NeutroGeometry of Rashomon Decision Boundaries: Partial Geometric Knowledge and Joint Axiom Compatibility

Near-optimal classifiers can agree on every label and still draw different decision boundaries. We study what a Rashomon set knows about boundary geometry, using an exactly enumerated class of axis-aligned trees of depth at most 2 over quantile thresholds. At each test point, four geometric properties (local robustness, segment class preservation, nearest-face orientation, local flatness) receive a supervaluation state: true in every near-optimal model, false in every one, or indeterminate. Their shares over the test points are taken as NeutroGeometric degrees in Smarandache's sense. Every property is a NeutroAxiom on all five datasets; the information specific to the Rashomon set is concentrated in the indeterminacy degree, which is positive for every property. A joint obstruction is a set of properties, each achieved by some near-optimal model, that none achieves together. It instantiates the known non-truth-functionality of conjunction under supervaluation, and our propositions are elementary; we contribute its exact certification for decision geometry within a finite class and its measured frequency. In the pre-declared primary configuration, obstructions occur at 2.4% to 9.6% of test points and at 153 of 3,499 points with unanimous labels. They depend on the orientation property, defined relative to a reference model, and on the discretization: with 7 instead of 5 thresholds per feature the rate falls to 1.47%–3.33% and the unanimous count also falls. The predictive result is negative: the reference margin anticipates obstruction with AUC near 0.9, partly by construction, and the marginal frequencies with cross-validated AUC 0.92 to 0.96.