Short companion to "An empirical subleading correction to Wolf's formula for consecutive prime gaps" (Sestak 2026, v1, Zenodo 10. 5281/zenodo. 19796305). The v1 paper proposed a two-parameter, no-intercept correction R (g, N) ≈ a·√ω (g) − b·log log N to Wolf's 1998 heuristic, fitted on n = 140 points covering N ∈ 10⁵, 10¹3 under the primary filter ρ = g·Cg/ln N ∈ 0. 05, 1. 10. This companion extends the dataset to N ≤ 3·10¹4 (28 values of N, n = 169) and reports: (i) out-of-sample validation — the v1 fit, frozen at (a, b) = (0. 855, −0. 202), predicts the 29 new (g, N) points with weighted R² = 0. 986; (ii) coefficient stability — refit on n = 169 gives (0. 836, −0. 195), inside the pre-extension block-bootstrap 95% intervals, and the intercept remains statistically unjustified (LR p = 0. 18, ΔBIC = −3. 30) ; (iii) first ω (g) = 3 datapoint at g ≠ 30 — g = 42 enters the relaxed filter at N = 3·10¹4, the first within-stratum variation in g and Cg at ω = 3. The qualitative reading of v1 is unchanged. 5 pages, 1 figure. Code and data: github. com/dkrse/math-02-wolf. In memoriam Marek Wolf (1949–2026).
Kristian Sestak (Fri,) studied this question.