Two Ledgers, One Row: The First-Row CKM Deficit Reconciled, and Its Correction Stack Priced to the Obstruction

I have priced the same missing money twice, in two of my own publicly deposited preprints, and the two prices do not match. The Missing Fifteen Ten-Thousandths (my paper #170) spends a global fit and reports the first-row CKM deficit as Δ_CKM = −0.00151(53). The Row That Doesn't Sum (#181) spends superallowed inputs only and reports three sums instead: 0.99791, 0.99867 and 0.99836 — deficits of −0.00209, −0.00133 and −0.00164. This paper reconciles the two ledgers exactly. Every digit of the difference between them is carried by two named input choices: the fit's |V_ud| sits 0.00012 above the superallowed value (worth +0.000234 in the row sum), and the fit's |V_us| is a compromise that sits 0.00075 above the semileptonic kaon road, 0.00026 below the scaled kaon average and 0.00095 below the leptonic road (worth +0.000336, −0.000117 and −0.000427 respectively). |V_ub| contributes less than one part in two million. The difference between my two papers is therefore an input-set artifact, accounted to the last digit — but the deficit itself is not: in a cross-table of every printed |V_ud| road against every printed |V_us| road, every precision cell is short, and the shallowest precision cell (superallowed × leptonic) is still short by 0.00133. The attack also finds the one genuine bookkeeping error in either ledger: the leptonic road's error bar spends the |V_ud| uncertainty twice, and corrected for the correlation its shortfall is 1.9 sigma, not 2.0. For the correction stack both papers point at, I compute everything the printed record supports — the row sum under all four printed evaluations of the universal radiative correction, the exact correction each kaon road would require to close the row, and the mutual consistency of the evaluations — and I prove that the decisive step, an independent recomputation of Δ_R^V and δ_NS from first principles, is obstructed by inputs that are in print nowhere: the per-transition correction table and the γW-box integrand itself. Since the two ledgers were printed, the world's literature has re-derived pieces of the stack three times; the moves are one to two ten-thousandths in |V_ud|, they point in both directions, and none of them closes the row. Grade: EXTENSION — argued in §6, not asserted. Keywords: CKM unitarity; Cabibbo angle anomaly; V_ud; V_us; radiative corrections; superallowed beta decay.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23929033
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Two Ledgers, One Row: The First-Row CKM Deficit Reconciled, and Its Correction Stack Priced to the Obstruction

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

Two Ledgers, One Row: The First-Row CKM Deficit Reconciled, and Its Correction Stack Priced to the Obstruction

William Alexander Aldred
preprint en

Abstract

I have priced the same missing money twice, in two of my own publicly deposited preprints, and the two prices do not match. The Missing Fifteen Ten-Thousandths (my paper #170) spends a global fit and reports the first-row CKM deficit as Δ_CKM = −0.00151(53). The Row That Doesn't Sum (#181) spends superallowed inputs only and reports three sums instead: 0.99791, 0.99867 and 0.99836 — deficits of −0.00209, −0.00133 and −0.00164. This paper reconciles the two ledgers exactly. Every digit of the difference between them is carried by two named input choices: the fit's |V_ud| sits 0.00012 above the superallowed value (worth +0.000234 in the row sum), and the fit's |V_us| is a compromise that sits 0.00075 above the semileptonic kaon road, 0.00026 below the scaled kaon average and 0.00095 below the leptonic road (worth +0.000336, −0.000117 and −0.000427 respectively). |V_ub| contributes less than one part in two million. The difference between my two papers is therefore an input-set artifact, accounted to the last digit — but the deficit itself is not: in a cross-table of every printed |V_ud| road against every printed |V_us| road, every precision cell is short, and the shallowest precision cell (superallowed × leptonic) is still short by 0.00133. The attack also finds the one genuine bookkeeping error in either ledger: the leptonic road's error bar spends the |V_ud| uncertainty twice, and corrected for the correlation its shortfall is 1.9 sigma, not 2.0. For the correction stack both papers point at, I compute everything the printed record supports — the row sum under all four printed evaluations of the universal radiative correction, the exact correction each kaon road would require to close the row, and the mutual consistency of the evaluations — and I prove that the decisive step, an independent recomputation of Δ_R^V and δ_NS from first principles, is obstructed by inputs that are in print nowhere: the per-transition correction table and the γW-box integrand itself. Since the two ledgers were printed, the world's literature has re-derived pieces of the stack three times; the moves are one to two ten-thousandths in |V_ud|, they point in both directions, and none of them closes the row. Grade: EXTENSION — argued in §6, not asserted. Keywords: CKM unitarity; Cabibbo angle anomaly; V_ud; V_us; radiative corrections; superallowed beta decay.

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