Reinforcement Scaling and Reparodynamics: Toward a Unified Compute–Repair Law (v1.0) and Empirical Validation of the Compute–Repair Law: Simulations and Physical Benchmarks (v1.0)

This dual release unifies the theoretical and experimental foundations of the Compute–Repair Law (CRL) — the central scaling principle of Reparodynamics. Paper 1 – Theory: “Reinforcement Scaling and Reparodynamics: Toward a Unified Compute–Repair Law” formalizes the CRL, proving that reinforcement learning post-training scaling curves and repair-stability curves share a single governing equation: S(R) = S_{\max} - \Delta\,g(R) where g(R) follows exponential or power-law forms depending on efficiency and noise structure. The paper derives a variational equivalence between learning and repair, formulates budget-optimal allocation, stop rules, and efficiency diagnostics, and introduces the Tier-3 Box protocol for physical benchmarking. Paper 2 – Empirical Validation: “Empirical Validation of the Compute–Repair Law: Simulations and Physical Benchmarks” provides the first dual validation of the CRL: Simulation: stochastic gradient descent reproduces both exponential and power-law CRL branches from Gaussian vs heavy-tailed noise. Physical Tier-3 Box: an ESP32-S3 thermal regulator validates the CRL in a real energy–stability system, confirming cross-substrate convergence. Together, these works demonstrate that both informational (AI) and physical (hardware) systems follow a shared efficiency-bounded scaling law, supporting the Reparodynamics framework as a substrate-agnostic science of repair, stability, and resource optimization.