TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DYNAMICAL-HIGGS-SOURCE-PROOF.txt Original file SHA-256: eda5bb664b1fb20370e59b39dbd5e3cb04d79864a8d1d0a0eb6c791cdaf98f49 Inclusive original lines: 1-95 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 | ORIGINAL-DYNAMICAL-HIGGS-SOURCE-20261031 000002 | F1 continuation: full original shared Higgs/matter coupling, not a new source. 000003 | 000004 | 1. Question, original consumer and retained results 000005 | 000006 | Continue R022-R025 into dynamical bosons. Yukawa, Flavor, Alpha and the actual 000007 | Clifford field/state/reflection/same-time and P2 wedge maps are retained. The 000008 | old free or decoupled g+ channel need not equal the whole interacting source. 000009 | 000010 | Original carrier008, lines157-188 and237-242, contains the primitive tensor 000011 | vol(s_Q wedge c_H s_uc). Its specified original component is +1. The positive 000012 | weak one-form consumer was already established in MU-CURRENT-DZ-FINITE- 000013 | INSERTION-REVIEW.txt and its real-span supplement. It is REUSED, not newly 000014 | claimed. With H=(h1,h2)=(bar t3,bar t4), that original real-algebra chart has 000015 | q(H)=[[bar h2,h1],[-bar h1,h2]], 000016 | M_H^q=q(H)diag(Yu,Yd), M_H^l=q(H)diag(Ynu,Ye). 000017 | The different supplied lepton and quark Yukawa matrices are not identified. 000018 | The same H acts on all families and colors. No factor1/sqrt2, physical vev, 000019 | new Yukawa parameter, coupling strength or independent sector Higgs is fitted. 000020 | 000021 | The original v252 representation and a=pi(0,q,0), b=pi(1,0,0) give the actual 000022 | one-form a[D_F,b]. Its selfadjoint and J_F real completion gives the whole96 000023 | internal Higgs derivative. check_dynamical_higgs_source.py checks its ENTIRE 000024 | real-linear coefficient class:72 real coordinates of the four supplied3x3 000025 | matrices times four real H directions,288 original matrix identities. All are 000026 | exact Gaussian-integer basis computations, with no tolerance. Real linearity 000027 | then gives arbitrary supplied Y. Each derivative is Hermitian, gamma_F odd 000028 | and J_F real. This verifies the actual forward consumer, not a new Y search. 000029 | The fixed Majorana block is a separate existing field-independent contribution. 000030 | Internal KO reality is NOT a proof of spacetime reflected source invariance. 000031 | 000032 | 2. Whole original H integration and all higher induced words 000033 | 000034 | Work first at a finite regulated field/source algebra. Keep all remaining 000035 | original fields A fixed only as CONDITIONAL arguments of the SAME Z_adm. 000036 | Let Z_H[J|A] denote its actual H fiber integral, with its original measure, 000037 | regulator, support, reference, phases, eta and Jacobian information. It is not 000038 | an extra Gamma_H added to a master that already contains this contribution. 000039 | 000040 | On the declared original affine Yukawa sector, write 000041 | S_Y=integral[ h_a j_a + bar h_a jbar_a ], 000042 | where j are Grassmann-even bilinears from the above whole q(H)M. More 000043 | generally use real component labels r=1,...,4 and S_Y=h_r j_r. Since the 000044 | currents are even, they commute in the Euclidean Grassmann algebra. Exactly 000045 | int DH exp(-S_H+J.H-S_Y)=Z_H[J-j|A]. 000046 | If Z_H[J] is nonzero this equals 000047 | Z_H[J|A] exp[ sum_(n>=1) (-1)^n/n! kappa_H,n[J|A](j,...,j) ]. 000048 | Finite Grassmann nilpotency terminates the sum, requiring only finitely many 000049 | original H moments for any specified finite word. No Gaussianization, small 000050 | Y expansion or inverse-heat convergence claim is involved. Analytic infinite 000051 | field limits need their actual moment/domain/limit controls separately. 000052 | 000053 | In induced action notation, with no additional H-dependent fermionic vertices, 000054 | S_eff=S_F,0-log Z_H[J|A] 000055 | +kappa_1 j -(1/2)kappa_2 jj +(1/6)kappa_3 jjj 000056 | -(1/24)kappa_4 jjjj + ... . 000057 | These are2,4,6,8-fermion terms respectively. The cubic and quartic boson 000058 | cumulants are retained; the boson density need not be Gaussian. All original 000059 | external fermion sources and subsequent Grassmann integrations remain. 000060 | The conditional log Z_H[J|A] depends on A and must not be dropped as a global 000061 | constant; it contributes to the total Z[0] and its geometry/reference scores. 000062 | 000063 | IMPORTANT: the original full S_adm allows higher vertices. If its actual 000064 | interaction has an additional term S_extra(H,psi), the affine rule alone is 000065 | not the full answer. Retain it explicitly: for a polynomial admissible finite 000066 | interaction the exact replacement is 000067 | exp[-S_extra(delta_J,psi)] Z_H[J-j|A], 000068 | with the actual operator/source order and the corresponding moments. Extra 000069 | H-dependent four-fermion terms, for example, can already modify the induced 000070 | four-fermion coefficient. No such term is silently assumed absent in the full 000071 | primitive theory. Without a declared polynomial/analytic representation, use 000072 | the original unnormalized fiber integration directly. This is the R024 rule. 000073 | 000074 | 3. First explicit common-sector coefficient and correct meaning 000075 | 000076 | For a pair U,D=(nu,e) or (u,d), suppress color/family sums and use the usual 000077 | already oriented charged Dirac chart. The above Yukawa bilinear plus its 000078 | specified adjoint gives 000079 | j1=bar U_L Yd D_R - bar U_R Yup^dagger D_L, 000080 | j2=bar D_L Yd D_R + bar U_R Yup^dagger U_L, 000081 | jbar1=-bar D_L Yup U_R + bar D_R Yd^dagger U_L, 000082 | jbar2=bar U_L Yup U_R + bar D_R Yd^dagger D_L. 000083 | For leptons replace Yup,Yd by the actual Ynu,Ye. Each current is summed over 000084 | all original families, and over three colors only for quarks. The quaternion 000085 | signs and the original adjoint determine these currents. They are not a new 000086 | choice of physical reflection or a Majorana-independent Dirac doubling. 000087 | 000088 | Write G_ab(x,y)=_c in the ORIGINAL conditional boson fiber. 000089 | The induced action has the term -integral j_a(x)G_ab(x,y)jbar_b(y), plus 000090 | -(1/2)_c jj and its conjugate. No symmetry that kills anomalous 000091 | is imposed here, and no translation invariance or local limit is assumed. 000092 | 000093 | In particular the original common H2 gives, in the displayed ordered word, 000094 | -G_2bar2(x,y) Ynu[a,b] conjugate(Yu[d,c]) 000095 | * [bar nu_L,a(y) nu_R,b(y)] [bar u_R,c(x) u_L,d(x)].