GRO J1655–40 as a Harmonic Resonance Laboratory Folding the 3:2 HFQPO Pair into the Cross-Domain Ratio Lattice

This paper applies the Cosmic Algorithm Theory-12 (CAT-12) harmonic framework to GRO J1655–40, treating it as a stellar-mass resonance laboratory. Using high-frequency QPO data, the analysis classifies the source’s oscillation structure in ratio space before applying any specific gravitational model. The observed HFQPO ratio is mapped onto the pre-declared 3:2 corridor of the CAT-12 Periodic Table of Resonance (PTR), establishing harmonic family membership through primary ratio alignment, secondary ratio coherence, and cross-metric verification. The study follows the standard CAT-12 ladder process: Ratio-space classification using Law of Dynamic Precision corridors Multi-ratio coherence checks with nodal frequencies RPI contribution breakdown to identify dominant oscillatory modes Cross-metric robustness tests showing invariance under Kerr, Horndeski, MOG, and accelerating black hole metrics Placement on the SNHS ladder, revealing that GRO J1655–40 shares the stellar-mass 3:2 rung with XTE J1550–564, GRS 1915+105, and Cygnus X-1 Seven figures illustrate the corridor placement, ratio posteriors, cross-metric invariance, and ladder embedding. A concise mathematical appendix provides a worked example of the harmonic classification procedure using observed frequencies, addressing reviewer expectations for explicit calculations. This work demonstrates how CAT-12 classification precedes theory, providing a metric-agnostic harmonic scaffold for analyzing black hole QPOs across gravitational models. GRO J1655–40 serves as a clear empirical anchor for the stellar-mass 3:2 family within the broader cosmic resonance lattice. Keywords: CAT-12, Cosmic Algorithm Theory-12, GRO J1655–40, QPO, harmonic resonance, SNHS ladder, Periodic Table of Resonance, Law of Dynamic Precision, black holes, stellar-mass systems, metric-independent classification, Horndeski, MOG, Kerr