We analyze Conjecture 59.2 (the spectral derivative bound for residual block sums of the ρ-stripped sequence) via Taylor expansion in the spectral parameter t. Three findings emerge from a fine-grained scan over dyadic blocks j = 14 to 32 (N = 10^10, 455 million primes). First, the variance baselines Viid(B^(k))/Viid(B^(0)) decay geometrically and match the even moments of the uniform distribution Uniform[-ln 2/2, ln 2/2] to within 3% across all tested j — the prime number theorem manifesting in the spectral hierarchy. Second, the excess ratios R_j^(k) = (B^(k))^2 / Viid(B^(k)) show no systematic growth in k, a geometry-arithmetic orthogonality between the deterministic dlp^k weights and the arithmetic correlations of h(p)/p. Third, sup_{|t|≤1} 2^j |E_j(t)|^2/t^2 is dominated by the B^(1) term (attained at t → 0 for j ≥ 26), with all 19 tested values bounded by 0.069. Combining these with the unconditional Guy + Chebyshev baseline 2^j D_j ≤ C_Guy · j, we prove that Conjecture 59.2 is a conditional corollary of Conjecture 59.1 (R_wt = O(1)) plus a structural input we call k-uniformity: existence of a constant C_1 with R_j^(k) ≤ C_1 · j for all k ≥ 0. The remaining distance to H' is reduced from "two independent conjectures" to "one conjecture (59.1) plus one empirically confirmed structural input (k-uniformity)". Keywords ZFC-rho, integer complexity, spectral derivative bound, Beurling-Lax, Taylor hierarchy, geometry-arithmetic orthogonality, k-uniformity, conjecture 59.1, conjecture 59.2, H' conjecture, weighted spectral ratio, dyadic block sums, prime distribution Language English Access Open Access License Creative Commons Attribution 4.0 International (CC-BY 4.0) Related identifiers (all "is continuation of") 10.5281/zenodo.19381111 — Paper L (foundation) 10.5281/zenodo.19476508 — Paper LVIII (deterministic DSF + BL) 10.5281/zenodo.19480518 — Paper LIX (two-conjecture closure) 10.5281/zenodo.19480563 — Paper LX (series closure) Notes Sixty-first paper in the ZFC-rho series. Reduces the spectral derivative bound (Conjecture 59.2) to a conditional corollary of the weighted spectral ratio bound (Conjecture 59.1) plus k-uniformity, a structural input on the excess ratios. Reviewed by ChatGPT, Grok, and Gemini. Version 1.0 Publication date 2026-04-16