Stepped Flavour by Flavour: The Mass Spectrum Certifies, Moves Nothing, and Closes the Certifiable Remainder

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24015573
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Stepped Flavour by Flavour: The Mass Spectrum Certifies, Moves Nothing, and Closes the Certifiable Remainder

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Stepped Flavour by Flavour: The Mass Spectrum Certifies, Moves Nothing, and Closes the Certifiable Remainder

William Alexander Aldred
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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