NFKS — Structural Reference for Recoverability and Irreversibility Boundaries in Complex Systems

NFKS — Structural Reference for Recoverability and Irreversibility Boundaries in Complex SystemsThis document is structurally aligned with and superseded in canonical form by: https://doi.org/10.6084/m9.figshare.31937418Navigation and document structure are defined in the Master Index: https://doi.org/10.6084/m9.figshare.31919058This document provides reference structures for recoverability, irreversibility, and boundary behavior across complex systems.This work provides a domain-independent structural abstraction for representing system evolution relative to recoverability and irreversibility boundaries.The framework describes system structure using entities, events, constraints, state transitions, and abstract identifiers independent of domain.All narrative and domain-specific terminology is removed from the operational description and replaced with neutral structural representations. This enables cross-domain interpretation across mathematics, physics, computer science, systems theory, law, economics, and artificial intelligence.Core structureThe dataset includes:canonical structural representation (S1–S5 segments)structured JSON definitions of entities, events, and transitionsformal paper with mathematical interpretationsystem diagrams illustrating dynamic and cyclic behaviorrecoverability-centered architecture (v4.x)reference implementation (non-operational)Recoverability extension (v4.x)This version introduces a structural model for describing irreversibility in system evolution.The framework represents recoverability, effective recoverability, hidden instability, detection delay, and degradation pace.Effective recoverability is expressed as:r_eff = r − λ·d − μ·hIrreversibility is defined as the condition in which effective recoverability falls below a critical threshold, indicating that prior system states are no longer structurally recoverable.The framework distinguishes:pre-boundary (recovery feasible)boundary zone (recovery degrading)post-boundary (recovery no longer possible)MethodThe system is constructed by identifying invariant structural components, removing narrative redundancy, and encoding them as reusable structural elements under a neutrality constraint.This work provides a structural abstraction only. It does not provide decisions, recommendations, or operational control.ScopeThis material is descriptive and non-operational. It does not replace human judgment, interpretation, or responsibility.Version historyv1.1 — multi-agent interaction and collapse dynamicsv1.2 — governance structuresv1.3 — temporal cyclesv2.0 — observabilityv2.1 — irreversibility layerv3.0 — mathematical formalizationv3.1 — worked examplev4.0 — recoverability architecturev4.1 — reference implementation layerThis work operates within a recoverability-constrained system framework and does not modify the admissibility conditions defined in the core.Core reference: https://doi.org/10.6084/m9.figshare.31937418Framework index: https://doi.org/10.6084/m9.figshare.31919058