Meta-Rationality as Layered Closure: Lawlike Updating via Factorization and Commutation

A unified meta-structural account synthesizes two tightly related strands of work on rational updating. The first strand (fixed-architecture decomposition) decomposes updating inside a fixed admissible architecture into distinct roles: admissibility refinement, state transport, optional posterior selection, and envelope projection to observable bid/ask prices. The second strand (drift/rectangularity analysis) studies diachronic rationality under evolving admissible architecture and identifies rectangularity/commutation as the feasibility condition for dynamic stability under representational drift. We show how to treat both strands as instances of a layered closure regime: closure/interior operators on multiple representational layers whose commutation governs diachronic stability. We formalize a three-layer framework (observable envelopes, credal geometry, and admissible architecture) and prove representation theorems showing when update policies admit a canonical factorization into orthogonal structural components. We then classify systematic extension modes: situations in which component-wise closure holds (each layer is locally coherent) but global factorization is non-canonical or commutation is obstructed, producing order effects, non-liftable observable policies, or time-book vulnerabilities under drift. Philosophically, this picture leads to a conditions-of possibility thesis: meta-rationality is governance of closure regimes that remain composable under self-iteration.