A Reproducibility Index for Artificial Intelligence Systems A Quantitative Measure of Determinism, Invariance, and Replayability

Modern artificial intelligence systems are widely deployed in scientific, medical, financial, legal, and safety-critical domains, yet they frequently fail basic reproducibility requirements: identical inputs can yield different outputs, semantically equivalent representations can produce divergent decisions, and internal reasoning trajectories often cannot be replayed or audited. Existing reproducibility practices-such as seed fixing, experiment logging, and environment pinning-improve empirical consistency but do not provide structural guarantees, and they largely ignore representational invariance and replayability of reasoning. Building on the Deterministic Computation Law (DCL), which characterizes reproducible computation as necessarily factoring through canonicalization followed by deterministic, replayable reasoning , this paper introduces a Reproducibility Index (RI) for AI systems. The RI quantitatively measures a system’s degree of compliance with the three axioms underlying DCL-Input Determinism, Representation Invariance, and Replayable Reasoning-via three normalized component scores: an Input Determinism Score (IDS), a Representation Invariance Score (RIS), and a Replayability Score (RS). These components may be reported as a vector for auditing and certification, or aggregated into a scalar index using domain-specific weights to support procurement and risk decisions. The RI converts reproducibility from a binary claim into an enforceable, measurable property, enabling objective comparison across systems, explicit certification thresholds for regulated settings, and principled identification of irreproducibility sources in modern AI deployments.