The O25 programme identified the ratio n₁ (q) /q as the central open asymptotic variable controlling the finite-size drift of ₀₈ₑ (q), and O26--O27 identified the effective dimension r₄₅₅ = d_² of the per-pair covariance operator in End (V_) as the key falsifiability criterion for the representation-theoretic identification. The present paper reports two measurements from the Q5a-O5 checkpoints for q \29, 61, 101, 151\. First, we extract n₁ (q) from the auto-calibrated fitting windows and fit n₁ (q) = \, q + by ordinary least squares, obtaining 0. 053 with R² 0. 879. The O14 correction yields ₂₎ₑₑ (q) 7. 4, 10. 6 for all q \29, 61, 101, 151, 211\, confirming the structural conclusion of O25. Second, using the per-block Weil vector projections c (v) stored in the Q5a-O5 checkpoints, we perform the formal effective-dimension computation of O26 Criterion 5. 4 in End (H₄₅₅), where H₄₅₅ = C³ is the admissible projection space (HEFF\DIM = 3, consistent with c (n₃) = 3 from O23. The covariance Cc has rank exactly r₄₅₅ = 3 for every conjugate pair and every prime q \61, 101, 151\ (100\% of pairs), with normalised eigenvalue structure ₁: ₂: ₃ = 1: 12: 12 invariant across all pairs and primes. This rank-3 result fills H₄₅₅ completely. The gap from the spin-12 prediction d_² = 4 reflects that H₄₅₅ V_: the formal test within End (V_) requires first identifying V_ H₄₅₅, which is the object of O29.
Jérôme Beau (Sun,) studied this question.