Asymptotic Stability of Exact Weil-Block Capacity on Heisenberg Graphs: Extended Prime Range, Variance Reduction, and Requalification of the delta–beta* Tension

The O-series of the Cosmochrony admissibility sub-programme extracts the projective capacity exponent δ from exact Weil-block representations on Heisenberg Cayley graphs Cay(Gq, S) with Gq = Heis₃(Z/qZ). O12 measured δexact ≈ 4.3–$4.8$ at primes q ≤ 61; its corrective revision shows this is a finite-q crossover statistic, exactly independent of the central coordinate γ by an algebraic identity, and derives the intrinsic unfolded exponent exactly, δexact=3. The present paper, whose own numerical results were obtained independently of that closed form, extends the computation to q ∈ \101, 151, 211\ (with $q=211$ a robustness extension under reduced BFS coverage) to test whether δexact(q) was a finite-size artefact drifting toward the phenomenological target range $[7.4,10.6]$. The central result is that δexact exhibits a monotone decrease from $q = 61$ onward: the sequence $4.42, 4.80, 4.51, 4.27, 3.59$ at q ∈ \29, 61, 101, 151, 211\ shows no upward drift toward the target range, and all fitting strategies are consistent with δ_∞ < 5.0 — indeed, consistent with convergence toward the exact value $3$ now established independently. Two further findings sharpen this conclusion. First, the inter-block variance ratio Vₙᵐᵃˣ decreases from $5.20$ to $0.30$ as q increases from $29$ to $211$; condition (E2) is satisfied at q ≥ 151, establishing the extracted exponents as block-by-block properties, not merely means — a decrease now understood exactly, as the shrinking fraction of degenerate blocks in a finite covering problem, not a central-phase effect. Second, the fitting window grows from $4$ to $11$ points and R² > 0.993 throughout: the measurement becomes strictly more reliable at larger q. The finite-size hypothesis is ruled out in its strong form — namely that the exact-block exponent would drift toward the phenomenological target range at larger primes. The tension with β^*∈(0.09,0.13) is not resolved by a central-coordinate degree of freedom, which plays no role in this observable at any prime tested: its resolution requires determining which of several structurally distinct quantities — the finite-q crossover slope, the unfolded exponent δexact=3, or the saturation-scale scaling function of the same construction — the structural relation δ ↦ β^* is meant to take as input. No numeric constraint on β^* is drawn here.