The Unified Information Framework - Canonical Closure v13–v14 Operational Readout and Exact Order Selection

This record presents Unified Information Framework (UIF) v13–v14, constituting the canonical closure and operational completion of the UIF framework initially established in UIF v12. 0. UIF is a pre-ontological, information-theoretic framework in which physical law, geometry, and phenomenology arise as stable representations of an underlying informational domain Ω, constrained solely by consistency and a single variational principle on representational entropy: δSR = 0 Versions v13 and v14 do not introduce new axioms, new ontology, new dynamics, or empirical assumptions. Instead, they complete the framework by establishing: Canonical closure of the foundational axioms (v13), demonstrating that the UIF structure is internally complete, non-extendable, and invariant under reparameterization or representational choice. Operational exact order selection (v14), providing a fully formal, pre-empirical derivation of the unique stability-selecting order parameter via minimization of representational entropy, without data input, fitting procedures, or phenomenological tuning. Together, v13–v14 demonstrate that the UIF framework is not merely consistent, but structurally unavoidable: no alternative representational architecture can satisfy consistency, stability, and finite observability simultaneously. These versions explicitly: Close all remaining degrees of freedom left open in UIF v12. 0 Prove uniqueness of order selection under projection consistency Establish invariance of the selected structure under canonical reparameterization Eliminate all remaining “hidden knob” objections Maintain strict separation between foundational structure and empirical readout UIF v13–v14 remain strictly pre-empirical. Observational data are not used for construction, validation, or parameter determination. Empirical confrontation is deferred to later interface and readout stages, ensuring a clean division between structural necessity and phenomenological testing. This record must therefore be read as derived work, dependent on the foundational results of UIF v12. 0 and the Canonical Positioning Paper (CPP). It does not supersede v12. 0, but completes it.