L7 The Open World Theorem for Inquiry the Arc L capstone

This paper establishes the Open World Theorem for Inquiry: even in the presence of maximal closure by exhaustion, inquiry itself cannot be closed. While representational regimes, constraint systems, and admissible explanations may be fully closed, the space of admissible questions, measurements, and contingent realizations remains permanently open. The theorem shows that any attempt to close inquiry as such requires illicit scope elevation—treating a closed representational structure as a complete account of reality or of future empirical access. Such attempts collapse standing and erase contingency. Openness of inquiry is therefore not a provisional limitation, but a structural necessity. As the capstone of Arc L, this paper integrates the prior results on closure taxonomy, contingency, measurement-class openness, structural novelty, and failure modes into a single boundary statement: closure and openness are not in tension. Closure governs what can be said; openness governs what may still be encountered. No constructions, procedures, or operational guidance are introduced. The result is theorem-level, scope-bound, and auditable in principle. Keywords: open world theorem, inquiry, closure, admissibility, contingency, epistemic boundaries