Polynomial-Growth Capacity Dynamics at Large 𝑞: Volumetric Growth Confirmation, Capacity Decay, and the Weil Decomposition Roadmap

O9 resolved the geometric obstruction that prevented δ extraction on LPS graphs by replacing them with Cayley graphs of the discrete Heisenberg group Heis₃(Z/qZ), whose polynomial shell growth restores an exploitable BFS window. The present paper performs the first computation at the large prime $q = 101$ (|Gq| = 1,030,301), using a random-walk BFS at fraction $f = 0.20$ and a TensorSketch fingerprint of dimension D = 16,384.Three results are established positively. The ball growth exponent D̂ = 3.05 continues the convergence toward the Bass--Guivarc'h prediction Dₕₒₘ = 4. The mean capacity Σₙ decays by $23.5%$ over the pre-saturation window (n^* = 13 BFS steps), providing the first direct evidence of projective depletion at large q. The state law Rₙ⁽³⁾ ≈ Φ(ηₙ) is confirmed at $q = 101$. The log-log regression gives δ̂ = 0.01, which is not a reliable δ measurement. This reflects a structural incompatibility between the dense TensorSketch and the pre-saturation window: reaching the power-law onset within |Bₙ| ≤ q² requires D q⁴ (i.e. D 10⁸ at $q = 101$), which is computationally impractical. O10 therefore converts this limitation into an algorithmic obstruction: the geometric obstruction of O8--O9 is resolved, and the remaining limitation is representational.We identify two regimes with distinct necessary conditions for a reliable log-log fit of δ, and show that only the second---based on the Weil decomposition of ρaff⊗ 3 into blocks of dimension $O(q)$---is computationally viable. The Weil-block fingerprint is formulated as open problem O10-O1; its implementation and the extraction of δ are deferred.