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

O9 resolved the geometric obstruction that prevented 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 D = 3. 05 continues the convergence toward the Bass--Guivarc'h prediction D ₇₎₌ = 4. The mean capacity ₙ 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) (ₙ) is confirmed at q = 101. The log-log regression gives = 0. 01, which is not a reliable 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, and show that only the second---based on the Weil decomposition of ₀₅₅^ 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 are deferred.