Physics-Informed Ordinal AI

Physics-informed machine learning typically encodes scientific structure as differential residuals. Many observational regimes are better described by order among events than by continuous trajectories that satisfy a known PDE. This preprint defines Physics-Informed Ordinal AI (PIO-AI): learning and control systems whose inductive bias, discrete clock, and/or adaptation alarm are grounded in ordinal and event-order structure on a shared event index. Systemic Tau provides a concrete instance: pairwise Kendall-type concordance and signed mean τₛ; absolute concordance change DE with the exact identity DE = |Δ̄E| + CE and cancellation index κ = CE/DE; beyond-pairwise ordinal residuals (Res_pair / excess³); and the Discrete Extramental Clock (RECD) with tick ΔT = g(τₛ)·|τₛ|. Circular-shift nulls are discussed as a methodological device. PIO-AI is contrasted with PINNs without claiming equivalence. The contribution is definitional and synthetic: minimum membership criteria, a map of existing Zenodo deposits onto paradigm layers, and explicit limits (zero-heavy counts; excess³ and RECD Φ are not operational alarms without pre-registration). No new experiments or numerical claims are introduced. Related manuscripts under journal review elsewhere are mentioned without naming venues. This record contains the English article (PDF, DOCX, Markdown), a Spanish summary, and CITATION.cff. No funding is declared. Text under Creative Commons Attribution 4.0 International. Version 1.0.0 is the cleaned final manuscript with continuous academic prose and Figure 1 (Physics-Informed Ordinal AI stack: Kendall/Systemic Tau → DE/κ → Res_pair/excess³ → RECD tick). Prior v0.1.0 remains available under the same concept DOI.