Asymptotic Stability of Exact Weil-Block Capacity on Heisenberg Graphs: Extended Prime Range, Variance Reduction, and Requalification of the δ–β∗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 established δexact ≈ 4.3--$4.8$ at primes q ≤ 61 and identified a tension with the phenomenological window β* ∈ (0.09, 0.13), leaving open two candidate explanations: a finite-size artefact, or a structural gap in the exact-block δ ↦ β^* relation. The present paper tests the finite-size hypothesis by extending the computation to q ∈ \101, 151, 211\, with $q = 211$ serving as a robustness extension under a reduced BFS coverage protocol. The central result is that δexact exhibits a monotone decrease from $q = 61$ onward: the sequence $4.42, 4.80, 4.52, 4.27, 3.59$ 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. 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. 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. While subleading corrections beyond the explored range cannot be strictly excluded, the observed stability of δexact under improving measurement conditions strongly disfavours a finite-size explanation of the tension. The tension is requalified: its resolution requires revisiting the structural relation δ ↦ β^* in the exact-block setting, where the observable retains a central-coordinate degree of freedom whose contribution to β^* is not yet derived.