Refined Spectral Balance in the Adaptive Framework (ABF v9.1)

This work introduces the Adaptive Balance Framework (ABF) — a reproducible analytic and computational model designed to study NB/BD stability within a weighted Hilbert structure.
It builds on the weighted kernel

K_{mn} = e^{-\frac{1}{2}|\log(m/n)|}

The framework measures mean-squared deviation  across logarithmic scales and performs regression fits of

\log(MSE^*) = \alpha + \beta \log\log N, \quad \theta = -\beta,

The ABF serves not as a proof of the Riemann Hypothesis, but as a rigorous and transparent experimental tool for investigating the boundary stability implied by its analytic equivalents (NB/BD).
It integrates reproducible code, data tables, and visualization scripts for full transparency and replication.