Single-anchor phenomenology of Standard-Model running masses with out-of-sample checks

We report a single-scale regularity in Standard-Model running masses. Using conventional MS kernels (QCD 4L, QED 2L) and a non-circular audit, the integrated residue

f_i(mu_star, m_i) := lambda^(-1) integral from ln(m_i) to ln(mu_star) of gamma_i(mu) d ln mu

at a universal anchor mu_star = 182.201 GeV collapses to a closed form

f_i = lambda^(-1) ln(1 + Z_i/kappa)

with no fitted parameters, where Z_i is an integer fixed by (Q_i, sector). Calibration uses a species-independent PMS/BLM stationarity (mass-free window) to determine (mu_star, lambda) and a small-Z slope to set kappa. Holding out all species beyond (e, mu), we verify the equality to 10^(-6) for quarks and charged leptons; equal-Z families are degenerate at mu_star. Policy/loop/scheme variants shift families coherently and stay within the quoted tolerance. We list concrete falsifiers and provide CSV/CI artifacts for re-runs.

One-line result (scan-friendly). Anchor mu_star = 182.201 GeV. We set kappa = phi = (1 + sqrt(5))/2 (golden ratio) and lambda = ln(phi). Canonical constants

(lambda, kappa) = (ln(phi), phi) ≈ (0.4812118251, 1.6180339887).

At mu_star,

f_i(mu_star, m_i) = gap(Z_i) = ln(1 + Z_i/phi)/ln(phi),

with the fixed integer map

Z = {
    4 + (6Q)^2 + (6Q)^4, quarks (color fundamental),
    (6Q)^2 + (6Q)^4, charged leptons,
    0, Dirac neutrinos.
}

Validated to 10^(-6) under QCD 4L + QED 2L and the declared threshold policy.

Audit summary (numbers). Central run (all charged fermions): max_i |f_i - F(Z_i)| ≤ 10^(-6). Worst case across scheme/threshold variants: 2.27 × 10^(-8). QCD 3L/5L cross-checks: 2.1 × 10^(-8) and 3.4 × 10^(-8). Electromagnetic alpha(mu) half-band: 3.39 × 10^(-8). IR-stability (light quarks): 5.9 × 10^(-8).

PDG-input half-band at the anchor. Propagating the quoted PDG uncertainties in alpha_s(M_Z) and heavy thresholds (m_c, m_b, m_t) through the fixed policy yields a combined anchor half-band of 3.0 × 10^(-8) on f at mu_star (charged fermions). This statistical/systematic band is reported separately from the identity residuals above.