Uniform Coercivity, Pointwise Large-Field Suppression, and Conditional Closure of the Lattice Yang-Mills Mass Gap at Weak Coupling in d = 4

We address the remaining interface gaps in the programme [E26I]-[E26VIII] toward a uniform log-Sobolev inequality (LSI) and transfer-matrix spectral gap for lattice SU(N_c) Yang-Mills in d = 4 at weak coupling. Four gaps are treated: (G1) the pointwise-in-background validity of Balaban's T-operation small-factor bound -- stated in v2 as the explicit hypothesis (H-PTW), since the detailed audit appendices announced in v1 were absent from the document (their references rendered as "??"); (G2) a uniform small-field coercivity estimate for the effective action; (G3) uniform analyticity of boundary terms; (G4) a quantitative bootstrap of all constants. The central correction of v2: the sign of the one-step coupling drift in v1's Theorem 5.2 (g_{k+1}^{-2} = g_k^{-2} + 2 b_0 ln L_RG, coupling weakening toward the infrared) is inverted relative to asymptotic freedom, and contradicts the companions' own use of n_max ~ 1/(2 b_0 g^2 ln 2) (ai.viXra:2602.0032 Sec. 8, 2602.0033, 2602.0041 Sec. 7.3), a formula meaningful only if the coupling grows along blocking and exits the weak regime. With the corrected sign the monotone bootstrap of v1's Theorem 5.3 reverses: the inductive conditions are guaranteed only up to the finite horizon k*(beta) = (g_0^{-2} - gamma_0^{-2})/(2 b_0 ln L_RG) + O(1), and since the multiscale construction uses log_2 L scales, the conclusion holds on the volume window log_2 L <= k*(beta), i.e. L <= e^{C/g^2 + O(1)} with C = 1/(2 b_0) = 24 pi^2/(11 N_c) -- exactly the window of the companion papers ai.viXra:2602.0032/0033 (v2). Full volume-uniformity would additionally require a strong-coupling handoff beyond the crossover scale (Osterwalder-Seiler regime), stated as hypothesis (H-XOVER) and not established here; accordingly the "unconditional closure" of v1 is retitled to conditional closure. Version 2 also repairs the dangling "??" references, supplies the missing proof of Lemma 3.1, rewrites the proof of Lemma 7.4 in the series' fundamental-trace convention (its statement W''(0) = 1/(2N_c) is correct; the v1 proof mixed normalized and fundamental traces), corrects sum_{k>=0} (k+1) 2^{-3k} = 64/49 (v1: 8/49), and fills in the companion identifiers. All corrections are verified in a companion numerical suite.