{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:QNQYSAGHTYJ7IZ5JDEYZJIODWV","short_pith_number":"pith:QNQYSAGH","schema_version":"1.0","canonical_sha256":"83618900c79e13f467a9193194a1c3b577e8c5c2bca24a73e46a396dbb268e3d","source":{"kind":"arxiv","id":"2207.11591","version":5},"attestation_state":"computed","paper":{"title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Facundo M\\'emoli, Nathaniel Clause, Woojin Kim","submitted_at":"2022-07-23T20:04:11Z","abstract_excerpt":"In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its application.\n  One of the best known quantifications of persistence for multi-parameter persistent homology is the rank invariant, which has recently evolved into the generalized rank invariant (GRI) by naturally extending its domain. This extension enables us to quantify persistence across a broader range of regions in the indexing poset compared to the rank invariant. However, the size of the domain of the GRI is gene"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2207.11591","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2022-07-23T20:04:11Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"813ec5d8ae66cb273cfffb629a8d871d47a0afeea9c9f9475bc3a94611313a6e","abstract_canon_sha256":"edd4ccc58140e777b6a254cb2c04d2de1140c2f5861dbc6317ff5221b96b413e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:41:35.799526Z","signature_b64":"5F7H+7i7o9TQ0MFJH623NExeuQ5jgCL1DH3kppk2dEdB/FTMEZO4H+7fa2mXOtfVeFRCvOvpVpl62ydt2JJVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83618900c79e13f467a9193194a1c3b577e8c5c2bca24a73e46a396dbb268e3d","last_reissued_at":"2026-07-05T08:41:35.798951Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:41:35.798951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Generalized Rank Invariant: M\\\"obius invertibility, Discriminating Power, and Connection to Other Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Facundo M\\'emoli, Nathaniel Clause, Woojin Kim","submitted_at":"2022-07-23T20:04:11Z","abstract_excerpt":"In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its application.\n  One of the best known quantifications of persistence for multi-parameter persistent homology is the rank invariant, which has recently evolved into the generalized rank invariant (GRI) by naturally extending its domain. This extension enables us to quantify persistence across a broader range of regions in the indexing poset compared to the rank invariant. However, the size of the domain of the GRI is gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.11591","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/2207.11591/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2207.11591","created_at":"2026-07-05T08:41:35.799012+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.11591v5","created_at":"2026-07-05T08:41:35.799012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.11591","created_at":"2026-07-05T08:41:35.799012+00:00"},{"alias_kind":"pith_short_12","alias_value":"QNQYSAGHTYJ7","created_at":"2026-07-05T08:41:35.799012+00:00"},{"alias_kind":"pith_short_16","alias_value":"QNQYSAGHTYJ7IZ5J","created_at":"2026-07-05T08:41:35.799012+00:00"},{"alias_kind":"pith_short_8","alias_value":"QNQYSAGH","created_at":"2026-07-05T08:41:35.799012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2509.24233","citing_title":"Interleaving Distance as a Galois-Edit Distance","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07022","citing_title":"An Algebraic Introduction to Persistence","ref_index":74,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV","json":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV.json","graph_json":"https://pith.science/api/pith-number/QNQYSAGHTYJ7IZ5JDEYZJIODWV/graph.json","events_json":"https://pith.science/api/pith-number/QNQYSAGHTYJ7IZ5JDEYZJIODWV/events.json","paper":"https://pith.science/paper/QNQYSAGH"},"agent_actions":{"view_html":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV","download_json":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV.json","view_paper":"https://pith.science/paper/QNQYSAGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.11591&json=true","fetch_graph":"https://pith.science/api/pith-number/QNQYSAGHTYJ7IZ5JDEYZJIODWV/graph.json","fetch_events":"https://pith.science/api/pith-number/QNQYSAGHTYJ7IZ5JDEYZJIODWV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV/action/storage_attestation","attest_author":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV/action/author_attestation","sign_citation":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV/action/citation_signature","submit_replication":"https://pith.science/pith/QNQYSAGHTYJ7IZ5JDEYZJIODWV/action/replication_record"}},"created_at":"2026-07-05T08:41:35.799012+00:00","updated_at":"2026-07-05T08:41:35.799012+00:00"}