Recursive Boundary Admissibility Test: A Boundary-Coherence Method for Testing Declared Structural Patterns

Abstract This paper defines the Recursive Boundary Admissibility Test (RBAT), a deterministic method for evaluating whether observed system boundaries align with a declared structural rule more strongly than expected under chance, permutation, random baselines, clustering, and simpler competing rules. RBAT is not a pattern-discovery tool. It is a falsification and admissibility framework for claimed structural patterns. The method requires that the boundary class, coordinate system, structural rule, hit condition, tolerance, and failure threshold are all declared before testing. Any parameter changed after result inspection invalidates the test. The method enforces five gates before statistical testing: boundary-class declaration, extraction validity, boundary reliability, rule declaration, and tolerance justification. It requires five controls: random equal-density boundary sets, permuted boundary positions, shuffled unit order, alternative competing rules, and cluster baselines. Results are classified into five states: PASS, WEAK, FAIL, INVALID, and UNTESTABLE. This paper provides sufficient operational detail for independent implementation. Two worked examples are included: one where the method produces a PASS result against a synthetic document with a planted structural pattern, and one where the method produces a FAIL result against a synthetic document with no planted pattern. Both examples are fully reproducible from the information provided. Keywords: boundary coherence, structural admissibility, pattern testing, falsification, density normalization, deterministic method, preregistration-compatible