The Romero Law of Relational Stability (RZS) in Black-Hole Timing: An Operational Dictionary, Replicable Pipeline, and Real-Data Results for Cyg X–1 and MAXI J1820+070

This work applies the Romero Law of Relational Stability to accreting black-hole X-ray binaries using a fully operational and replicable framework. A domain-specific dictionary maps effective capacity, informational noise, and latency onto standard spectral-timing observables, including power-colour ratios and reverberation time lags. Using published hard-state measurements for Cygnus X-1 and MAXI J1820+070, we compute both a relative stability index and a bounded stability index on a normalized scale. The manuscript provides explicit definitions, derived quantities, computed results, and a reproducible numerical script, enabling independent verification and alternative proxy testing. The study emphasizes operational clarity, falsifiability, and cross-domain portability of the stability framework.