CLOSURE ONTOLOGY Entropy Constants and Closure Limits in Atomic Ontology

This work assumes the closure-first ontology and admissibility principles developed in AtomicOntology I–VII; we do not re-argue closure, re-derive AO-V.P₁, or redefine coherence. Our aim is narrower: we treat entropy as a constrained measure of closure degradation the loss, export,or mapped reduction of admissible circulation relative to finite closure capacity rather than asa primitive statistical disorder quantity. The guiding question is therefore structural: whatinvariant limits constrain closure degradation, and how do those limits appear as entropyconstants across scales? This reorients the discussion from distributions to bounds: instead of taking statistical ensembles as foundational and introducing constants late, we show that finite closure, admissibility restriction, and compatibility-limited restoration force ceilings and thresholds a priori, motivating entropy constants (per-event maxima, irreversibility boundaries, and architecture ceilings) that remain compatible with standard thermodynamic and information-theoretic entropies as projection-level descriptions. This work assumes the closure-first ontology and admissibility principles established in AtomicOntology I–VII. We do not re-argue closure, re-derive admissibility (AO-V.P₁), or redefinecoherence. Instead, we treat entropy as a constrained measure of closure degradation—i.e.,admissible circulation that has been partially lost, externalized, or reduced under mapping—sothat “entropy growth” is read as bounded closure damage rather than a primitive statisticaldisorder. We propose an ontology-first reframing of entropy within a closure-based Atomic Ontology:entropy is defined as closure degradation the loss, export, or mapped reduction of admissiblecirculation—rather than as a primitive statistical quantity. From the finiteness of closurecapacity, admissibility constraints, and triadic closure limits, we show that closure degradationadmits invariant bounds, motivating the existence of entropy constants that constrainirreversible change across scales. We separate (i) internal entropy (intrinsic closure loss), (ii) transport entropy (externalized degradation), and (iii) projection entropy (observer/mapping reduction), and provide a taxonomy of candidate constants(maximal loss per interaction, irreversibility thresholds, coherence half-lives, and closuregeometriclimits). Thermodynamic and information-theoretic entropies are then treated asprojections and descriptions of these bounded closure-degradation processes. The result is a scale-bridging framework for irreversibility and decoherence that is ontologically anchored,numerically noncommittal, and structurally compatible with standard statistical mechanics. Keywords: closure degradation, admissibility, irreversibility threshold, decoherence bounds,entropy constants, transport, projection, atomic ontology