Algebraic α as a Diagnostic Reference for Fundamental Metrology

If the algebraic fine structure constant α⁻¹ = 137.035999177 (Carpenter, 2026s) is treated as exact — the source of truth, not a prediction to be validated — then every deviation in a measured constant becomes a diagnosable systematic with a traceable root cause. This paper demonstrates the method and applies it to the full variance register. We recompute every α-dependent CODATA 2018 fundamental constant using the algebraic α, holding all α-independent inputs at their CODATA values. Every α-dependent constant shows a coherent ~4.4σ offset. Every α-independent constant agrees to <0.01σ. The pattern is not noise — it is a single systematic, amplified through every derived quantity. Root-cause analysis identifies the source: Parker et al. (2018), a Cs-133 recoil measurement that disagrees with all other modern α determinations by 5.5σ, was included in CODATA 2018's global fit. It pulled the adjusted α low by ~0.7 ppb (4.4σ relative to CODATA's stated uncertainty). Because every α-dependent constant inherits the fit, one bad input corrupts the entire table. The 2022 CODATA adjustment (Tiesinga et al., 2025) validated this diagnosis. Parker was downweighted; Morel (2020) and Fan (2023) were incorporated. The adjusted α⁻¹ shifted by +93 in the last three digits — from 137.035999084(21) to 137.035999177(21) — converging to the algebraic value exactly. Every α-dependent constant moved in the direction and by the magnitude this analysis specified. The method is then extended beyond Parker. Every remaining variance in the diagnostic programme is root-caused: the proton-to-electron mass ratio (133σ) is resolved to 0.01σ by a fourth-order correction with rational coefficient 22/27; the Morel Rb-87 offset (2.7σ) is diagnosed as a predicted recoil systematic; the Parker Cs-133 deficit (4.8σ) is identified as a species-specific systematic common to all Cs measurements; and the gravitational constant G (0.37σ) is shown to be limited by measurement precision, not formula precision. A head-to-head comparison of Fan's electron g−2 extraction and the Carpenter algebra demonstrates that both agree to 0.3σ, but the algebra has zero empirical inputs, zero theory dependencies, and identified the Parker systematic before CODATA did.