{"paper":{"title":"A Structural Criterion for the Applicability of Algebraic Phase Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Joe Gildea","submitted_at":"2026-02-08T20:23:53Z","abstract_excerpt":"Algebraic Phase Theory (APT) exhibits a marked structural selectivity. In certain mathematical and physical settings it gives rise to rigidity phenomena, constrained representation behaviour, and reductions in apparent degrees of freedom, while in many analytic or dynamical contexts the finite-depth APT framework does not naturally apply. This paper studies the structural origin of this asymmetry.\n  We establish a structural criterion for the existence of a nondegenerate finite-depth Algebraic Phase Theory structure. The criterion isolates three conditions: nondegenerate phase duality, compati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.08111","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.08111/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}