TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE54-ORIGINAL-POLARIZATION-AND-HIGGS-TADPOLE.txt
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000001 | THE ORIGINAL PRIMITIVE POLARIZATION AND THE ACTUAL FORWARD HIGGS CALL
000002 | 30 October 2026. Focused source review and one exact actual-builder trace check.
000003 | No original/Atlas/ledger edit; no new covariance, measure or field family.
000004 | 
000005 | 1. Original primitive selector: retain the existing precise verdict
000006 | Read the actual archived boundary source001:192-289, not the external summary:
000007 | documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/
000008 | 001-section-primitive-core-and-carrier-interface-handoff.tex,
000009 | SHA256 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79,
000010 | research-source:c1565366722f99a531f2beb6.
000011 | It defines Pprim=P_(Sigma,+) Pgap, with
000012 |   Pgap=1_[epsilon_adm^2/4,infinity)(P_(Sigma,+) Dprim*Dprim P_(Sigma,+)).
000013 | Dprim is the APS-realized restriction of the primitive sector operator,
000014 | controlled by Drel relative to the geometric anchor (208-216).
000015 | 
000016 | The literal subspace consequence Pprim<=P_C and the disappearing negative
000017 | carrier polarization are already finding:positive-compression-erases-carrier-
000018 | minus-sector. Its high-pass does not by itself choose a finite carrier:
000019 | finding:original-primitive-action-is-present-highpass-is-not-finite-selector.
000020 | These are reused, not new exclusions. If the covariance is the SAME pure
000021 | projector G and P_F<=G, then P_F G P_F=I on its own range, and the strict
000022 | log-odds reader is undefined there. This conditional first branch is correct.
000023 | It does not exclude the existing whole source, its adjoints or a mixed face.
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000042 | 
000043 | 3. The genuine original forward caller varies a field, not arbitrary Y entries
000044 | The original renormalized caller is QFT source007:3-27,115-145:
000045 |   exp W_k[J]=int_Hadm Dvarphi exp(-Sadm[varphi]-varphi R_k varphi/2+J varphi),
000046 |   Gamma_k[phi]=Legendre(W_k)-phi R_k phi/2.
000047 | Its derivatives are with respect to the declared mean fields, with the
000048 | propagator and higher vertices of Sadm retained. This does not by itself
000049 | promote every coefficient in the initial Dirac matrix to an integration field.
000050 | 
000051 | The relevant original field direction IS explicit. The real SM one-form
000052 | acts on the GIVEN right-to-left block M=diag(Y_up,Y_down) as q(H)M.
000053 | See actual v252 dirac_block:86-99 and rep:139-168; graph-first read of
000054 | v254_inner_fluctuations.run:80-87 first supplies its four Y matrices, then
000055 | builds one-forms from that D. The full already proved block formula is in
000056 | seam-joint-source-origin-audit-20261016/HIGGS_VARIATION_PROOF.txt:145-171.
000057 | Only its real radial quaternion direction is used here; no extra complex
000058 | one-form span or independently variable family matrix is inferred.
000059 | 
000060 | The ORIGINAL printed local action actually evaluates this field:
000061 | documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/
000062 | 002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex:39-61,
000063 | paper-source:1cee7daa7a306afb8295d265,
000064 | SHA256 313dade0e18117f8b4f5c7ad88d8e91caeaa11fe4a23cf32fc3f7bac238dab58.
000065 | It contains the scalar potential
000066 |   V(H,chi_geo)=-mu_H^2(chi_geo) H*H+lambda_H(H*H)^2.
000067 | Here H denotes that printed Higgs field, distinguishing it from the full96
000068 | finite coefficient. Its genuine local field tadpole at fixed chi_geo is
000069 |   delta V/delta H*=[-mu_H^2+2lambda_H(H*H)]H.             (1)
000070 | On the actual radial field H=t H0, u0=H0*H0,
000071 |   dV/dt=2t u0[-mu_H^2+2lambda_H t^2 u0].               (2)
000072 | Thus a nonzero stationary amplitude obeys t^2 u0=mu_H^2/(2lambda_H)
000073 | in this printed local contribution. These are genuine original forward
000074 | equations. They are not separate equations dGamma/dY_f=0 for every entry.
000075 | The source's stated field normalization must still be used when translating
000076 | this amplitude to v_geo. Loops, other fields and the full bound action are
000077 | not silently declared equal to this local tree contribution.
000078 | 
000079 | 4. Retain the WHOLE actual96 coefficient and its fixed Majorana term
000080 | The same radial field is exactly Phi(t)=t D_Y+D_MR, t=1+s. Both are the
000081 | original full_D blocks, not independent selected neutrino channels. Write
000082 |   A2=Tr D_Y^2, A4=Tr D_Y^4,
000083 |   M2=Tr D_MR^2, M4=Tr D_MR^4, B=Tr(D_Y^2 D_MR^2).
000084 | Their actual left/right/Majorana support gives
000085 |   Tr(D_Y D_MR)=0, (D_Y D_MR)^2=0,
000086 |   Tr Phi(t)^2=A2 t^2+M2,
000087 |   Tr Phi(t)^4=A4 t^4+4B t^2+M4.                        (3)
000088 | Consequently the finite-coefficient part of the retained a2/a4 potential
000089 |   V24=c2 Tr Phi(t)^2+c4 Tr Phi(t)^4
000090 | has the exact radial tadpole, for fixed coefficients,
000091 |   dV24/dt=2t[c2 A2+4c4 B+2c4 A4 t^2].                 (4)
000092 | This keeps the actual mixed Majorana/Yukawa contribution 4B. With c4 A4>0
000093 | its nonzero root is t^2=-(c2 A2+4c4 B)/(2c4 A4), when positive.
000094 | c2,c4 stand for the coefficients of that particular retained trace block,
000095 | including the original normalization and moment factors; none is fitted.
000096 | v255_spectral_action_expansion.run:74-102 explicitly evaluates its a,b
000097 | from GIVEN Y/mass inputs and types the Higgs-quartic boundary relation as
000098 | conditional. Equations(3)-(4) are not its claimed full renormalized Gamma.
000099 | 
000100 | If the actual bound source makes c2,c4 or its reference depend on t, the
000101 | chain terms must be retained. For this displayed block alone they are
000102 |   c2'(t)[A2 t^2+M2]+c4'(t)[A4 t^4+4B t^2+M4]
000103 | in addition to(4). The original gap response, reference, eta and the rest of
000104 | Gamma have their own actual terms. No Phi-independent normal trace or
000105 | unbound chi substitution is used to remove them.
000106 | 
000107 | One focused exact check imports v252.full_D without calling run(), using
000108 | the SAME Gaussian-integer control as check_finite_typing.py:25-29. It gives
000109 |   A2=1024, A4=17968, M2=66, M4=1170, B=1934,
000110 |   Tr Phi(t)^2=1024t^2+66,
000111 |   Tr Phi(t)^4=17968t^4+7736t^2+1170.
000112 | All five symbolic identities pass. Data: workspace outputs/multi-model-
000113 | source-search-20261029/ACTUAL-RADIAL-HIGGS-TADPOLE-TRACE-CHECK.json,
000114 | SHA256 c9a104b4f3b5edf85ebe93a58fe6445e275fec2acf33d76b4b878a4d1c77b1a5.
000115 | 
000116 | 5. Preserve legitimate modulus variation and the scalaron/sigma scope
000117 | This is not a prohibition against varying Dirac moduli in a declared
000118 | spectral-action theory. Chamseddine-Connes-Marcolli, hep-th/0610241,
000119 | Lemma5.2, equations5.17-5.19, printed p56, explicitly sets M_R=x k_R
000120 | with k_R FIXED. In flat space with negligible Higgs amplitude it obtains
000121 |   x^2=2f2 Lambda^2 Tr(k_R* k_R)/(f0 Tr((k_R* k_R)^2)).
000122 | Primary text: https://www.math.fsu.edu/~marcolli/SMpaper.pdf, PDF page55.
000123 | It selects an amplitude under those stated variation assumptions, not the
000124 | whole arbitrary flavor shape. TFPT v254:129-164 likewise retains the
000125 | Majorana/sigma direction in the beyond-first-order Pati-Salam realization;
000126 | its sigma=scalaron identification is explicitly conditional. v253:77-127
000127 | computes the scalaron scale and an RG/moment ratio for M_PS/M_s; it does
000128 | not solve arbitrary entrywise Yukawa stationarity in that implementation.
000129 | 
000130 | The concrete corrected next origin operation is the ORIGINAL field tadpole
000131 | along the declared H/sigma or geometric directions, with the whole bound
000132 | source and marked transport insertions retained. The missing step in C54
000133 | is its promotion of this field stationarity to free matrix-Y stationarity
000134 | without specifying that larger original variation contract. The already
000135 | present HolK/Y producer may provide other origin constraints; Hardy=wholeY
000136 | or one bare spectral potential is not imposed as its architecture.