TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/WHOLE-ALPHABET-ORIGINAL-CALLER-AND-PH-REVIEW.txt Original file SHA-256: 291762f7a4ebd7d6f98fbbbb5ca50e761cbbf4517f575d948330403699766c84 Inclusive original lines: 1-160 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 | WHOLE ALPHABET: THE ORIGINAL CALLER, ITS DOMAIN, AND THE ACTUAL PH TERM 000002 | 30 October2026. Source review and analytic calculation, no Atlas mutation. 000003 | This is a bounded continuation/pending caller audit, not a new P1 conclusion. 000004 | 000005 | 1. THE STRONGEST ORIGINAL COMMON SOURCE CALLER ACTUALLY READ 000006 | 000007 | Under documents/archive--tfpt-45--source_extracts--04_qft_source/sections/: 000008 | 002-section-closure-theorems-from-the-admissibility-complex.tex:256-265 000009 | defines Zrel[J,eta,bareta]=Zadm[J,eta,bareta]/Zref[0,0,0]. The reference 000010 | is a source-independent normalizer. This gives no additional insertion. 000011 | 005-subsection-admissible-schwinger-functions-minkowski-loca.tex:144-160 000012 | defines Wrel=logZrel and its local-source functional derivatives. The 000013 | actual common source includes bosonic J and the fermionic eta,bareta. 000014 | 008-section-relative-reflection-positivity-with-fermions.tex:181-212 000015 | uses local source monomials and Schwartz test distributions;217-225 gives 000016 | the conditional OS/CAR reconstruction and its positive Euclidean time. 000017 | 007-subsection-renormalized-physical-and-scheme-readout-laye.tex:3-22 000018 | actually writes the source integral 000019 | exp Wk[J]=integral Dvarphi exp[-Sadm[varphi]-/2 000020 | +]. 000021 | Its121-140 uses Gk,phi=(Sadm^(2)[phi]+Rk)^-1 and the true higher action 000022 | vertices. The source test is linear in its specified field variable, 000023 | not automatically an arbitrary one-particle matrix tilt. 000024 | 000025 | The already bound primitive action in boundary_source001:302-316 and 000026 | BMU-ORIGINAL-ACTION-FIRST-RESPONSE-REVIEW.txt is retained: its Dref/Drel, 000027 | R, gap scale, eta and domain variations cannot be dropped. In particular 000028 | the geometric Bmu form does not by itself define an admissible dotD. 000029 | No old H1/clock/G/W/WEDGE link is reopened by this observation. 000030 | 000031 | FIRST ACTUAL OPERATION STILL TO IDENTIFY IN THIS CALLER 000032 | Which original local field/source monomial, sewn boundary restriction, 000033 | or actual admitted action tangent has the already computed Bmu response? 000034 | This is a concrete typed application, not a demand that every theory use 000035 | one fixed compression prescription or identify Hardy with the whole Y. 000036 | A quadratic source test uses two Grassmann derivatives (with their true 000037 | endpoints/order); its connected product uses the FULL four-field response. 000038 | For a free source, fourth Grassmann cumulants vanish, but connected 000039 | correlations of quadratic composites still have cross Wick contractions. 000040 | Those two meanings of 'connected second response' must not be conflated. 000041 | 000042 | 2. THE ACTUAL WHOLE CROSS-FACE CANDIDATE AND ITS FIRST DOMAIN TEST 000043 | 000044 | Reuse the given graph P=G, E=V E0, J=Swap tensor j and the fixed original 000045 | normal one-form Mmu on both labeled faces. Its entire formal neutral 000046 | quadratic test is Tmu=J* Mmu=Swap tensor(j* Mmu). No new q/p species, 000047 | state, finite defect Hamiltonian or dGamma(Mfinite) is introduced here. 000048 | If this test is the one claimed in Z, its finite spectral restrictions 000049 | have the standard CAR connected word 000050 | omega(Q(T)* Q(S))_c=Tr[P T* (I-P) S] 000051 | =<(I-P)T P,(I-P)S P>_HS. (1) 000052 | This is obtained directly from the existing full projector state's Wick 000053 | rules. It is not multiplication of the six compressed matrices. 000054 | 000055 | The actual induced mu_ab has, on a nonzero surviving normal/Hom component, 000056 | f(theta)~A_j |theta-theta_j|^(-2/3) at a ramification mark. It is L1, 000057 | but not L2. See SPIN-PRODUCT-BOUNDARY-WEIGHT-REVIEW.txt:55-140: the 000058 | retained G metrics and both W halfdensities do not erase this multiplier 000059 | weight. In scalar induction the norm is the sum over the three actual 000060 | cables, not a scalar sum that can cancel a nonzero leading matrix norm. 000061 | One therefore has a smooth original NS test column e on which Mmu e 000062 | is not L2. This does not invalidate its already convergent L1 form reader. 000063 | 000064 | There is a particularly small test of the SAME unsmoothed quadratic 000065 | interpretation in(1). Use the original n=0 NS mode, p=1/2, in a nonzero 000066 | surviving component. Let v=(c,d), c,d>0, be its graph vector, and let 000067 | a_m be the Fourier coefficients of j* Mmu applied to that test column. 000068 | Since j is unitary on the given q/p spaces, sum_m||a_m||^2=infinity. 000069 | The output face vector of Tmu is Swap v=(d,c). At large positive m, 000070 | P_m ->diag(1,0); at large negative m, P_m ->diag(0,1). 000071 | Consequently 000072 | ||(I-P_m)Swap v||^2 -> c^2 or d^2, 000073 | and it is bounded below by a positive constant on both tails. Thus the 000074 | canonical finite-spectral-cutoff norms in(1) diverge already on this 000075 | single occupied input column. The bare whole quadratic has no vacuum 000076 | L2 vector with this unmodified singular multiplier interpretation. 000077 | 000078 | This is a DOMAIN DIAGNOSTIC of that specific proposed application. It 000079 | does not show that the original Z chooses it, exclude a sewn/relative 000080 | or renormalized insertion, or contradict the given source's RP, state 000081 | and time. The original generic source definition has not selected this 000082 | composite prescription. Do not promote the diagnostic to a general P1 000083 | exclusion or replace the source by a better-converging test by choice. 000084 | 000085 | [OMITTED: non-scientific conversation or execution metadata] 000086 | 000087 | In the same actual source let Vperp=(-sqrt(1-A),sqrt A)^t and Eh=Vperp E0. 000088 | This is the orthogonal complement of the graph; it is not a new source. 000089 | With c^2=a,d^2=1-a, using the full J=Swap tensor j gives the face table 000090 | pp: (Swap v)*v=2cd, 000091 | ph: (Swap v)*vh=a-(1-a), 000092 | hp: (Swap vh)*v=a-(1-a), 000093 | hh: (Swap vh)*vh=-2cd, vh=(-d,c). (2) 000094 | The spatial R, actual spin, G/Kummer/Hom and normal factor are identical 000095 | in all four entries. They were carried in the proven pp period; changing 000096 | only v to vh therefore leaves the SAME period and the same P_gamma,+. 000097 | In a transported p-hole chart J vh has an extra minus sign relative to 000098 | the canonical hole vector at energy -p. Formula(2) already retains it. 000099 | 000100 | Put mF=I02 E02+I21 E21, mN=-i(I02 E12+I21 E20), with the six original 000101 | cubic phases from HARDY-BMU-ALL-SIX-INPUT-READER.txt. At NS p=1/2, 000102 | Lmu=(2/pi)mmu, 000103 | pp=sech(ell_NS/2)Lmu=Mmu_finite, 000104 | ph=hp=tanh(ell_NS/2)Lmu=sinh(ell_NS/2)Mmu_finite, 000105 | hh=-pp. (3) 000106 | This is a genuine finite summand of the whole proposed Wick word, not 000107 | the whole covariance or an original instruction to keep only that term. 000108 | For two unadjointed tests its contribution is 000109 | (2/pi)^2 tanh^2(ell_NS/2) Tr(mmu mnu), 000110 | and for the actual normal/internal trace multiply by rank(P_gamma,+)=16 000111 | per family. In particular 000112 | Tr(mF^2)=Tr(mN^2)=0, 000113 | Tr(mF mN)=Tr(mN mF)=-2i I02 I21 000114 | =2i C^2 L[L+pi(sqrt2-1)]. (4) 000115 | Its phase is exactly -pi/3 with the existing normalized periods. With 000116 | the adjoint test the positive finite summand is instead 000117 | (2/pi)^2 tanh^2(ell_NS/2)(|I02|^2+|I21|^2), 000118 | again times the retained carrier trace. It is a lower summand of the 000119 | positive full-cutoff variance, which need not be finite in the limit. 000120 | The statements 'all physical products only couple F with N' and 'this 000121 | is the whole physical CP phase' do not follow from(3)-(4). 000122 | 000123 | 4. A DIFFERENT EXISTING REFLECTED CALLER, NOT AN AUTOMATIC REPLACEMENT 000124 | 000125 | GRADED-HS-REFLECTION-AND-TIME.txt:138-161 gives the actual existing even 000126 | half-period form Tr(sqrt(rho) O* sqrt(rho) O), beta=2ell, for bounded 000127 | source operators. For centered finite-cutoff neutral quadratic tests A, 000128 | its connected Wick form is 000129 | Tr(X A* X B), X=(2cosh(ell h))^-1. (5) 000130 | For A=j* Mmu, the matching Hom form is equivalently controlled by 000131 | ||Xp^(1/2) Mmu Xq^(1/2)||_HS^2. 000132 | The old L1/smoothing proof gives its finite canonical extension. It is 000133 | a separated-time/reflected form, not the equal-time full-cross-face word 000134 | (1), and not a proof that an unsmoothed observable has a vacuum-domain 000135 | vector. The fixed heat factors and rho come from the existing source; 000136 | no new state is selected. But replacing the primitive caller by(5) 000137 | merely because it converges would be an extra application, not a source 000138 | derivation. The original actual field/source map must decide the caller. 000139 | The same source's circle automorphism transports these tests and its 000140 | state. Its circle parameter, half-period separation, HS Liouvillian and 000141 | physical P1 time retain their already distinguished meanings. 000142 | 000143 | SOURCE STATUS / NEXT DECISIVE APPLICATION 000144 | The complete six-letter finite response and original WEDGE consumer are 000145 | finished and retained. The exact first original application now to find 000146 | is the displayed Z/Sewing source test or admitted tangent producing that 000147 | geometric mu composite, including its endpoint/contact prescription. 000148 | Then(1), the finite ph term(3), or the genuinely selected sewn form(5) 000149 | can be compared to that SAME caller. There is no new requirement that 000150 | the entire physical source equal the Hardy defect or a finite algebra. 000151 | 000152 | [OMITTED: non-scientific conversation or execution metadata] 000153 | [OMITTED: non-scientific conversation or execution metadata] 000154 | [OMITTED: non-scientific conversation or execution metadata] 000155 | [OMITTED: non-scientific conversation or execution metadata] 000156 | [OMITTED: non-scientific conversation or execution metadata] 000157 | [OMITTED: non-scientific conversation or execution metadata] 000158 | [OMITTED: non-scientific conversation or execution metadata] 000159 | [OMITTED: non-scientific conversation or execution metadata] 000160 | [OMITTED: non-scientific conversation or execution metadata]