TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-PH-CORRELATIONS-ADJOINTS-AND-CALLER-REVIEW.txt Original file SHA-256: c76ed8821af4e35e6803db6a7ce05e60ca77d300e6fae4e5744774b5abb5f462 Inclusive original lines: 1-91 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 | [OMITTED: non-scientific conversation or execution metadata] 000002 | [OMITTED: non-scientific conversation or execution metadata] 000003 | 000004 | 1. The given source, not a new quantum model. 000005 | The original pure graph G=V V* and its complement Vperp=(-sqrt(1-A),sqrt A) 000006 | give E=V E0 and Eh=Vperp E0. The existing normal symbol of M_mu acts 000007 | identically on the two graph faces as2z alpha_mu/dz times P_gamma,+. 000008 | The actual J is Swap tensor j, with the R_x/G/Kummer/spin factors retained. 000009 | Thus replacing only the face vector yields 000010 | pp=sech(ell/2)L_mu, ph=hp=tanh(ell/2)L_mu, hh=-pp, 000011 | L_mu=(2/pi)m_mu tensor P_gamma,+. 000012 | The target hole-chart minus under J at negative energy is already included 000013 | by the direct JEh pairing. No extra sector/phase was chosen. 000014 | 000015 | [OMITTED: non-scientific conversation or execution metadata] 000016 | [OMITTED: non-scientific conversation or execution metadata] 000017 | [OMITTED: non-scientific conversation or execution metadata] 000018 | [OMITTED: non-scientific conversation or execution metadata] 000019 | [OMITTED: non-scientific conversation or execution metadata] 000020 | [OMITTED: non-scientific conversation or execution metadata] 000021 | [OMITTED: non-scientific conversation or execution metadata] 000022 | [OMITTED: non-scientific conversation or execution metadata] 000023 | [OMITTED: non-scientific conversation or execution metadata] 000024 | [OMITTED: non-scientific conversation or execution metadata] 000025 | [OMITTED: non-scientific conversation or execution metadata] 000026 | [OMITTED: non-scientific conversation or execution metadata] 000027 | [OMITTED: non-scientific conversation or execution metadata] 000028 | [OMITTED: non-scientific conversation or execution metadata] 000029 | 000030 | Adjoints cannot be dropped. The POSITIVE covariance is instead 000031 | C(F*,F)=C(N*,N)=g h>0, C(F*,N)=0. 000032 | Consequently same-orientation physical fluctuations are not absent merely 000033 | because C(F,F)=0. The phase in an unstarred component does not determine 000034 | the full real observable by itself. 000035 | 000036 | 3. Four ordinary selfadjoint quadratures are completely determined. 000037 | For (ReF,ImF,ReN,ImN), with each quadrature normalized by1/sqrt2, 000038 | the real symmetric finite covariance is 000039 | g [[h,0,Re z,Im z], [0,h,Im z,-Re z], 000040 | [Re z,Im z,h,0], [Im z,-Re z,0,h]]. (2) 000041 | Its eigenvalues are g(|I02|+|I21|)^2 and g(|I02|-|I21|)^2, each twice. 000042 | Both are strictly positive since |I21|/|I02|=3.347597664... is not1. 000043 | Thus the two directed letters give four positive real fluctuation channels 000044 | in this retained finite corner. This does not identify that corner with 000045 | the complete J_F/KO-real field; those additional actual slots stay typed. 000046 | 000047 | An independent explicit64-dimensional CAR representation, containing the 000048 | three occupied source modes and their three empty complements, verifies 000049 | (1)-(2) and the Pauli statement exactly. Its face parameters sech,tanh 000050 | are SYMBOLIC, not chosen physical values. It uses actual period phase 000051 | -5pi/12 and arbitrary real signed amplitudes. All11 checks pass. 000052 | For the separate pp-only compression Pi K Pi, Pi<=G, a traceless bilinear 000053 | annihilates the filled defect. This does not make full K_mu invisible. 000054 | 000055 | 4. The whole unsmoothed operator and the fixed original source quotient. 000056 | The actual multiplier of mu has a nonzero |theta-theta_j|^(-2/3) jet 000057 | after all original metric/half-density maps. It is L1 but not L2. 000058 | For the BARE proposed T=Swap tensor(j* M_mu), test the original occupied 000059 | n=0 NS mode with v=(c,d), c,d>0. Write the spatial output coefficients a_m. 000060 | Their squared sum is infinite. The hole projection satisfies 000061 | ||(I-G_m)Swap v||^2 ->c^2 as m->+infinity and ->d^2 as m->-infinity. 000062 | Therefore the full positive cutoff norm in the connected equal-time word 000063 | Tr(G T* (I-G)T) diverges already on that one occupied test column. 000064 | The finite (1) remains a well-defined component; it is not the whole limit. 000065 | This excludes only the unsmoothed bare quadratic vacuum-domain claim. 000066 | Sewn, reflected, relative or genuinely renormalized callers are distinct. 000067 | 000068 | The ORIGINAL QFT002:256-265 and QFT008:143-151 state 000069 | Zrel[J,eta,bareta]=Zadm[J,eta,bareta]/Zref[0,0,0]. 000070 | For every positive source-derivative order, the derivative of log Zref[0] 000071 | is zero. This fixed normalizer does not subtract a mu contact/variance 000072 | term or select the finite corner as a regular part. A bound ACTION curve 000073 | can vary its reference and is the different already recorded Sprim test. 000074 | QFT005:144-160 and QFT007:3-22,121-140 specify the true local sources and 000075 | action vertices; no bare mu multiplication is silently selected there. 000076 | 000077 | 5. Preserve the positive original finite consumer. 000078 | The original WEDGE/Clifford rule can read already FINITE F,N coupling 000079 | contributions without making geometric mu itself an unsmoothed local 000080 | CAR current. Its subsequent finite Dirac/field operator has no such Ram 000081 | multiplier singularity. The domain result above must not become a new 000082 | universal gate or undo this existing constructive path. The actual 000083 | original HolK/marked-jet producer and whole common action remain the 000084 | source comparison, not a new arbitrary regularization prescription. 000085 | 000086 | [OMITTED: non-scientific conversation or execution metadata] 000087 | [OMITTED: non-scientific conversation or execution metadata] 000088 | [OMITTED: non-scientific conversation or execution metadata] 000089 | [OMITTED: non-scientific conversation or execution metadata] 000090 | [OMITTED: non-scientific conversation or execution metadata] 000091 | [OMITTED: non-scientific conversation or execution metadata]