Domain-License Exhaustion and Residual Null Boundaries: A Proof-Carrying Semantics of Reference-Relative V0 Approximation

This preprint develops a proof-carrying formal semantics for domain-license exhaustion, residual null boundaries, and reference-relative V0 approximation. The central idea is that a boundary condition should not be represented as an object becoming false, zero, or empty, but as a certified loss of domain applicability for selected structural predicates. The paper distinguishes ordinary absence from domain-license exhaustion, introduces residual registers such as radiation, trace, memory, causal and informational residues, and proves obstruction principles showing when such residues block raw or translation-robust relative nullity. It also gives a validator-oriented certification framework, finite-registry test cases, and a compact reverse-boundary account of domain-license activation. The framework is formal-semantic rather than physical: it does not identify V0 with vacuum, cosmological nothing, singularity, observation collapse, or any physical state.