SABO as the L0 Mother-Theory: Meta-Reduction, Reverse Characterization, and Categorical Auditability of World Interfaces

This paper formalizes the SABO (State, Action, Boundary, Observer) framework as an "L0 Mother-Theory": a universal interface schema capable of expressing any fundamental (L0) contribution as an explicit world instance. The study presents three key theoretical advancements: Meta-Reduction Theorem: Proves that any L0 contribution (defined as the objectification of implicit premises) can be represented as a SABO tuple (S,A,B,O)(S, A, B, O)(S,A,B,O). Reverse Characterization & Mother-Depth: Establishes the "Objectification Criterion" to distinguish valid L0 contributions and introduces "Mother-Depth" as a quantitative metric for world complexity, invariant under isomorphism. Categorical Auditability: Elevates the framework to Category Theory, defining a category of SABO worlds where refinement morphisms are specified by commuting diagrams. The paper applies the Yoneda Lemma to demonstrate that worlds are uniquely identifiable by their refinement behaviors. Finally, the paper provides a lineage mapping table demonstrating how historical L0 artifacts—from DNA and Euclidean Geometry to Turing Machines and WorldSeed—map onto the SABO architecture.