Proposition: The Proton–Electron Mass Ratio

From Lemmas 1–4:

m_p / m_e = 1836 + α_em × 21 × (1 − 1/(84π)) + α²_em × 21 × 16/1836 + O(α³_em)

Static resistance (Lemmas 1–2): three independent layers from three axiom subsets, summing to 1836.

Dynamic maintenance (Lemma 3): substrate coupling across all channels at rate α_em, giving α_em × 21.

Isotropic leakage (Lemma 4): radiation loss normalised by the dimensional expression count and the solid angle, reducing the dynamic term by factor (1 − 1/(84π)).

O(α²_em) correction: the leakage of the leakage — the break operating on its own maintenance.

The coefficient 21 × 16/1836 arises from the same channel geometry (21) acting on the ratio of a dimension-count factor (16, whose structural decomposition from {21, 3, 4} is owed under KS-30.3 — it is not Layer 3, which is 9) to the static resistance (1836).

This term is structurally required by the recursive nature of 1:1 + 1×ε @ AS: the break breaks its own repair.

O(α³_em) and higher: each successive order is smaller by a factor of roughly α_em. The series converges but never terminates. This is ε operating recursively.

Numerical evaluation:

1836 + (0.0072974 × 21 × 0.99621) + (0.0072974² × 21 × 16/1836)

= 1836 + 0.15266370 + 0.00000975 = 1836.15267344

Measured (CODATA 2022): 1836.15267343(11)

Residual: +0.000000014 ≈ 0.008 parts per billion — 7.5× smaller than the experimental uncertainty (±0.06 ppb).

(The factors in the line above are shown rounded to the displayed digits; the products and the final ratio are evaluated at full precision — α = 0.00729735, 1 − 1/(84π) = 0.99621060.)

Precision

The O(1) term captures 99.992% of the ratio. The O(α_em) correction captures the remaining 0.008%. The O(α²_em) correction captures the residual to within 0.008 ppb — below the current experimental uncertainty — using a coefficient whose structural decomposition is owed under KS-30.3; the parameter-free claim is therefore stated firmly at order α.

Each successive order in the perturbative expansion is smaller by a factor of roughly α_em. This is the signature of a natural perturbative series, not a fitted approximation.