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.
Beau Jérôme (Sun,) studied this question.