Structural Axioms and Theorems of Coherence, Drift, and Directionality for Long-Horizon Adaptive Systems

This release (v1.3) refines and extends a compact axiomatic and theorem-based foundation for long-horizon adaptive systems operating under structural coherence constraints. The Concept DOI refers to the complete evolving body of work; the Version DOI uniquely identifies this release.

Information is treated not as stored data or retrievable memory, but as a persistent structural constraint shaping admissible future evolution. The framework formalizes coherent structural closure, residual-driven reactivation, inevitable drift, internal time as a bounded viability horizon, and directionality (Will) as a primary ontological operator rather than a goal- or reward-derived construct.

Version 1.3 explicitly incorporates phase-related structural cost—including latent phase residual and phase transition load—as first-class contributors to drift accumulation and internal-time depletion. This extension clarifies the distinction between state-based coherence and phase-coherent closure, and accounts for latent-to-explicit residual projection without altering the original axiomatic chain.

The resulting axioms and theorems establish invariant principles governing coherence preservation, identity continuity, and controlled adaptation under prolonged interaction with a changing environment. Drift is shown to be unavoidable, inertial propagation to be energetically dominant, residual structure to be the sole carrier of relevance, and internal time to bound structural validity independently of instantaneous error or performance.

These axioms and structural theorems constitute a minimal but non-trivial theoretical core applicable to coherence-preserving adaptive architectures, including systems such as PETRONUS, in which spin, drift, residual, internal time, and directionality are realized as explicit operational variables, without restricting the framework to any specific implementation or platform.