A Stability-Constrained Phase-Dependent AR(2) Framework for Discovering Cross-Tissue Circadian Gating Architectures

This repository accompanies the manuscript "Phase-Amplitude-Relationship (PAR2) Analysis Reveals Emergent Temporal Dynamics in Circadian-Cancer Gene Networks." The PAR(2) framework models target gene expression as a function of clock gene phase through AR(2) dynamics, with eigenvalue modulus |λ| serving as a stability metric that is approximately preserved across continuous, discrete, and autoregressive representations. Key findings include: (1) cross-tissue consensus reduces false positive rates from ~16% to ~1-5%; (2) healthy tissues show ultradian eigenperiods (~10h) while cancer models show near-circadian periods (~23h); (3) Wee1 emerges as the top computational candidate for circadian-cell cycle coupling. Validation spans GEO datasets including GSE54650 (12 mouse tissues), GSE157357 (intestinal organoids), GSE262627 (PDA organoids), and GSE245295 (aging pancreas). Package includes: compiled PDF manuscript, LaTeX source, analysis reports, core algorithm code (TypeScript), and raw results data.