PAR(2): A Phase-Amplitude-Relationship Framework for Quantifying Circadian Clock–Target Gene Dynamics Across Tissues and Species

Superseded by 10.5281/zenodo.17920427 — earlier working paper in the same series. The PAR(2) Discovery Engine is a statistical validation platform for analyzing circadian clock–target gene dynamics using second-order autoregressive eigenvalue profiling. The eigenvalue modulus |λ| quantifies temporal persistence—values in the stable band (0.52–0.72) indicate healthy dynamics, while drift toward |λ| → 1.0 signals instability observed in cancer models. Key features: 721 completed analyses across 72 biological contexts 129 consensus gene pairs validated in 3+ independent datasets Cross-kingdom validation: mouse tissues, human blood/organoids, Arabidopsis 39 embedded circadian datasets ready for analysis AR(2) model order validated by Boman C-P-D ODE model (Cancers 2026) Granger causality confirms clock→target directionality in constant darkness Includes complete source code (TypeScript/Python), manuscripts (LaTeX), standalone CLI tools, and Docker deployment. Free for academic use.