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Original ledger classification: Identity [I] (one-loop coefficients exact) + [P] (F_transfer gauge inputs)

Recorded statement: PYRATE GAUGE CROSS-CHECK (independent third-party confirmation of EM.BUDGET.01/CAR.SM.01 and an F_transfer gauge-input check): the carrier/SM field content gives, by the textbook one-loop formula in GUT normalisation,…

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Paper context: Standard Model and flavor structure

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EM.BUDGET.02

Original ledger classification: Identity [I] (one-loop coefficients exact) + [P] (F_transfer gauge inputs)

Original claim text

PYRATE GAUGE CROSS-CHECK (independent third-party confirmation of EM.BUDGET.01/CAR.SM.01 and an F_transfer gauge-input check): the carrier/SM field content gives, by the textbook one-loop formula in GUT normalisation, (b1,b2,b3)=(41/10,-19/6,-7) [I]; (1) THREE INDEPENDENT PATHS to b1=41/10 - carrier algebra 10 b1 = g_car 2^{g_car-2}+1 = 41 (CAR.SM.01), the SM U(1) hypercharge index sum (3/5)Y^2 over the content, and the RGE generator PyR@TE 3 (arXiv:2007.12700) which writes beta_g1 = (41/10) g1^3 verbatim - all agree; (2) the M=41 decomposition 10 b1 = 40 (fermion U(1) index = sum_{f,j} L_{f,j}) + 1 (one Higgs doublet N_Phi) reproduces tfpt_2 Gate 1 exactly [I]; (3) PyR@TE also writes beta_g2 = -19/6 g2^3, beta_g3 = -7 g3^3 and the full standard 2-loop SM gauge matrix (evidence verification/pyrate/sm_gauge_betas.txt, regenerated by verification/pyrate/reproduce.sh) [I]. SCOPE [P]: confirms the gauge sector of the F_transfer functor (its running inputs are not free knobs but follow from the carrier content); PyR@TE is the right external tool for the transfer/RGE gates (gauge running, and - with a seesaw model - the neutrino-Yukawa running behind eta_B), NOT for premise (A) (a 2d boundary-CFT question)

Original classification detail

Identity [I]: carrier content -> (41/10,-19/6,-7); PyR@TE 3 (external) reproduces them verbatim; F_transfer gauge inputs confirmed

Dependencies as recorded

EM.BUDGET.01; CAR.SM.01; v2_carrier_pascal.py; v13_open_gates.py

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Registered verification modules

  • v159_pyrate_gauge_crosscheck.pyRegistered verification module · registry
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    PyR@TE cross-check of the F_transfer gauge inputs: the carrier/SM content gives (b1,b2,b3)=(41/10,−19/6,−7) by the textbook one-loop formula; b1=41/10 holds THREE independent ways — carrier algebra 10 b1 = g_car·2^(g_car−2)+1 = 41, the SM U(1) hypercharge index Σ(3/5)Y², and the external RGE generator PyR@TE 3 (arXiv:2007.12700) which writes β_g1=(41/10)g1³ verbatim; the M=41 split 10 b1 = 40 (fermion index) + 1 (Higgs) reproduces tfpt_2 Gate 1; evidence in verification/pyrate (reproduce.sh regenerates it). The transfer functor's gauge inputs are not free knobs.

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