This work identifies and formalizes a failure mode that arises exclusively in engineered, formal, and representational systems when reachability and admissibility are enforced under an externally imposed finite resolution. The paper isolates what is termed a forced resolution induced reachability obstruction: a situation in which a state is formally declared admissible and symbolically reachable, yet every admissible operational path to that state collapses to a null set under the system’s own declared resolution, while the state nevertheless appears in execution or output. The contradiction is not stochastic, numerical, or dynamical in origin. It is structurally forced by the system’s representational rules. Crucially, this phenomenon does not occur in natural processes. Natural systems do not declare admissibility rules, do not enforce symbolic reachability, and do not operate under externally imposed resolution limits. The obstruction exists only because an external framework formal, computational, or engineered imposes constraints and representational granularity that nature itself does not impose. Any apparent analogue in physics, chemistry, or biology reflects limitations of human constructed models, not properties of natural dynamics. The obstruction is therefore not a physical law, not a natural principle, and not an empirical claim about reality. It is a diagnostic classification of semantic failure modes in forced formalization: systems that assert reachability while simultaneously enforcing resolution constraints that eliminate all admissible operational corridors. The analysis applies to formal mathematical frameworks, numerical simulations, verification systems, control architectures, and optimization pipelines that operate under finite precision or symbolic admissibility. The result provides a clear criterion for identifying when a system’s reachability claims are internally inconsistent and require revision of resolution semantics, admissibility definitions, or reachability assertions. This work is presented as a structural and conceptual contribution to the analysis of engineered systems and formal representations, independent of any ontological or physical interpretation.
Kearon Allen (Fri,) studied this question.