Operational Deductive Rules for Real-Economy Acceleration in the AI Era

Real-economy growth acceleration in the AI era is often limited not by capability growth itself, but by translation bottlenecks that prevent AI progress from becoming realized output.This supplement provides an operational, theorem-driven rule system that converts a structural “capability -> reality” decomposition into deductive rules linking measurable indicators to intervention levers.It is designed for searchability and reuse by researchers, policy teams, and automated agents, with machine-readable rule registries and closed-loop operational protocols. Core identities The framework separates latent capability output from realized real-economy output via: Translation decompositionY^R_t = Omega^P_t * Omega^I_t * Y^I_twhere Omega^P_t (physical translation factor) and Omega^I_t (institutional translation factor) lie in (0,1]. Translation gap (additive)g_t := log(Y^I_t) - log(Y^R_t) = -log(Omega^P_t) - log(Omega^I_t) Window speed ratio (observable diagnostic)v_t^(h) := Delta_h log(Y^R_t) / Delta_h log(Y^I_t)which measures how fast realized growth tracks latent progress over window h. What this supplement contributes A large catalog of nontrivial theorems expressed as “deductive acceleration rules,” grouped by:(A) capability growth, (B) physical translation improvement, (C) institutional translation improvement, (D) allocation/control, (E) risk/events/robustness. Operational closure: each theorem is closed as an explicit mapping from observables (e.g., gap, speed ratios, bottleneck pressure indices, event-attributed shocks) to actionable levers (investment shares, policy controls, safety/risk constraints). Results for bottleneck switching (min-type effective capacity), time-to-target bounds, local cost-effectiveness ranking, fixed-point dynamics for institutional states, and expectation shifts under diffusion/jump risks. Extensions that support real-world deployment: robust allocation under measurement noise, lead-time (implementation delay) effects, event attribution protocols, and tail-risk-aware policy design. Machine-readable assets (for AI-assisted operations) To maximize reuse and implementability, the paper includes: A machine-readable rule registry schema (rule_id, required observables, admissible levers, conditions, decision predicate, expected direction/sign, and validation constraints). A closed-loop operational protocol (observe -> compute diagnostics -> attribute events -> allocate robustly -> enforce safety/floor constraints -> update registry). Text-extraction-friendly ASCII anchors for key identities to support deterministic reconstruction and automated parsing. Companion paper (required reference) This supplement is model-consistent with the main paper and intended to be used alongside it: Takahashi, K. (2026). From AI Capability Growth to Real-Economy Growth: A Semi-Endogenous Model of Physical and Institutional Bottlenecks. Zenodo. https://doi.org/10.5281/zenodo.18677068