Closure Provenance Physical Admissibility and Effective Ontology in Multiscale Fluid Models

The framework addresses four questions that are frequently conflated. 1. Does a reduced equation possess a mathematically admissible solution? 2. Does a written proof establish the stated theorem, and does a formal proof encode the written theorem faithfully? 3. Does the reduced solution remain a controlled projection of an admissible underlying system? 4. Does the effective identity used by the model remain dynamically persistent? The first two are mathematical questions. The third is a model-realizability question. The fourth concerns effective ontology. No conclusion is allowed to cross from one question to another without an independently justified bridge. Several ingredients used below have established relatives in projection-operator methods, lumpability, predictive-state theory, causal states, kinetic limits, large-deviation theory, metastability, and quasi-stationary distributions. The proposed contribution lies in composing them into one closure architecture and deriving consequences for singularity interpretation, multiscale turbulence, proof verification, and ontology transitions. The present paper does not claim a proof of global Navier–Stokes regularity, a refutation of any announced blowup construction, or an absolute microscopic ontology. Continuum fluid equations can be mathematically admissible outside the regime in which they remain physically realizable. This paper develops a Unified Coherence Closure Framework for separating those questions. A reduced model is treated as a projection of an underlying dynamics together with a controlled defect, a validity interval, and a realizability boundary. Exact closure occurs when all underlying states represented by the same reduced state have the same reduced future. Approximate and statistical versions are measured by future fiber diameter, conditional mutual information, closure rank, and memory depth. These definitions lead to a compositional provenance graph in which logical proofs, formal verification, asymptotic reductions, and physical realization are distinct bridges that require separate certificates. The framework is applied to continuum singularities, turbulence onset, intermittency, cavitation, kinetic limits, and effective particle identity. A finite continuum cutoff makes every physically resolved velocity gradient finite at finite energy; if an unfiltered continuum observable diverges, a fixed finite validity threshold must be crossed before the nominal blowup time. This yields a physical preemption conjecture rather than a claim of mathematical Navier–Stokes regularity. Closure basins and closure shields provide a parallel account of persistent effective entities. Quasi-stationary concentration, slow leakage, and a large separation between internal organization and exit times characterize robust effective ontology. Cavitation bubbles occupy a relational partial-closure regime, while atoms and long-lived particles occupy broader internally shielded basins. The paper distinguishes established mathematics from framework propositions, interpretive reconstructions, and falsifiable conjectures. Its main result is a common mathematical language for model reduction, proof provenance, physical admissibility, metastability, and mass.