Stability at the Boundary of Formal Domains – A Minimal Mathematical Framework

eThis manuscript presents a minimal and rigorous mathematical framework for distinguishing accessible and inaccessible regions in formal domains. Using standard tools from topology and real analysis, it formalizes accessibility via locally admissible functions and characterizes boundary regions as topological interfaces between domains of definition and their complement. The approach emphasizes local stability at the boundary without assuming global extendability, and clearly separates provable local results from stronger global assumptions, which are treated as axiomatic or left as open questions. The contribution is foundational and conceptual, providing structural clarification rather than new extension theorems.