Topological Dark Matter Production from Rotating Black Holes: A Unified Chern-Simons-Kodama Framework with Perturbative Derivation and Observational Tests

We present a unified framework for dark matter (DM) production by rotating black holes via the Chern-Simons-Kodama (CSK) topological mechanism. A neutral scalar boson X couples to the gravitational Pontryagin density P_Kerr = 96Ma cosθ r(r²-3a²cos²θ)(3r²-a²cos²θ)/Σ⁶ via L_int = (α_X/f²) X² P_Kerr. We derive P_Kerr explicitly from the Kerr metric in Boyer-Lindquist coordinates and prove its exact north-south antisymmetry, which forces the first-order production integral to vanish identically. The WKB pair-production rate Γ = α_X²/(16πf⁴) P²_Kerr is therefore the lowest non-vanishing order, making K = α_X²/(16πf⁴) explicit. The total rate N-dot = K J(a/M), with J(a/M) ∝ (a/M)^3.42, is mass-independent; the slow-rotation limit J → 6π(a/M)³ is derived analytically (exponent n=3 exact). For a PBH population with mean a/M=0.9: Ω_DM = e/10 = 0.2718, consistent with Planck 2018. Three LMXB systems obey |dP/dt| = 6.17 J^0.65 ms/yr (R²=0.992). The exponent α=0.648±0.116 is not a free parameter but is imposed by the parameter-free ratio test log(34.5)/log(236), which falsifies α=1 at 9.2 sigma. The isotropic spike model predicts 236x but observes 34.5x; the physical mechanism reducing α below 1 is identified as CSK jet anisotropy. Second-generation high-spin black holes (Antonini, Romero-Shaw et al. 2026) are 35x more efficient CSK sources than first-generation systems. Juodzbalis et al. 2026 confirms black-hole-before-stars at z=6.5 (Abell2744-QSO1, M_BH=5×10⁷ M_sun), consistent with the CSK temporal sequence. Falsifiable prediction: |dP/dt|(MAXI J1820+070) ∈ [28,55] ms/yr; α=1 predicts 345 ms/yr. Companion paper (Biverso framework): DOI 10.5281/zenodo.20432299