Retro-Augmented Spatiotemporal Causal Decision Trees for Cellular Rejuvenation: A Mathematical Framework Integrating Reinforcement Learning, Renormalization Group Theory, and Partial Differential Causal Inference

Abstract

Chur Chin*

Cellular aging represents one of the most profound biological challenges of our time, characterized by progressive accumulation of epigenetic alterations, transcriptomic dysregulation, and attractor basin displacement in high- dimensional gene expression state spaces. We present a novel mathematical architecture—the Retro-Augmented Spatiotemporal Causal Decision Tree (RA-SCDT)—that unifies reinforcement learning, causal inference, renormalization group (RG) theory, entanglement entropy formalism, and locally stable partial differential equations (PDEs) to model and optimize cellular rejuvenation trajectories. The central innovation is the incorporation of future-state information (I_{t+1→t}) into past decision nodes via retro-augmented state definitions, enabling backward-propagated optimization of transcription factor interventions. We formalize the aging process as a stable attractor in a multi-scale RG flow, model the Yamanaka factor (OSKM) cocktail as a relevant RG perturbation operator, and derive closed-form optimal control policies using Hamilton-Jacobi-Bellman (HJB) equations subject to Lyapunov identity-preservation constraints. Bifurcation analysis using Feigenbaum constants and Wilson loop causal conservation conditions provide global stability bounds. Simulation confirms bifurcation thresholds at α_c ≈ 2.90 and optimal reprogramming stopping times near Day 11–13, where cellular biological age approximates 23–25 years while fibroblast identity is preserved. Our framework identifies sparse transcription factor candidates beyond OSKM—including TET1, TET2, KDM6A, FOSL1, and ATF4—as high-leverage causal interventions.

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