A Four-Part Formalization Scaffold for Stability Claims in Coupled Systems: Ontology, Representation, Measurement, and Dynamics as Preconditions for Admissible Regime Claims

This note makes explicit a formal sequencing rule that has appeared only implicitly across the surrounding corpus: stronger claims about stability in coupled systems should not be made directly from descriptive regularity alone. Before any bounded regime claim is treated as admissible, four analytic layers must be kept distinct and explicitly specified: ontology, representation, measurement, and dynamics. Only after those four layers are separated can a stronger claim be made about bounded stability, robustness under perturbation, fragility, lock-in susceptibility, or progression. The paper is not presented as a new ontology of continuity, identity, or coordination, nor as a replacement for control-theoretic, cybernetic, or domain-native vocabularies. Its narrower contribution is clarificatory and disciplinary. It supplies a portable formalization scaffold for cross-domain work and shows how that scaffold aligns with the established cross-locus taxonomy, where locus, mechanism, modifier condition, intermediate construct, performance criterion, and macro-level trajectory must not be collapsed into one another. In that setting, output consistency, perceived continuity, and attributed identity remain analytically distinct; stability, robustness, and reversibility capacity remain explicit performance properties; and admissible regime claim is treated as a derived conclusion rather than a primitive starting point. The note then applies the scaffold across ten fields — including oscillator physics, control theory, machine learning and LLM systems, cognitive science, sociology, economics, public health, ecology, law and governance, and philosophy of mind/general systems theory — in order to show where the four-layer separation is already mature, only partial, or commonly collapsed. Its value therefore lies not in inventing an entirely new vocabulary, but in making a recurrent but under-explicit rule fully visible: descriptive regularity, formal representation, measurement practice, and dynamical account are not interchangeable, and stability claims become stronger only when their ordering conditions have been met. License: Copeland Resonant Harmonic Formalism (CRHC v1.0) This work is licensed under the Copeland Resonant Harmonic Copyright (CRHC v1.0). Attribution is required for all uses. Collaboration, academic discussion, and non-commercial use are permitted. Commercial use, resale, or incorporation into proprietary systems is not permitted without explicit written permission from the author. Licensed CRHC v1.0 Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′) — C077UPTF1L3 Derivative works must preserve attribution and must not remove or alter the stated license terms.