TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/RECOVERED-NATIVE-SOURCE-PROOF.txt Original file SHA-256: b6f3ea16db2b8d54e7fb593e69ba6c0752408be65ae2deab1593e4760347112c Inclusive original lines: 1-154 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 | R077. RECOVER OLD ORIGINAL SOURCE CALLERS BEFORE BUILDING NEW ONES 000002 | 1 November2026. Source recovery and actual finite native-consumer execution. 000003 | F1 remains in progress. No physical subgoal or new Lean theorem closed. 000004 | 000005 | 1. What was actually searched and what was not proved absent 000006 | 000007 | The live sole Atlas revision at entry was27ed786678a18f5a1062d8ff. 000008 | Paper coverage reports118 document views and6876 sections,33 source-error 000009 | and394 stale summary records. This is navigation coverage,not scientific 000010 | review. Hybrid searches were used for transport counts,source-dependent 000011 | transfer,T_V,S_adm,blocked tensor,source-functional and readout layers. 000012 | Noisy broad lexical/vector results were narrowed by exact original paths. 000013 | The source/code graph located v311,v486,v990 and v1015 actual functions. 000014 | Current plan49,its audit and latest results were read. Existing experiments 000015 | were inspected,including the October13source-functional audit,October25 000016 | paper recovery/older circle and current coupled inner-form response. 000017 | This is targeted original-source review,NOT re-review of every paper, 000018 | experiment,Lean proof or of all6876 sections. No absence inference from 000019 | truncated searches,missing paper_evidence links or stale summaries. 000020 | 000021 | 2. Recovered solution packet; exact original scope must be reused 000022 | 000023 | A. Older fullv21 circle/shift already has a twisted H1 domain and u=M_z. 000024 | ORIGINAL-CIRCLE-REVIEW.txt supplies the necessary B=-D_Gamma orientation 000025 | repair and exact Ward/index/defect calculation. Do not invent another 000026 | circle as a missing generic operator. This representative is not thereby 000027 | identified with every later physical B_Sigma or with physical OS time. 000028 | 000029 | B. The actual microscopic theorem at tex-artefacts/toe_research_20260909.tex 000030 | 16-96 already maps a specified filled QWZ strip to a charged chiral CAR 000031 | field,its adjoint,charge,time and every fixed smooth finite timed word on 000032 | a common finite-energy core. The existing MICROSCOPIC-TO-OCTIC-COMPOSITION 000033 | then uses ONE channel/eightfold fold and the fixed original current map. 000034 | No eight new source copies or charged E8 exhaustion is needed for that 000035 | neutral field. The primitive same-source/collar identification still 000036 | has its own domain,reflection,reference and physical scope. 000037 | 000038 | C. v42 section035 explicitly defines the formal parent exp W_k[J] with 000039 | S_adm,R_k and J phi,Legendre Gamma and Hessian inverse. The 1PI expansion 000040 | retains ALL higher S_adm derivatives. It is false to call the parent 000041 | formula entirely missing. It is also false to call a formal integral 000042 | an established measure solely because it has been displayed. Existing 000043 | OS-SOURCE-REPAIR must restore full moments from exp(W-W0);log derivatives 000044 | are connected cumulants,not full reflected OS moments. 000045 | 000046 | D. ACTUAL-ONEFORM-COUPLED-SOURCE-RESPONSE.txt already supplies the genuine 000047 | v252/v254 radial inner-fluctuation witness and the WHOLE coupled two-face 000048 | G_s at an existing Higgs background,including Majorana,noncommutative 000049 | Frechet derivative and all given CAR words. Later full Higgs-fibre work 000050 | remains inherited. No new Yukawa optimization or missing-Phi claim. 000051 | A background-conditional source is not its actual primitive bosonic 000052 | integration. Keep the whole measure,vertices,Z0,Ref/Eta/H0 and source 000053 | placement. Nor is bosonic Hessian=Dirac or Sbos=-logPf a new requirement. 000054 | 000055 | E. Native v990 implements an ACTUAL source W(J,theta)=logTr exp[-betaH(theta) 000056 | +sum J_a O_a]. It is positive finite Gibbs data with a real nonzero mixed 000057 | link/seam response. It uses two species of charges1 and0,two sites,one 000058 | quantumZ6 link. Its separately checked five-multiplet anomaly table is 000059 | not the particle content of this W. Original parameters lambdaE1,w.7, 000060 | mass.5,beta.35,mu.5 are supplied. It does not derive these from P1. 000061 | This is a useful reference consumer,not originalQFT004 T_V or the full 000062 | SM functional by a dimension/label match. All13 original checks pass now. 000063 | 000064 | F. v486 really solves stay/hop from the ALREADY specified survival 000065 | spectrum2/3,1/3. The actual source says direction:spectrum->rates and 000066 | retains the primitive split selection as open. All5 original checks pass 000067 | now. No new rates search or claimed first-principle selection. 000068 | 000069 | G. The existing central Lean audit and794-declaration export remain the 000070 | October30 evidence,not a new kernel run today. The old StageD interface 000071 | note specifies its exact supplied predicates;it does not show that later 000072 | solved Yukawa constructions are absent. v1015.claim_closure uses True 000073 | and source_contains for some closure-prose guards alongside genuine 000074 | finite computations elsewhere. Passing such guards is not execution of 000075 | an operational source law. Neither observation invalidates the proved 000076 | finite algebra or its existing audited Lean theorem. 000077 | 000078 | 3. Recover the old finite source's entire timed word caller 000079 | 000080 | Use v990.run UNCHANGED. A temporary Python return-frame observer records 000081 | its actual H_W0,O_Z,OPS after construction. No copied Hamiltonian,no new 000082 | couplings,no global modifications. Restore the previous profile function. 000083 | Let H denote that actual96matrix,beta its original value,Z0=Tr exp(-betaH). 000084 | For0<=t1<=...<=tn<=beta and the given even observables,define the caller 000085 | 000086 | M(O_n,t_n;...;O_1,t_1)= 000087 | Tr[e^(-(beta-t_n)H)O_n e^(-(t_n-t_(n-1))H)...O_1 e^(-t_1H)]/Z0. (1) 000088 | 000089 | This is the original Gibbs representation's imaginary-time ordered word: 000090 | insert O(t)=exp(tH)O exp(-tH) and telescope the existing exponentials. 000091 | It retains every intermediate propagator and the absolute original Z0. 000092 | The computational shift H->H-Emin cancels only in normalized(1);absolute 000093 | Z0 retains exp(-betaEmin). No new chosen continuum,positive-time or OS 000094 | identification with primitive TFPT is inferred. Odd direct matrix words 000095 | can retain their literal order;graded source derivatives/permutations 000096 | would separately need the actual Grassmann convention. Here OPS is even. 000097 | 000098 | For O=O_Z=O*,p_m=exp(-betaE_m)/Z0,its connected2word is exactly 000099 | C(tau)=sum_mn p_m exp[tau(E_m-E_n)]|O_mn|^2-^2. (2) 000100 | Since the original constant source enters as J O,NOT beta J O, 000101 | D_J^2 W|0 = int_0^1 C(s beta)ds=(1/beta)int_0^beta C(tau)dtau. (3) 000102 | Duhamel differentiation of the SAME matrix exponential proves(3). 000103 | The native kubo_connected is precisely this divided-difference integral. 000104 | Its output is not in general the equal-time variance C(0). 000105 | Pairing(m,n) and(n,m) proves C(tau)=C(beta-tau). Also C''>=0,and if 000106 | [H,O]!=0 it is strictly positive. Hence C(mid) =0.011037549114042717 000115 | C(0) =0.49988408263643075 000116 | native Kubo =0.49033650199002465 000117 | C(beta/2) =0.48558570858218447 000118 | C(0)-native Kubo =0.009547580646406095 000119 | ||[H,O_Z]||HS =9.797958971132712. 000120 | 64point Gauss integral matches nativeKubo within1.7e-16. One full4word 000121 | at times0,beta/4,beta/2,3beta/4 is0.3589907819211865. Values are arithmetic 000122 | controls of the original finite model,not physical TFPT predictions. 000123 | 000124 | 4. Actual representation and the misleading96 shortcut 000125 | 000126 | Native w_ferm=I6 tensor four-mode Jordan-Wigner annihilators. Their 000127 | unital *algebra is I6 tensor M16:occupation projectors and creation/ 000128 | annihilation words give all16x16matrix units. Its commutant is M6 tensorI16. 000129 | The common kernel of the four annihilators has dimension6. This is the 000130 | empty-CAR-sector multiplicity,NOT the thermal state or ground degeneracy 000131 | of H. Adding both link clock/shift gives the fullM96;the actual H couples 000132 | link and matter. Thus the commutant is not a spectator dynamics theorem. 000133 | The internal96 finite-triple coefficient space has a different operator 000134 | role. A bare equality of dimensions supplies no field/charge/source map. 000135 | For an unconstrained complex96modeCAR,the Fock dimension would be2^96; 000136 | this statement makes no claim about the physically constrained/KO doubled 000137 | SM Fock space or exclusion of all possible regulator representations. 000138 | 000139 | 5. Outcome and next decisive original call 000140 | 000141 | Recovered formal parent,microscopic field/time chain and coupled background 000142 | consumer are mandatory reuse. v990 supplies a genuine executable time/ 000143 | source comparison;v486 supplies a typed spectral reconstruction. No old 000144 | candidate reviewed here establishes the whole physical F1 source. This 000145 | is not a corpus-wide absence or TFPT impossibility theorem. 000146 | Next derive/execute the actual SAME original primitive-field map and 000147 | weight producer in S_adm/W_k or C_Sigma->P_F C_Sigma P_F,with its own 000148 | field support,time,domain,Ref/Eta/H0/Z0 and higher mixed words. C6/TV is 000149 | one named original route,not universal MPS or v990 identification duty. 000150 | Do not replace this by a freely selected Gaussian,Higgs law,96space, 000151 | profile,clock or new coupling. Preserve R035/R037/R043,R054/R063/R067/ 000152 | R068/R069/R071,all charged intermediate paths,memory,State/Time/RP, 000153 | E8/clocks and solved Y/flavor/alpha. Physical3+1 and universal spin2 remain 000154 | same-source targets. F1 stays in progress,38 existing scoped subtasks kept.