OD-35: Logarithmic Rectification of Alpha-Driven Growth Models for Prime Density Estimation

This record documents OD-35, a rectified alpha-driven model derived as a methodological extension of OD-34. While OD-34 identified a locally linear evolution of a growth-rate parameter α(k) across sieve scales, OD-35 examines the real alpha sequence extracted directly from exact values of π(10^k). Empirical analysis shows that the real α(k) does not follow a linear law globally, but instead converges asymptotically according to a logarithmic decay law: α(k) ≈ 1 + log10(k) − log10(k + 1) OD-35 therefore provides a logarithmic rectification of the linear OD-34 model, explaining its local validity and extending it into a globally coherent asymptotic framework. No claims of optimality or closed-form exactness are made.The purpose of this release is documentation, reproducibility, and diagnostic clarity, particularly for applications involving prime density profiling and scale extrapolation. The record includes: a reference Python implementation, extracted real alpha tables, curvature and asymptotic diagnostics, comparison with OD-34 and OD-33. OD-33 remains the closed and validated estimator; OD-34 and OD-35 serve as structural probes intended to inform future density models or factorization heuristics.