Physics theoremStatement: Literature-sourcedProof: AI-adaptedPipeline-generatedverified 2026-10-15 (gpt-6-luna, gpt-6.1-sol, and delegated Codex review/repair agents; see completed run evidence)

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Qualified reported anomaly by exact affine subtraction

Physical scope

Exact affine derivation from the 2022 reported one-electron Penning-trap estimate. The anomaly inherits the source's apparatus, correction, 11-field weighting, stated 1 sigma uncertainty, correlation caveat, and omitted-data limitations; no theory comparison or new statistical inference is made.

Statement

Let the source-reported dimensionless ratio be denoted $\hat{g_{s} / 2} : = - \hat{μ} / μ_{B}$ , where $μ_{B} = e ℏ / (2 m)$ is the Bohr magneton, with $e > 0$ the elementary-charge magnitude in coulombs, $ℏ$ the reduced Planck constant in joule-seconds, and $m > 0$ the electron rest mass in kilograms, as specified in Fan2022 reported electron magnetic-moment determination. The hat marks an empirical estimate, not an exact constant. Define the derived dimensionless anomaly estimate ${\hat{a}}_{e} : = \hat{g_{s} / 2} - 1$ . Under the empirical premise from Fan2022 reported electron magnetic-moment determination, whose reported central value is $\hat{g_{s} / 2} = 1.00115965218059$ , exact subtraction gives ${\hat{a}}_{e} = 0.00115965218059.$ The source-stated $1 σ$ uncertainty remains $1.3 \times 10^{- 13}$ , and all apparatus, correction, weighting, correlation, and source-data qualifications of the experiment remain in force. This is only an affine transformation of a reported estimate; it supplies no comparison with a theoretical prediction.

Facts & Assumptions

Given: The empirical premise and its reported qualifications in Fan2022 reported electron magnetic-moment determination.

[F1]

Fan2022 reported electron magnetic-moment determination: the authors report $- μ / μ_{B} = g / 2 = 1.00115965218059 (13)$ as the weighted average of eleven corrected field determinations; they state a $1 σ$ uncertainty of $1.3 \times 10^{- 13}$ and note correlated nearby-field cavity uncertainties. The report's raw trials, covariance matrix, and weights are not reconstructed here.

[A1]

The reference value $1$ in ${\hat{a}}_{e} = \hat{g_{s} / 2} - 1$ is exact and dimensionless.

Proof

Given: [F1], [A1], and the definition of ${\hat{a}}_{e}$ in the Statement.

1.1givenF1A1algebra

Subtracting the exact reference gives ${\hat{a}}_{e} = 1.00115965218059 - 1 = 0.00115965218059$ .

2.1F1step 1.1algebra∎

If the reported ratio is shifted from its central value by any deviation $δ$ , subtracting the same exact $1$ leaves that deviation unchanged. Therefore the source-stated $1 σ$ uncertainty remains $1.3 \times 10^{- 13}$ , with the same measurement conditions, correction, weighting, correlation caveat, and omitted raw-data limitations from [F1]. No sampling distribution or theory comparison is introduced.

Depends on

Fan2022 reported electron magnetic-moment determination

Dependency tree · 2 levels

Sources

X. Fan et al., Measurement of the Electron Magnetic Moment, Physical Review Letters 130, 071801 (2023), arXiv:2209.13084v2 (2022)