The Afterlessness Boundary: Typing Limits of Continuity, Irreversibility, and Impossibility

This work introduces the Afterlessness Boundary, a formal framework for classifying and excluding claims that violate fundamental constraints of continuity, irreversibility, or logical impossibility. Rather than proposing new mechanisms or speculative models, the framework is deliberately negative-law oriented: it identifies what cannot occur, and therefore what any admissible theory or process must avoid. At the core of the framework is an abstract termination threshold, denoted Ω, representing a boundary beyond which no further state (“no after”) can exist within a given system. Claims that implicitly or explicitly require states, events, or processes beyond such a boundary are shown to be inadmissible by construction. This idea is formalized through Afterlessness Boundary Typing (ABT), a typing system that separates the structural form of a claim from its domain-specific semantics, allowing constraint violations to be detected in a domain-agnostic manner. Three constraint regimes are treated as distinct types: Impossibility (violations of conservation laws or formal no-go theorems), Irreversibility (violations of one-way processes such as entropy increase or information loss), Continuity (violations involving discontinuous jumps or infinite completion in finite steps). Building on these types, the paper presents: the ABT-Ω Theorem, establishing the existence of an afterlessness boundary in any admissible system; the ATA-Ω Axiom, asserting decidability of admissibility for well-formed claims up to Ω; the ABT-GAC Clause, ensuring global consistency across sets of individually admissible claims; and the Admissibility Test Algorithm (ATA-Proc), a prioritized procedure for classifying claims. The framework is applied to benchmark examples across physics, computation, mathematics, and logic, reproducing known impossibility results (e.g., perpetual motion, halting problem solvers, supertasks) without invoking observers, agency, or metaphysical assumptions. The resulting Rhys Canon and continuity pattern catalog provide a compact reference for permissible process behaviors under foundational constraints. Overall, the work offers a unified, austere logic for filtering inadmissible claims across disciplines, clarifying the structural limits imposed by continuity, irreversibility, and impossibility, and providing a reusable foundation for foundational analysis in science, mathematics, and computation.