Null Structural Protocol for Constraint Geometry Frameworks: Axiom Minimality, Genericity Filtering, and Cross-Structure Independence Tests

This paper introduces a formal null-testing protocol for evaluating structural claims within constraint geometry frameworks. Such frameworks frequently produce distinguished constants, contraction rates, and phase thresholds that may appear structurally significant but can arise from generic axioms, coordinate choices, or interpretive overlays. The protocol establishes five classification tests: (1) Genericity filtering, (2) Coordinate invariance analysis, (3) Structural independence testing, (4) Optimization–dynamics interaction analysis, and (5) Empirical nontriviality assessment. A complete worked example—harmonic mean iteration on a binary partition—is used to demonstrate the method. The analysis shows that several seemingly nontrivial results (including the contraction rate 1/2 and the identification of \ln 2 with Shannon entropy) collapse under null testing to generic consequences of mean axioms or to coordinate renaming, while a smaller subset of results survive as genuine structural invariants. The paper establishes a reusable methodological infrastructure for distinguishing: Axiomatically forced results Generic consequences of broad classes Coordinate artifacts Genuine cross-structure intersections Empirical claims Interpretive overlays The protocol is framework-agnostic and intended for application to future work involving constraint geometries, distinguished constants, or cross-domain structural analogies.