | 
000080 | require('exact actual original joint record-final probabilities',p_rs/3600==sp.Rational(1,10800) and p_sr/3600==sp.Rational(1,3600))
000081 | a=2;Rloop=exact(Rs[54])*r
000082 | require('exact two-record phase loop flips sector on same label',Rloop*exact(P[a])*Rloop.conjugate().T==-exact(P[a]) and perms[54][perms[0][a]]==a)
000083 | walsh=np.array([[1,1,1,1],[1,1,-1,-1],[1,-1,1,-1],[1,-1,-1,1]])
000084 | context_data=[]
000085 | for L,rs in groups.items():
000086 |     U0=clock[rs[0]];H=[clock[i]@U0 for i in rs]
000087 |     if not np.array_equal(H[1]@H[2],H[3]):raise RuntimeError('relative Klein group')
000088 |     qs=[sum(c*h for c,h in zip(row,H))/4 for row in walsh]
000089 |     if not all(np.array_equal(q@q,q) for q in qs):raise RuntimeError('character projection')
000090 |     if not all(np.array_equal(q@v,np.zeros((10,10))) for i,q in enumerate(qs) for v in qs[i+1:]):raise RuntimeError('character orthogonality')
000091 |     if not np.array_equal(sum(qs),np.eye(10)):raise RuntimeError('character completeness')
000092 |     if sorted(int(np.trace(q).real) for q in qs)!=[2,2,2,4]:raise RuntimeError('character ranks')
000093 |     # Remove common sqrt15: original branches are U_j/2, rotated U0 Qchi.
000094 |     if not all(np.array_equal(sum(c*clock[i] for c,i in zip(row,rs))/4,U0@q) for row,q in zip(walsh,qs)):raise RuntimeError('Walsh Kraus identity')
000095 |     left=sum(np.kron(clock[i],clock[i].conj()) for i in rs)/4
000096 |     right=sum(np.kron(U0@q,(U0@q).conj()) for q in qs)
000097 |     if not np.array_equal(left,right):raise RuntimeError('coarse channel preserved')
000098 |     context_data.append(dict(line=list(L),ray_indices=rs,character_ranks=[int(np.trace(q).real) for q in qs]))
000099 | require('all fifteen actual contexts have relative Klein four and rank4/2/2/2 character projectors',len(context_data)==15)
000100 | require('all fifteen actual coherent record rotations preserve coarse CP map with exact Kraus identity',len(context_data)==15)
000101 | L,rs=next(iter(groups.items()));U0=clock[rs[0]];H=[clock[i]@U0 for i in rs];q=sum(H)/4;rank=int(np.trace(q).real)
000102 | require('conditional character readout gives selected outcome probability1',np.trace(q@(q/rank))==1)
000103 | require('native global event effects are I/60',all(np.array_equal(U.conj().T@U,np.eye(10)) for U in clock))
000104 | require('coherent rotated global effect is Q/15 by Walsh unitarity',np.array_equal(walsh@walsh.T,4*np.eye(4)))
000105 | res=dict(result_id='R064',date='2026-11-01',all_passed=True,controls=len(checks),checks=checks,original_source_sha256=hashlib.sha256(SOURCE.read_bytes()).hexdigest(),original_source_inherited_controls=len(s.checks) if hasattr(s,'checks') else None,routing_cases=720,unique_incidence_cases=180,actual_intertwining_cases=900,unsigned_label_walk='(3I+2A)/15; spectrum 1^1,(1/3)^9,(-1/5)^5; labels only',fundamental_signed_mean='W_p/5; not the full End(Sym2 C4) channel',actual_clock_dimension=10,actual_clock_full_spectrum_reused='1^1,(1/3)^9,(1/5)^45,(1/15)^45',ordered_witness=dict(input_label=list(labels[1]),effect_label=list(labels[8]),ray_indices=[0,13],conditional_rs=str(p_rs),conditional_sr=str(p_sr),joint_rs=str(p_rs/3600),joint_sr=str(p_sr/3600),difference=str((p_sr-p_rs)/3600),scope='explicit mathematical preparation/effect, not physical vacuum or causal spacetime'),same_label_opposite_sector_witness=dict(label=list(labels[2]),ray_indices=[0,54]),context_data=context_data,record_basis_scope='alternative coherent readout conditional on access; original specified record instrument is retained',physical_origin_closed=False,new_lean_formalization=False)
000106 | out=Path(__file__).with_name('DOILY-RECORD-ORIENTATION.json');out.write_text(json.dumps(res,ensure_ascii=False,indent=2)+'\n');print(json.dumps({k:res[k] for k in ['result_id','all_passed','controls','routing_cases','actual_intertwining_cases','ordered_witness']}))