Stepped Flavour by Flavour: The Mass Spectrum Certifies, Moves Nothing, and Closes the Certifiable Remainder
Year: 2026
Type: preprint
Abstract: AF-30 integrated the one fragment of the next completeness class that owned sources certify (the QCD three-loop diagonal) and charged the rest forward in two kinds: matrices that are literature (uncertifiable here, bounded at ≤ 0.025 in α⁻¹) and the full mass spectrum, which is data — every Standard Model fermion's measured mass — and was left unintegrated only because the ported bench steps thresholds generation-wise. This paper integrates it. The bench is AF-30's, itself AF-25's verified machinery, copied unchanged; its calibration block reproduces V0, V3, and V6 digit for digit (V6: 47.786 / 38.300 / 28.410 at E_ind by the inherited read; crossings 13.05 / 14.20 / 16.35) before variant 9 is switched on. Variant 9's construction: the declared spectrum (e 0.000511, μ 0.10566, τ 1.77686, u 0.00216, d 0.00467, s 0.0934, c 1.27, b 4.18, t 172.69 GeV) has exactly one threshold inside the bench's range [m_Z, 10¹⁹ GeV] — the top's — and every lighter mass sits below the floor, already inside the measured α_i(m_Z) inputs; stepping those inside the run would double-count, and the paper says so on its face rather than performing nine thresholds for show. The one real correction is at that one threshold: V6's nf = 5 electroweak coefficients remove the third generation's whole quark share — (t + b) together, shares 0.360526 (ΣY⁴ structure) and 0.550000 (ΣY² structures) of each entry's fermion part — across the whole interval [m_Z, m_t], although the b quark (4.18 GeV) is active there. Variant 9 splits the share by flavour on AF-25's own declared charge table (Q_L split half per flavour): the removal becomes the top's share alone — 0.338158 / 0.425000 — restoring b's 0.022368 / 0.125000 share of each fermion part in that interval (restored coefficient amounts 0.028333 / 0.112500 / 0.037500 / 0.187500 across b₁₁/b₁₂/b₂₁/b₂₂). The effect, graded under the point-probe convention (§2): at E_ind, V9 − V6 = −0.0000 / −0.0001 / −0.0000 in α⁻¹; the three crossings move by 0.0000 dex at four-decimal print; the nearest-sample read returns V9's at-E_ind line identical to V6's at print precision (47.786 / 38.300 / 28.410). The interval is short (ln(m_t/m_Z) = 0.6385, against the run's 39) and the restored shares are small; the bench evaluates the repair at a tenth of a print unit on one coupling. Verdict in AF-30's own grading language: the mass spectrum joins the QCD diagonal in the certified column, the no-crossing verdict's bench-dependence is now closed at every address the record can certify, and the class's only remaining address is the uncertified matrices — bounded, armed, and unchanged.
Author: Aldred, William Alexander
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225410674