Follow the source behind the result.

The registered Python source is shown as text. Displaying it does not execute the code.

"""v163 -- F_transfer scale-tagging: the TFPT lepton-mixing predictions are
RG-STABLE outputs, while the quark mass-ratio readouts carry a scale tag.

The compiler reads its flavor observables as dimensionless seeds (phi0-ladder).
A fair confrontation with experiment must ask at WHICH renormalization scale a
seed is a prediction, and whether RG transport between that scale and the
measurement scale shifts it. PyR@TE makes the answer structural: every Yukawa
beta is proportional to its own coupling, and the only mixing-ROTATING term is
(3/2) Y Y^dagger Y, whose size is the largest Yukawa eigenvalue squared
(verification/pyrate/sm_yukawa_betas.txt). Hence:

  [I] 1. LEPTON MIXING IS y_tau^2-SUPPRESSED.  The PMNS angles run only through
         the charged-lepton Y_e Y_e^dagger eigenvalue gap = y_tau^2 ~ 1.0e-4.
         The natural one-loop running scale 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.
  [I] 2. THE LEPTON PREDICTIONS ARE RG-STABLE.  With the TFPT spectrum (normal
         ordering, hierarchical => no quasi-degenerate enhancement, factor O(1)),
         |Delta sin^2 theta_ij| <~ kappa_tau is two to three orders below current
         precision (sin^2 th12 +-0.013, sin^2 th13 +-0.0007). So 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. QUARK MASS RATIOS ARE SCALE-TAGGED.  The up-sector runs through y_t^2 ~
         0.9, so kappa_t = y_t^2/(16 pi^2) * ln ~ 0.15 = O(10-15%). The
         m_t/m_b ~ 41 readout is therefore NOT scale-free; it is defined at a
         specific scale (the EW/M_Z readout) and must be transported, unlike the
         lepton angles. (Honest asymmetry, not a defect.)
  [P] 4. F_transfer TYPING.  The lepton-mixing sector of the transfer functor is
         trivial (no scale ambiguity); the quark-mass sector is a genuine running
         map. Both beta-structures are the PyR@TE-confirmed SM Yukawa RGEs.

Scope: one-loop magnitude bound (the y^2-suppression argument), not a precision
PMNS evolution; the conclusion (lepton angles stable to << precision; quark
ratios O(10%) scale-dependent) is robust to the O(1) spectrum factor. External
backing: verification/pyrate/sm_yukawa_betas.txt (regenerated by reproduce.sh).
Ref: Antusch-Kersten-Lindner-Ratz-Schmidt 2005 (SM PMNS running). Python-only.
"""
import math
import os

from tfpt_constants import check, summary, reset, phi0, c3, Mbar

V_EW = 246.0            # GeV, Higgs vev
M_TAU = 1.77686         # GeV
MT_RUN = 163.0          # GeV, m_t(m_t) MS-bar (running mass for y_t)
M_Z = 91.1876           # GeV
LOOP = 1.0 / (16 * math.pi**2)


def run():
    reset()
    print("v163 F_transfer scale-tagging (lepton angles RG-stable; quark ratios tagged)")

    y_tau = math.sqrt(2) * M_TAU / V_EW
    y_t = math.sqrt(2) * MT_RUN / V_EW
    M_scal = float(c3)**(3.5) * float(Mbar)             # seam/scalaron scale
    t = math.log(M_scal / M_Z)
    kappa_tau = y_tau**2 * LOOP * t
    kappa_t = y_t**2 * LOOP * t

    # 1. lepton mixing is y_tau^2-suppressed
    check("LEPTON MIXING y_tau^2-SUPPRESSED: y_tau^2 ~ 1.0e-4, so the one-loop "
          "PMNS running scale kappa_tau = y_tau^2/(16pi^2) ln(M_scal/M_Z) ~ 1.8e-5 "
          "(M_scal = c3^{7/2} Mbar ~ 3e13 GeV)",
          abs(y_tau**2 - 1.04e-4) < 1e-5 and 1e-5 < kappa_tau < 3e-5)

    # 2. the lepton predictions are RG-stable (well below precision)
    prec_th13 = 7e-4         # PDG/NuFIT sin^2 th13 uncertainty (the tightest)
    prec_th12 = 1.3e-2
    enh = 5.0                # generous O(1)-O(few) spectrum enhancement for NO
    delta_max = kappa_tau * enh
    sin2_th12 = 1.0/3 - float(phi0)/2
    sin2_th13 = float(phi0) * math.exp(-5.0/6)
    check("LEPTON PREDICTIONS RG-STABLE: |Delta sin^2| <~ 5 kappa_tau ~ 9e-5 is "
          "below even the tightest precision (sin^2 th13 +-7e-4) and ~100x below "
          "sin^2 th12 +-0.013 -> 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",
          delta_max < prec_th13 and delta_max < prec_th12
          and abs(sin2_th12 - 0.3067) < 1e-3 and abs(sin2_th13 - 0.0231) < 1e-3)

    # 3. quark mass ratios are scale-tagged (NOT scale-free)
    check("QUARK RATIOS SCALE-TAGGED: y_t^2 ~ 0.9 gives kappa_t = "
          "y_t^2/(16pi^2) ln ~ 0.15 = O(10-15%) -- 4 orders larger than the lepton "
          "running, so the m_t/m_b ~ 41 readout carries a scale tag (EW/M_Z), "
          "unlike the lepton angles",
          0.10 < kappa_t < 0.20 and kappa_t / kappa_tau > 1000)

    # 4. F_transfer typing: lepton sector trivial, quark sector a running map
    check("F_transfer TYPING [P]: the lepton-mixing transfer is trivial (no scale "
          "ambiguity, ratio kappa_t/kappa_tau = %.0f); the quark-mass transfer is a "
          "genuine running map; both are the PyR@TE-confirmed SM Yukawa RGEs"
          % (kappa_t / kappa_tau), kappa_t / kappa_tau > 1000)

    # external backing present
    here = os.path.dirname(os.path.abspath(__file__))
    ev = os.path.join(here, "pyrate", "sm_yukawa_betas.txt")
    backing = os.path.isfile(ev) and "beta_Ye" in open(ev).read()
    check("EXTERNAL BACKING: verification/pyrate/sm_yukawa_betas.txt records the "
          "PyR@TE SM Yukawa betas; the mixing-rotating term (3/2) Y Y^+ Y carries "
          "y_max^2 (y_tau^2 leptons, y_t^2 up-quarks) -- the structural source of "
          "the asymmetry", backing)

    return summary("v163 F_transfer scale-tagging")


if __name__ == "__main__":
    raise SystemExit(1 if run() else 0)

003d51e2802a67f94111c48eba5b2048a841abc5a0a248b2da67469abba8416c

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.