{"paper":{"title":"Grassmannian Persistence Diagrams","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Aziz Burak G\\\"ulen, Facundo M\\'emoli, Zhengchao Wan","submitted_at":"2023-11-12T15:03:25Z","abstract_excerpt":"We introduce Orthogonal M\\\"obius Inversion $\\mathsf{OI}$, a concept analogous to M\\\"obius inversion on finite posets, which is applicable to order-preservings functions from a finite poset to the Grassmannian $\\mathsf{Gr}(V)$ of an inner product space $V$. This notion critically relies on the inner product structure on $V$ enabling it to capture much finer information than standard integer-valued persistence diagrams.\n  Orthogonal Inversion is a special case of the broader concept of Orthomodular Inversion, where the target space is any orthomodular lattice, which we also identify.\n  We apply "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06870","kind":"arxiv","version":5},"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/2311.06870/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"}