SAGE & RHCM: A Unified Physics-GroundedAutonomous Discovery Engine

This technical preprint introduces SAGE (Symbolic Autonomous Generation Engine), a computational discovery platform built on the Recursive Harmonic Collapse Matrix (RHCM) theoretical framework. The system integrates symbolic physics modeling, autonomous experimentation, and computational simulation into a single research environment spanning multiple scientific domains. Implemented as a unified Python codebase of approximately 78,000 lines, the platform derives physical structures, quantum gate implementations, and candidate materials directly from a recursive geometric substrate based on golden-ratio scaling. Unlike conventional machine-learning approaches that depend on pre-training and labeled datasets, the SAGE architecture performs discovery through curiosity-driven experimentation and symbolic rule induction. The system includes modules for quantum circuit synthesis, Navier–Stokes fluid simulation, particle collider event modeling, semiconductor band-gap prediction, and cross-domain materials discovery. The RHCM framework organizes physical phenomena along a dimensionless geometric coordinate derived from φ-scaled recursion. Within this model, particle masses, turbulence thresholds, superconductivity regimes, and astrophysical temperatures emerge at discrete φ-indexed depth shells. The paper presents the theoretical basis of the RHCM model, a detailed audit of the SAGE architecture, validation experiments performed within the framework, and a series of proposed experimental predictions designed for external testing. This work explores the possibility that physical laws and material properties can be derived from recursive geometric structure rather than empirical parameter fitting, and provides an executable computational environment for testing that hypothesis.