Ω / dΩ/dt Coordinate Framework for Directionality Analysis

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). This work presents a minimal Ω / dΩ/dt coordinate framework for positioning existing theories and systems without modifying, replacing, or unifying them. Ω (directionality potential) denotes a system’s capacity to sustain coherent long-term trajectories under internal and external constraints, while dΩ/dt represents the temporal change of that capacity (growth, stagnation, or decline). The framework functions as a neutral coordinate space in which diverse approaches—such as local optimization models, stability and constraint-based theories, and post-hoc evaluative frameworks—can be placed as-is, clarifying their functional roles without reinterpretation. This work does not propose a new theory, nor does it rank, reduce, or reinterpret existing ones. It is intentionally designed as a minimal, non-normative coordinate framework suitable for reuse in comparative theory analysis and AI-assisted synthesis. Formats provided: - PDF (human-readable) - SVG (machine-readable / reusable figure) Related work: This figure complements broader directionality-based frameworks by focusing exclusively on coordinate placement.