Event conditioned phase transitions and constant-dependent locking in a phase-FM system

This archive contains the full computational study, analysis outputs, and manuscript for a reproducible investigation of event-conditioned dynamics in a phase–frequency modulated (Phase–FM) oscillator.

The work introduces a geometric observable derived from the analytic signal and defines an event-conditioned enrichment statistic that quantifies deviations from randomized baselines. Using GPU-accelerated Monte Carlo experiments with extensive phase randomization and paired-contrast controls, the study demonstrates three key empirical findings:

1. A sharp regime transition in the enrichment statistic as a function of system parameters, tightly bracketed in parameter space.

2. Robust persistence of the observed structure under phase randomization, ruling out single-trajectory artifacts.

3. Systematic, statistically significant modulation of the effect by coupling ratio, with the constant e consistently outperforming a nearby control ratio across most tested regimes, while other constants exhibit strongly regime-dependent behavior.

The repository includes:

• The full LaTeX manuscript

• All generated figures

• Raw CSV outputs (*_per_rep.csv, *_summary.csv, *_contrasts.csv)

• Scripts used for analysis and visualization

• Reproducible command-line configurations

This work does not propose a physical theory. Instead, it documents a rigorously controlled computational phenomenon and provides a transparent methodological framework for further mathematical and dynamical investigation.