Geometric Constraint on Residue Phases: Resolving the N(2190) Anomaly and Implications for Exotic States

We derive a parameter-free geometric constraint on residue phases dictated by the pole-threshold angle. Using the N(2190) anomaly as a test case, this constraint reveals a sign ambiguity in prior data; correcting the sign ambiguity yields a phase of − 28 ∘ ± 10 ∘ , matching our prediction. This consistency validates the method as a model-independent diagnostic for distinguishing compact from molecular states, offering a rigorous tool for exotic spectroscopy.