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000001 | G: COMPLETE ORIGINAL WEIGHT, GAUGE QUOTIENT AND BEREZIN CALL
000002 | 2 November 2026. Independent relational_logic source review.
000003 | Canonical sources unchanged. Entry live plan85, Atlas babeae99b202b43dfe084d2f.
000004 | 
000005 | RESULT
000006 | 
000007 | Gauge fixing and ghosts are already presented in the Original as the
000008 | representation of an existing gauge quotient. They are not evidence of a
000009 | new independent physical interaction. The explicit geometric ghost
000010 | operator and physical projector occur in the original research contract;
000011 | the later spectral gravity theorem explicitly uses that same quotient.
000012 | Our earlier WEIGHT.txt wording about an unprinted gauge functional must
000013 | not be promoted into a fundamental missing-coupling claim.
000014 | 
000015 | The complete original source, including its given gauge/ghost/Berezin
000016 | weight, is transported directly by the fixed full U, as proved in
000017 | FUNCTOR.txt(10) and REFERENCE-SOURCE-COMPLETION.txt. It does NOT first
000018 | require identification with a separate Gibbs reference state. The latter
000019 | is an optional representation, with its own same-basis conditions.
000020 | 
000021 | No new physical structure is selected by this G continuation. Nor do
000022 | the inspected S_adm occurrences define a second competing action. They
000023 | call the given action and differentiate it. The first unsupported
000024 | identification would be replacing that whole original call by the compact
000025 | finite-coefficient spectral readout alone, without its actual geometric/IR
000026 | map. Ghost physics is not that obstruction.
000027 | 
000028 | 1. WHAT THE 23 LITERAL HITS ACTUALLY COVER
000029 | 
000030 | The supplied full-action-literal-hits.json has23 entries in7 unique files:
000031 |  tfpt31/012 particle/compiler:1; tfpt32/011 closure:1;
000032 |  tfpt42/023 strongCP:1; tfpt42/035 effective average action:9;
000033 |  Source45/carrier009 strongCP:1; Source45/QFT003 strongCP:1;
000034 |  Source45/QFT007 effective average action:9.
000035 | The18 effective-action hits repeat terms in the same W_k/1PI expansion
000036 | in two historical copies. The strongCP calls use e^-S_adm as the supplied
000037 | weight. Neither type is a new independent enumeration of its full terms.
000038 | This is the exact coverage of that list, not an all-corpus absence claim.
000039 | 
000040 | QFT007:3–26 defines e^W_k by integrating e^(-S_adm-phi R_k phi/2+J phi).
000041 | QFT007:119–143 gives Gamma_k=S_adm+(hbar/2)STr log(S_adm''+R_k)+...
000042 | and vertices S_adm^(n). Thus S_adm is the action supplied to the fields
000043 | still integrated; W_k and Gamma_k are the resulting different callers.
000044 | An already effective/coarse-grained input is still an input at that stage.
000045 | This distinction does not permit adding the same determinant a second time.
000046 | 
000047 | 2. THE ORIGINAL QUOTIENT IS CONCRETE
000048 | 
000049 | ResearchContract2:15–21 supplies a gauge slice on the stated Sobolev
000050 | metric class and the gauge-fixed gravitational complex
000051 |  Omega0(TM) --K--> Gamma(Sym2 T*M) --K*--> Omega0(TM),
000052 |  Delta_gh=K* K, Pi_phys=Pi_BRST/Hodge Pi_TT.
000053 | It calls the conformal direction BRST exact/nonpropagating in the stated
000054 | Calderon polarization. This is a geometric gauge-complex assertion, not
000055 | an arbitrary ghost coupling introduced in this review.
000056 | 
000057 | Metrology004:35–60 defines Q_geo to quotient diffeomorphism and local
000058 | frame gauge directions and Delta_tot={Q_adm+Q_geo,(Q_adm+Q_geo)*}.
000059 | Its proof at151–162 says the same complex removes pure gauge directions
000060 | from the common Einstein/Higgs/R2/gauge-curvature spectral package.
000061 | StandardModel007:29–32 explicitly identifies the physical sector with
000062 | this cohomology, under the stated Fredholm/APS condition.
000063 | 
000064 | Contract008:287–293 gives the relevant existing Ward premise
000065 |  <s O>=0,
000066 | with the eta boundary phase cancelling the APS anomalies. This is attached
000067 | to that contract's projective-limit/moment/regularity hypotheses. It is
000068 | not newly proved by the existence of a formal nilpotent matrix alone.
000069 | StandardModel007:141–155 likewise retains Ward/BRST in its named source
000070 | hypotheses and carefully limits the all-order EG result to its local
000071 | perturbative matter/gauge scope.
000072 | 
000073 | 3. THE SMALLEST DECISIVE GAUGE REPRESENTATION IDENTITY
000074 | 
000075 | Apply the existing Ward premise on its legitimate original caller and
000076 | domain. In a BRST gauge-fixed representation S_t=S_inv+s Psi_t, with the
000077 | original measure, eta, boundary conditions and common normalization
000078 | retained, let F be a BRST-closed physical source word. Then
000079 | 
000080 |  d_t I_t(F)=-I_t((s dotPsi_t)F)
000081 |            =-I_t(s(dotPsi_t F))=0.                       (1)
000082 | 
000083 | The same holds for finite products of physical insertions and hence their
000084 | source coefficients. Applied to both bound original calls, it preserves
000085 | their relative quotient. This follows from the ORIGINAL Ward premise;
000086 | it is not a new freely chosen model or density.
000087 | 
000088 | Equation(1) is not a claim that every gauge-variant W_k[J] or off-shell
000089 | Gamma_k is gauge independent. Generic elementary gauge/ghost source
000090 | insertions are not BRST closed; a regulator must carry its actual Ward
000091 | identity. Direct transport by the same U instead preserves ALL original
000092 | source legs in one given gauge, without changing that gauge at all.
000093 | 
000094 | The ghost determinant need not cancel pointwise between two different
000095 | backgrounds. K_g* K_g and its reference value can differ. The full quotient
000096 | integration, with its determinant/Jacobian/domain, is the invariant object.
000097 | Deleting its field-dependent ghost factor would change the given caller.
000098 | 
000099 | The primary BRST/BV distinction is standard: gauge fixing is represented
000100 | by a canonical antifield transformation; antighost/auxiliary variables
000101 | form a contractible sector. A nontrivial physical action deformation
000102 | belongs instead to BRST cohomology modulo exact terms. See Barnich,
000103 | Brandt,Henneaux, Local BRST cohomology in gauge theories, section2.6,
000104 | equations2.26–2.47: https://arxiv.org/pdf/hep-th/0002245 .
000105 | That local algebraic result is not a new global gauge-slice existence
000106 | theorem. The actual original quotient/Ward hypotheses remain attached.
000107 | 
000108 | 4. WHAT IS FIXED, AND THE FIRST ILLEGAL IDENTIFICATION
000109 | 
000110 | Boundary001:302–315 explicitly calls S_prim a relative spectral SEED and
000111 | introduces gauge fixing, ghosts and compatible fluctuations later.
000112 | Its spectral/reference ratio is fixed by its displayed same constructor,
000113 | as WEIGHT.txt proves. The old geometric residue constructor already
000114 | jointly fixes the Einstein, Higgs, gauge and curvature terms in its stated
000115 | branch. No independent copy of those terms is to be added here.
000116 | 
000117 | The actual original finite Higgs one-form/Yukawa/Majorana consumer and
000118 | same-collar kinetic pairing are already established. Given its actual
000119 | fermion bilinear and orientation, Berezin integration produces that same
000120 | determinant/Pfaffian and all external-source minors once. The fixed full
000121 | U carries the original bilinear, sources, Jacobian and reference exactly;
000122 | FUNCTOR.txt:section3 and equation10 provide the full source statement.
000123 | This transport neither adds a fermion law nor changes the original state.
000124 | 
000125 | Neither QFT007's higher-derivative notation nor an optional symbol S_extra
000126 | licenses independently selected new interactions. In each actual original
000127 | call those derivatives/terms are whatever its GIVEN action has. If a new
000128 | gauge-invariant, BRST-nonexact deformation were added, its selection would
000129 | be new physical input. None was added or forced by the inspected passages.
000130 | A missing displayed Psi cannot stand in for evidence of such a deformation.
000131 | 
000132 | The actual whole U transports D to mathfrakD_h, including derivatives and
000133 | boundary domains, NOT to Phi alone. Even on an original constant product
000134 | coefficient, mathfrakD_h^2 contains -partial_r^2+p^2+Phi^2. The compact
000135 | coefficient Phi has neither original derivative. Accordingly the current
000136 | v259 profile-moment and v255 finite heat-coefficient readings must retain
000137 | their actual geometric/IR expansion map. Equating their finite coefficient
000138 | trace to the entire unnormalized S_adm/Z_rel is the first unsupported step
000139 | in this proposed compact rewrite. It is not repaired by choosing ghosts.
000140 | 
000141 | The direct whole-source transport remains exact regardless of that optional
000142 | rewrite. The full given P1 state/RP/reference, all original null-source
000143 | factors and eta, and the common S/Z/OS/Gamma architecture remain present.
000144 | This review closes the spurious gauge-choice objection and does not claim
000145 | a complete fundamental solution or an all-corpus failure of full S_adm.
000146 | 
000147 | SOURCE RECORDS CHECKED THROUGH READ_SOURCE
000148 | 
000149 | Boundary001:296–343, paper-source:8027564739689dd02e02f11c,
000150 |  sha7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79.
000151 | ResearchContract2/007:1–21, paper-source:4493812a05dfb280095129c7,
000152 |  sha3bc402debcf11dbf7d5560b37e64c6afe6126bc121c9af39901bb39f90cb89fd.
000153 | Contract008:260–309, paper-source:2ef6f12ed69539ba7ea94be8,
000154 |  sha8fba02c4b93076592cd51ec0c3c69f8469cc9eabc0048bf085d74508e7f98a2b.
000155 | Metrology004:1–169, paper-source:3a81043815727ab8a8dbca23,
000156 |  sha669d088bea83eef25cfd9960905893cc57d2827c7b4d7558c5aa7b408b85581a.
000157 | StandardModel007:1–49,92–178,
000158 |  paper-source:c59f5347aabe949c45484c99 /5c596f27c86a48c72a794495,
000159 |  shad110376a2d97decdaa06d3f6c90375ec242e63a26ea7af299d45945f9658f91b.
000160 | QFT007:1–28,119–143, paper-source:f588a78cad85dd5237213db3,
000161 |  sha9c1c587cbd61fc4034649d778d16f1ee0e8c1e1189885babb3d8148a6fe72d7c.
000162 | Contract015:144–183, paper-source:167e6cda6ca60a72b6789845,
000163 |  sha2ec9c3ab6903e9d29823ee5a52ef588cf8504848df6c51c21f0412f31f9eb886.
000164 | Companion full action and source-map evidence: FUNCTOR.txt,
000165 |  REFERENCE-SOURCE-COMPLETION.txt, PAIR-TYPING.txt and WEIGHT.txt in
000166 |  this same work/reference_transport_G directory. Their exact scope and
000167 |  original source manifests are retained rather than reclassified here.