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Original ledger classification: All-order EG/BRST contract [C] (imported EG causal factorisation + BRST renormalisation on the TFPT finite dim-4 gauge+matter class + the seam gap); prerequisites power-counting/BRST-nilpotency/gap [E]

Recorded statement: The all-order Epstein-Glaser/BRST contract for the perturbative 4D S-matrix S_pert (2026-06-23, review Point 3): the 'all-order closing statement' for the 4D perturbative QFT leg, typing the standard causal-perturbation-theory closure for…

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Paper context: Standard Model and flavor structure

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QFT4D.EG.ALLORDER.01

Original ledger classification: All-order EG/BRST contract [C] (imported EG causal factorisation + BRST renormalisation on the TFPT finite dim-4 gauge+matter class + the seam gap); prerequisites power-counting/BRST-nilpotency/gap [E]

Original claim text

The all-order Epstein-Glaser/BRST contract for the perturbative 4D S-matrix S_pert (2026-06-23, review Point 3): the 'all-order closing statement' for the 4D perturbative QFT leg, typing the standard causal-perturbation-theory closure for the TFPT finite interaction class -- NOT a 4D path integral and NOT a new mechanism. [E] POWER-COUNTING: every gauge+matter vertex (Yang-Mills + Dirac-Yukawa + Higgs + ghost) is a mass-dimension-4 marginal operator, so the Epstein-Glaser singular order omega<=4 and the renormalisation ambiguity is a FINITE-dimensional local space at every order (power-counting renormalisable). [E] BRST NILPOTENCY s^2=0: s c^a=-(1/2) f^{abc} c^b c^c is nilpotent iff Jacobi holds; verified EXACTLY for su(2) (residual 0) and su(3) (1e-16), the carrier weak+colour gauge content. [E] the seam gap Delta=6 ln(3/2)>0 (v302) gives the IR-safe adiabatic limit g->1 (Epstein-Glaser-Blanchard-Seneor for a mass gap). [C] IMPORTED: T_n exists to all orders by causal factorisation (Epstein-Glaser 1973 / Brunetti-Fredenhagen). [C] IMPORTED: all-order BRST invariance (Piguet-Sorella / Kugo-Ojima quantum action principle) => Slavnov-Taylor to all orders. [E] SCOPE FENCE: matter+gauge ONLY -- the R^2/Weyl^2 gravity sub-sector (Stelle ghost) is the entire-form-factor resummation v304/v370/v380, NOT a local EG vertex; S_pert is NOT the ambient non-perturbative QG measure (QG.AMB.01, a [C] redundancy v369). NET [C], prerequisites [E]; NOT [E]. Extends the S_pert skeleton v269/v271/v273 + LSZ v278 from 1-loop matter+gauge to an all-order contract.

Original classification detail

[E] the three TFPT prerequisites (dim-4 power-counting -> finite counterterm space; BRST nilpotency via Jacobi for su(2)/su(3); the seam gap -> adiabatic limit); [C] the two imported heavy legs (all-order T_n existence by causal factorisation; all-order BRST invariance / Slavnov-Taylor); NOT [E] (no in-repo formal induction), matter+gauge only (gravity fenced to v304/v370/v380; ambient QG.AMB.01 a [C] redundancy). A typed all-order contract, not a path integral.

Dependencies as recorded

v269; v271; v273; v278; v302; v304; v370; v380; v369

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  • v381_qft4d_eg_allorder.pyRegistered verification module · registry
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    The all-order Epstein-Glaser / BRST contract for the perturbative 4D S-matrix S_pert -- the 'all-order closing statement' for the 4D perturbative QFT leg (review Point 3). Types the standard causal-perturbation-theory closure for the TFPT finite interaction class; does NOT build a path integral and is NOT a new mechanism. [E] POWER-COUNTING: every gauge+matter vertex (Yang-Mills + Dirac-Yukawa + Higgs + ghost) is a mass-dimension-4 marginal operator => the EG singular order omega<=4 => a FINITE counterterm space at every order (power-counting renormalisable). [E] BRST NILPOTENCY s^2=0 verified via the Jacobi identity for su(2) (residual 0) and su(3) (1e-16), the carrier weak+colour gauge content. [E] the seam gap Delta=6 ln(3/2)>0 (v302) gives the IR-safe adiabatic limit g->1. [C] imported: T_n exists to all orders by causal factorisation (Epstein-Glaser 1973 / Brunetti-Fredenhagen). [C] imported: all-order BRST invariance (Piguet-Sorella / Kugo-Ojima) => Slavnov-Taylor to all orders. [E] scope fence: matter+gauge ONLY -- the R^2/Weyl^2 gravity sub-sector is v304/v370/v380, not a local EG vertex; S_pert is not the ambient measure QG.AMB.01 (a [C] redundancy v369). NET [C] (imported EG+BRST on the TFPT dim-4 class + gap), prerequisites [E]; NOT [E], NOT a path integral. Extends v269/v271/v273/v278 from 1-loop to all-order.

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