Irreversibility Detection in Directional Systems: A Reproducible Framework Based on The Pleasure Order

Boundary note (added 2026-07-23): the Ω-centered empirical layer was self-retracted on 2026-05-31. Ω-centered validation is not currently supported as the active empirical basis; this record remains a historical, fixed, Ω-centered record and must not be cited as current validation. See the VOT Empirical Layer Boundary Note — https://doi.org/10.5281/zenodo.20474232. A later four-dataset head-to-head found that order gated by critical slowing does not beat free-energy signals (10.5281/zenodo.21422215, negative result). Main Description This paper proposes a reproducible methodological framework for detecting irreversibility in directional systems using directional potential (Ω) and recovery efficiency dynamics. Irreversibility is operationalized as sustained failure of recovery efficiency rather than terminal collapse. The framework introduces a minimal dynamic model separating recovery buffers and burdens and detects irreversible tendencies through critical dwell within evolving state space structures. To ensure empirical applicability, abstract directional changes are mapped into event-based inputs derived from publicly available policy intervention and outbreak event datasets. The framework further extends irreversibility detection into a three-dimensional phase space composed of directional potential (Ω), subsystem coupling (K), and thematic alignment (Align), enabling quantitative risk density estimation and transition probability analysis. This work does not claim a complete theory of irreversibility. Instead, it provides a falsifiable, reproducible, and extensible methodological entry point for detecting irreversible tendencies across complex directional systems. Methodological Scope Note The framework is designed to be compatible with publicly available policy and outbreak event datasets. Exact implementation may vary depending on domain-specific event transformation rules. The degradation function included in the dynamic model represents monotonic loss of recovery efficiency under excessive burden conditions. Theoretical Relation Note This framework is presented as an independent reproducible method. It is structurally related to the broader theoretical framework known as The Pleasure Order, which introduces directional potential as a general structural concept. Version Note Version: v1.0 This version presents the initial reproducible detection framework. Future revisions may extend empirical validation, boundary formalization, and cross-scale analysis.