TFPT scientific source excerpt Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-TOTAL-GRADE-PHASE-MAP.txt Original file SHA-256: b0fe83ca1d6798bc4ba8920857d1d52d82a18441424600241da7634598acc33a Inclusive original lines: 1-140 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 | TOTAL GRADE: THE ACTUAL FULL PHASE DICTIONARY AND PAIRING 000002 | 3 November 2026. Original source continuation, anonymous scientific record. 000003 | 000004 | RESULT AND CHANGED PREMISE 000005 | The earlier rejection of the FULL-OPERATOR equation gamma_F=gamma5 stays 000006 | valid. The already supplied TOTAL-grade fiber instead gives an exact 000007 | restricted intertwiner. No internal-grade projection is imposed and no 000008 | Yukawa or Majorana block is removed. The two-dimensional collar and the 000009 | existing ordinary four-dimensional product remain distinct source types. 000010 | This supplies a usable field/pairing dictionary, not primitive selection 000011 | of Spin4, a new bosonic action, a new state or the common physical spectrum. 000012 | 000013 | 1. ORIGINAL DATA AND AUDIT ANCHORS 000014 | The original SEED-FIELD.txt, SHA256 000015 | db9d551297ad797c51b8fef682db85f13a08cbb289592e238289b17e59b66a0b, 000016 | defines gamma=gamma_F, gamma^2=I, Phi*=Phi, {gamma,Phi}=0, 000017 | A=-i partial_x+a(x), [A,gamma]=0, and 000018 | N=[[0,-1],[1,0]], Z=diag(1,-1), S=NZ, 000019 | B=Z tensor A-S tensor Phi, D=N(partial_r+B), 000020 | Gamma_tot=Z tensor gamma, Ical=i Gamma_tot, C0=i N tensor I. 000021 | The original positive-total-grade map is 000022 | E v=(Pplus v,i Pminus v), Pplus/minus=(I+/-gamma)/2, 000023 | BE=Eh, h=A gamma-i gamma Phi. 000024 | Its NORMAL-KINETIC-PAIRING.txt, SHA256 000025 | 28061f015df5c5bb2a07a12ffd1d45f84cab49fb84939606201a1efe77b49f62. 000026 | That note supplies beta_L(x,y)=integral _new, L=-ND, 000027 | and opposite face signs (C0,-C0); the same complete chart is retained. 000028 | 000029 | The EXISTING ordinary Spin4 pairing note has registered source 000030 | research-source:66c66431e901c392e408f862, SHA256 000031 | e7200e2d30179214f0a63c856c3598cbffab7013d8747cc5b7f00f4beca96817. 000032 | Its actual 96-dimensional Phi contains four arbitrary complex 3x3 Yukawa 000033 | matrices and symmetric complex 3x3 Majorana matrix, not fitted numbers. 000034 | J=(C4 tensor KF)conjugation, Gamma=gamma5 tensor gamma_F, 000035 | Dprod=-i gamma^mu nabla_mu tensor I+gamma5 tensor Phi. 000036 | J gamma5=gamma5 J, J gamma_F=-gamma_F J, J Gamma=-Gamma J, 000037 | and {Dprod,Gamma}=0. Its total Weyl fibers have complex rank192. 000038 | The primitive origin of this ordinary Spin4 product was not established 000039 | by that note. That scope remains unchanged. 000040 | 000041 | 2. COLLAR: SAME ON E, DIFFERENT ON ITS COMPANION 000042 | Directly, (Z tensor I)E=E gamma. Thus, for real smooth chi, 000043 | UZ=exp(i chi Z) tensor I, U=exp(i chi gamma), UI=I2 tensor U, 000044 | UZ E=E U=UI E. But 000045 | UZ C0 E=C0 E U*, whereas UI C0 E=C0 E U. 000046 | Their actions on the whole unreduced space are different. 000047 | 000048 | With tangential chi the exact charged operator is 000049 | h_chi=U* h U=A gamma+(partial_x chi)I-i gamma Phi_chi, 000050 | Phi_chi=cos(2chi)Phi-i sin(2chi)gamma Phi. 000051 | The geometric collar rotation ALSO gives 000052 | N_chi=UZ* N UZ=cos(2chi)N+i sin(2chi)S, 000053 | N_chi^2=-I, C0_chi=UZ* C0 UZ. 000054 | Holding N or C0 fixed while using UZ changes the original source. 000055 | For normal-dependent chi, the full UZ* partial_r UZ connection remains; 000056 | a normal-independent formula is not substituted for that operator. 000057 | 000058 | There is nevertheless an EXACT FULL commuting diagram once the companion 000059 | chart is transported. Write old-complex coordinates unambiguously as 000060 | T(v,w)=Ev+C0Ew, T_chi(v,w)=Ev+C0_chi Ew. Then 000061 | UZ T_chi(v,w)=T(Uv,Uw), UI T(v,w)=T(Uv,Uw), 000062 | T_chi=R T, R=UZ* UI. Here R E=E, while R is nontrivial on C0E. 000063 | Thus R* (UZ* D UZ) R=UI* D UI as WHOLE differential operators with their 000064 | transported domains. Derivatives of R are included in this equality. 000065 | In new-complex notation the w slot is the original conjugate test space; 000066 | the corresponding coefficient action is conjugated, not a new copy. 000067 | The diagram holds on both oriented faces, retaining the minus on face1. 000068 | 000069 | For chi independent of r, beta_L with C0_chi and UZ*L UZ therefore pulls 000070 | back to the SAME charged K_chi=U*(partial_r+h)U as the UI transport. 000071 | The full graphs are G(h_chi) and I-bar(G(h_chi)), not only their diagonal 000072 | occupations. D_ref, boundary projector, regulator and source legs follow 000073 | the diagram. This is a coordinate equivalence; UZ is not declared UI. 000074 | 000075 | 3. EXISTING SPIN4 BRANCH: EXACT PAIRED IDENTITY 000076 | For psi in H_epsilon, Gamma psi=epsilon psi, epsilon=+/-1, 000077 | (I tensor gamma_F)psi=epsilon(gamma5 tensor I)psi. 000078 | Let Ui=exp(i chi gamma_F), Vs=exp(i epsilon chi gamma5). 000079 | Then Ui psi=Vs psi, J Ui=Ui J, J Vs=Vs* J. 000080 | Both J and Dprod carry H_epsilon to H_minus_epsilon. On that target 000081 | fiber Ui*=Vs. Consequently, for the actual full paired action, 000082 | 000083 | ==. 000084 | This is an identity of the whole bilinear form on H_epsilon. The target 000085 | fiber sign is essential, including for Majorana blocks. 000086 | 000087 | Putting chi=epsilon theta/2 gives, as a map FROM H_epsilon, 000088 | Ui*Dprod Ui=-i gamma^mu nabla_mu 000089 | +1/2 gamma^mu gamma5 partial_mu theta+gamma5 tensor Phi_theta, 000090 | Phi_theta=cos(theta)Phi-i epsilon sin(theta)gamma_F Phi. 000091 | The mass formula itself holds on the entire internal coefficient space. 000092 | The axial rewriting of the derivative is restricted to the input fiber. 000093 | The plus sign here uses EUCLIDEAN -i partial and the stated Ui*D Ui 000094 | direction. Removal of the historical LORENTZ -1/2 dtheta.J5 coupling 000095 | with kinetic +i slash(partial) uses the inverse axial rotation. Its sign 000096 | must not be copied from the Euclidean convention without this change. 000097 | 000098 | 4. SOURCE MEASURE, FIELD IMAGE AND GLOBAL DOMAIN 000099 | At a compatible finite regulator the paired skew matrix transforms by 000100 | M_chi=Ue^T M Ue. Pf(M_chi)=det(Ue)Pf(M), while the Berezin measure has 000101 | the inverse determinant. Source insertions and the original orientation 000102 | are transported once. At a genuine APS regulator, an uncomputed regularized 000103 | chiral trace is not set to zero by finite coefficient trace cancellation. 000104 | A numerical anomaly coefficient or eta correction is not inferred here. 000105 | 000106 | Ui need not belong to the original fixed-Yukawa/real-sigma field image or 000107 | the original gauge group. The coordinate change carries that field image 000108 | to its actual image; it does not enlarge the original admissible fields. 000109 | In particular, keeping Phi fixed while dropping its phase is not this map. 000110 | 000111 | If an ACTUALLY supplied theta has winding 2pi n, its half-angle U has 000112 | monodromy (-1)^n. The transported scalar twist alpha changes by n/2 mod1; 000113 | odd n exchanges quarters1/4 and3/4. This implication does not select a 000114 | period, a winding, the full clock network or new allowed sectors. 000115 | 000116 | 5. WHAT THIS IMPLIES FOR THE FULL PRIMITIVE ACTION 000117 | A whole simultaneously transported unitary source orbit has unchanged 000118 | spectral traces, reference-subtracted traces and eta spectra. In a finite 000119 | regulator, d Tr f(Ui*D Ui)/dtheta=0 exactly. With the original compatible 000120 | trace/relative domains the same covariance holds where defined. 000121 | Thus a phase dictionary alone cannot create a nonzero bosonic stiffness 000122 | or a new physical energy spectrum. The historical axial deformation with 000123 | Phi HELD FIXED is a different field path: the similarity above also moves 000124 | Phi by delta Phi=-i epsilon theta gamma_F Phi. The actual source field 000125 | image must decide which path is present. No new kinetic term is chosen. 000126 | 000127 | This advances the original field/pairing identification without promoting 000128 | the supplied Clifford source to the whole S_adm. The actual bosonic weight, 000129 | reference and physical restriction in R113 remain part of the same source. 000130 | Compiler, E8, alpha, flavor and coupled clocks keep their existing scope; 000131 | none is replaced by the collar or by the ordinary Spin4 product. 000132 | 000133 | DIRECT CONTROL 000134 | The actual full original symbolic 96-coefficient constructor was reused, 000135 | SHA256 6acaa9bc2c7a157a30730d7d6de75e944266afbf69b18a31c6fba654b8bd1c04. 000136 | All original Yukawa/Majorana entries remain symbolic. The recorded control 000137 | checks both rank192 fibers, antiunitary J, full paired mass congruences, 000138 | all four derivative coefficients, N transport and the full companion chart. 000139 | It does not compute S_adm or the common physical spectrum. External AI 000140 | agreement is retained as review, not substituted for these identities.