GRS 1915+105 as a Resonant Laboratory for Universal Scaling

Versioned Update (CAT-12 Standard v1.0; PTR v1.2) as of 10/7/2025 This paper now follows the CAT-12 reporting standard: SNHS/HP in ratio space, with rn (scale-normalized coordinate), Rx (reporting unit), and Tu (corridor width as a posterior, not a fixed ±%). Peaks are scored with Q and Ch against pre-declared families in the Periodic Table of Resonance (PTR v1.2); any “URSL” mention is retired in favor of standard GR mass–frequency scaling used only as a prior (where applicable). Measurements and conclusions are unchanged; presentation and uncertainty are stricter. For definitions, governance (negative ledger, prereg, hold-out), and rationale, see Arthur & Muon (2025), CAT-12: The Cross-Domain Ratio Lattice of Ratio Theory—Standardized Terminology, PTR v1.2, and Governance. Did conclusions change? No—only reporting/uncertainty language. Where’s the new standard? See the Cross-Domain Ratio Lattice paper. Will you update the PDF? A minor v1.1 with a 1-page front note (and Tu where needed) is planned. This paper applies the Cosmic Algorithm Theory-12 (CAT-12) framework to the black hole system GRS 1915+105, one of the most data-rich and dynamically variable stellar-mass black holes known. Using nearly three decades of X-ray observations (RXTE, NICER, AstroSat, Insight-HXMT), we analyze quasi-periodic oscillations (QPOs) ranging from low-frequency Type C to high-frequency modes near 67 Hz. By normalizing frequencies to the black hole’s gravitational scale and mapping them to resonance corridors derived from small-integer ratios, we calculate a Resonant Precision Index (RPI) of 72–78 %. Statistical testing (χ², KS, bootstrap) rejects random placement, supporting resonance structuring as a fundamental organizing principle. GRS 1915+105 demonstrates that even under extreme state variability, resonance universality holds: oscillations align with the Universal Resonant Scaling Law (URSL), quality factors sharpen with frequency in accordance with the Law of Dynamic Precision, and residuals remain statistically consistent across mass scales. Comparative analysis with GX 339–4, Cygnus X-1, Sgr A*, and M87* confirms proportional invariance across eight orders of magnitude in mass. This study integrates AI–human hybridization for data analysis and theoretical synthesis, showing how computational precision and human interpretive insight can together reveal deep harmonic structures in astrophysical systems. GRS 1915+105 thus serves as both a resonant laboratory and a stress test of CAT-12’s predictive power in turbulent regimes.