Phase-dependent autoregressive modelling maps tissue-specific clock-target gating architectures

Version 6 (August 2026): Corrects a preprocessing error in the GSE157357 intestinal organoid analysis (non-chronological column ordering without replicate averaging). Key corrections: WT clock/target hierarchy gap +0.347 → +0.073; Wee1 WT |λ| 0.093 → 0.655. Platform URL updated to par2discovery.com. Paper G companion paper status updated (accepted The Fibonacci Quarterly, August 2026). All cross-tissue findings (Tables S1–S3) are unchanged. A Stability-Constrained Phase-Dependent AR(2) Framework for Discovering Cross-Tissue Circadian Gating Architecturesv2.0 · 2026-03-21 Introduces PAR(2), a phase-dependent autoregressive framework of order two that quantifies temporal coupling between core clock genes and downstream targets across mammalian tissues. PAR(2) extends standard AR(2) models by allowing autoregressive coefficients to vary smoothly over circadian phase while enforcing dynamical stability. Applied to over 28,000 clock–target gene pairs across 22 publicly available circadian transcriptomic datasets, with hits classified into three confidence tiers using residual-based permutation testing (B = 1,000) and cross-tissue replication criteria. Wee1 emerges as the most robustly gated target — a Tier 0 hit across two independent liver datasets replicating in heart and cerebellum (eigenperiods 22.8–24.5 h). In intestinal organoids, Apc mutation increases gating density from 3.8% to 6.7% and inverts the clock/target hierarchy; the Apc/Bmal1 double mutant paradoxically restores the hierarchy gap through non-additive compensatory effects. Phase-gating terms improve in-sample fit but not out-of-sample prediction, confirming PAR(2) as a descriptive discovery framework. v2.0 corrects the abstract from the original Cell Systems submission (CELL-SYSTEMS-D-25-00764), which contained numerical claims inconsistent with the supplementary data; all figures now correspond directly to Supplementary Tables S3–S5. Clock–target pairs tested: 28,000+Datasets: 22 circadian transcriptomic datasetsPermutation tests: B = 1,000 per pairTop hit: Wee1 (Tier 0, liver × 2 datasets, replicated heart + cerebellum)Eigenperiods (Wee1): 22.8–24.5 hOrganoid hierarchy gap: +0.35 (WT) → −0.025 (ApcKO) → +0.11 (double mutant) Package contents: – LaTeX source (Paper_E_Phase_Gated_PAR2.tex)– Cover letter for journal submission– Supplementary Table S1 — Tissue gating module summary– Supplementary Table S2 — Golden-ratio eigenstructure enrichment by tissue– Supplementary Table S3 — Tiered hits (Tier 0/1/2) across tissues– Supplementary Table S4 — Intestinal organoid perturbation results (WT / ApcKO / BmalKO / double mutant)– Supplementary Table S5 — Per-tissue eigenvalue summaries for significant PAR(2) fits– Cross-tissue gating architecture data (JSON)– Phase-dependent coefficient examples (JSON)