WorldSeed Inference: Refinement, Degradation Monotonicity, and Claim Preservation with Progress/Preservation and Small-step Semantics

WorldSeed Inference is a formal semantic framework for declared empirical worlds.It treats the “world” underlying datasets, simulators, and embodied learning systems as a first-class, explicitly specified research object, equipped with states, actions, observers, sensing boundaries, and irreversible degradation. This release provides a POPL-style core calculus that enables mechanically checkable claims about learnability, comparability, and admissibility across worlds. Key Contributions World Semantics with Degradation ClosureA world is specified as W=(S,A,O,B,cl)\mathcal{W} = (S, A, O, B, \mathsf{cl})W=(S,A,O,B,cl), where degradation is formalized as a closure operator satisfying extensiveness, monotonicity, and idempotence. This makes irreversible information loss an explicit semantic entity rather than a hidden artifact. World Refinement via Forward SimulationRefinement is defined as a simulation relation between worlds that preserves admissible actions, observer semantics (up to re-encoding), boundary legality, and degradation monotonicity. Refinement forms a preorder and defines a semantic order over world representations. Claim Language and Complete Claim LinterWe introduce a minimal claim language for executability and observational distinguishability. Claims are typed as executable, boundary-failing, or blocked-by-undeclaration. A complete, decidable linter evaluates semantic admissibility and produces explicit verdicts independent of empirical performance. Small-step Semantics and Type SafetyThe claim evaluation system includes a small-step operational semantics with evaluation contexts. We prove Progress and Preservation, establishing type safety for executable claims. Claim Preservation under RefinementUsing a logical-relations style argument, we prove that refinement preserves the truth value of executable claims. We additionally characterize NOT_COMPARABLE as refinement incomparability and show how it admits witness claims. Intended Use WorldSeed Inference v2 is not a learning algorithm or benchmark.It is semantic infrastructure that conditions the interpretability and comparability of learning claims. It provides a rigorous interface layer for empirical AI, simulation-to-real transfer, multi-observer datasets, and representation learning under irreversible degradation. This Release This Zenodo release contains: the full LaTeX manuscript (WorldSeed Inference), the core definitions, inference rules, theorems, and proofs, a reference claim typing and evaluation specification suitable for downstream tool implementation.