Stability and out-of-sample validation of an empirical correction to Wolf's formula for consecutive prime gaps (companion to v1)

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 ∈ [10^5, 10^13] under the primary filter ρ = g·C_g/ln N ∈ [0.05, 1.10]. This companion extends the dataset to N ≤ 3·10^14 (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 = 3·10^14, the first within-stratum variation in g and C_g 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).