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A registered result in its source context

Original ledger classification: Identity [I] (y^2-suppression bound) + [P] (F_transfer typing)

Recorded statement: F_TRANSFER SCALE-TAGGING (the lepton-mixing predictions are RG-STABLE outputs; the quark mass-ratio readouts carry a scale tag): (1) the PMNS angles run only through the charged-lepton Y_e Y_e^+ eigenvalue gap y_tau^2 ~ 1.0e-4 [I] (the…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.RGSTAB.01

Original ledger classification: Identity [I] (y^2-suppression bound) + [P] (F_transfer typing)

Original claim text

F_TRANSFER SCALE-TAGGING (the lepton-mixing predictions are RG-STABLE outputs; the quark mass-ratio readouts carry a scale tag): (1) the PMNS angles run only through the charged-lepton Y_e Y_e^+ eigenvalue gap y_tau^2 ~ 1.0e-4 [I] (the only mixing-ROTATING Yukawa term is (3/2) Y Y^+ Y, PyR@TE SM RGEs), so the one-loop running from the seam/scalaron scale (M_scal = c3^{7/2} Mbar ~ 3e13 GeV) down to M_Z is kappa_tau = y_tau^2/(16 pi^2) ln(M_scal/M_Z) ~ 1.8e-5; (2) hence |Delta sin^2 theta_ij| <~ 1e-4 (normal ordering / hierarchical => O(1) spectrum factor, no quasi-degenerate enhancement) is two-three orders below current precision (sin^2 th12 +-0.013, sin^2 th13 +-0.0007) => the seeds sin^2 th12 = 1/3 - phi0/2 = 0.3067 and sin^2 th13 = phi0 e^{-5/6} = 0.0231 are SCALE-INDEPENDENT F_transfer outputs (seam value = measured value) [I]; (3) the up-quark sector runs through y_t^2 ~ 0.9, kappa_t ~ 0.15 = O(10-15%), so the m_t/m_b ~ 41 readout carries a scale tag (EW/M_Z), unlike the lepton angles [I]; (4) F_transfer TYPING [P]: the lepton-mixing transfer is trivial (no scale ambiguity), the quark-mass transfer is a genuine running map -- both the PyR@TE-confirmed SM Yukawa betas. Python-only (y^2-suppression magnitude bound, not a precision PMNS evolution; ref Antusch et al. 2005)

Original classification detail

Identity [I]: lepton angles RG-stable (y_tau^2-suppressed), quark ratios scale-tagged; F_transfer lepton sector trivial

Dependencies as recorded

EM.BUDGET.02; CAR.SM.01; v16_solar_dual_anchor.py; v21_solar_product_quark.py

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  • v163_rg_stability_flavor.pyRegistered verification module · registry
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    F_transfer scale-tagging: the lepton-mixing seeds (sin²θ₁₂=1/3−φ₀/2=0.3067, sin²θ₁₃=φ₀·e^(−5/6)=0.0231) are RG-STABLE — PMNS running is y_τ²-suppressed (~1.8e-5 ≪ precision), so seam value = measured value; the quark mass-ratio readouts (m_t/m_b~41) run through y_t² ~ O(10–15%) and carry a scale tag. The only mixing-ROTATING Yukawa term (3/2)YY†Y carries y_max² (PyR@TE SM RGEs back the asymmetry).

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