Carrier-Free Reflexive Closure: A Minimal Foundation for Stabilization and Representability

Translator This note develops a carrier-free formulation of reflexive closure in which stabilization and representability are treated as contingent structural outcomes rather than assumed primitives. No state space, algebraic carrier, geometric background, or semantic domain is presupposed. The framework introduces only minimal pre-representational scaffolding—admissible composition of acts, resolution-indexed indistinguishability, and closure as propagation of operational consequences—and isolates the conditions under which closure may stabilize. Stabilization is defined as exhaustion of distinguishability under iterated closure and is not assumed to occur generically. Partial stabilization, resolution dependence, and local failure of reflexivity are treated as structurally natural possibilities rather than pathologies. Representational structures, including mathematical formalisms, linguistic articulation, and finite-resolution physical regimes, are presented as downstream realizations that arise only once stabilization occurs within a chosen representational environment. The role of this note is foundational and clarificatory. It does not propose new physical laws or mathematical constructions, nor does it privilege any specific realization. Instead, it provides a minimal structural layer intended to underlie and contextualize subsequent work on invariant stabilization, language and symbolic continuation, and finite-resolution physics. The framework is explicitly provisional and open to refinement, and is released as a citable reference point rather than a closed or complete theory.