{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7BVUEAIFM6TQQ7RLHAA4422527","short_pith_number":"pith:7BVUEAIF","schema_version":"1.0","canonical_sha256":"f86b42010567a7087e2b3801ce6b5dd7c82b122afc62484854144ede7132f287","source":{"kind":"arxiv","id":"2303.08270","version":1},"attestation_state":"computed","paper":{"title":"Meta-Diagrams for 2-Parameter Persistence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Bei Wang, Facundo M\\'emoli, Nate Clause, Tamal K. Dey","submitted_at":"2023-03-14T23:16:45Z","abstract_excerpt":"We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the module. We then define the meta-diagram of a 2-parameter persistence module to be the M\\\"{o}bius inversion of the meta-rank, resulting in a function that takes values from signed 1-parameter persistence modules. We show that the meta-rank and meta-diagram contain information equivalent to the rank invariant and the signed barcode. This equivalence leads to computational benefits, as we introduce an algorithm for computin"},"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":"2303.08270","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2023-03-14T23:16:45Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"ceface3d351c8c24bcb0c3178da8b0661a6b90caccf896c275744ac0f0efd03a","abstract_canon_sha256":"3037bdcfef17ce2dea41bc26272e01e2be2aa2c70d62c95f0c612e689d9432a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:30.805548Z","signature_b64":"828n2KlKuMuvpY2Z4ZHQM5wjeHBxn2eW6LhAd3TYv0JkKqaH2HKQIQNcIdST6hWFaYkJkkXY+QlOL44OOCL2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f86b42010567a7087e2b3801ce6b5dd7c82b122afc62484854144ede7132f287","last_reissued_at":"2026-07-05T05:51:30.805120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:30.805120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Meta-Diagrams for 2-Parameter Persistence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Bei Wang, Facundo M\\'emoli, Nate Clause, Tamal K. Dey","submitted_at":"2023-03-14T23:16:45Z","abstract_excerpt":"We first introduce the notion of meta-rank for a 2-parameter persistence module, an invariant that captures the information behind images of morphisms between 1D slices of the module. We then define the meta-diagram of a 2-parameter persistence module to be the M\\\"{o}bius inversion of the meta-rank, resulting in a function that takes values from signed 1-parameter persistence modules. We show that the meta-rank and meta-diagram contain information equivalent to the rank invariant and the signed barcode. This equivalence leads to computational benefits, as we introduce an algorithm for computin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.08270","kind":"arxiv","version":1},"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/2303.08270/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":"2303.08270","created_at":"2026-07-05T05:51:30.805180+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.08270v1","created_at":"2026-07-05T05:51:30.805180+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.08270","created_at":"2026-07-05T05:51:30.805180+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BVUEAIFM6TQ","created_at":"2026-07-05T05:51:30.805180+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BVUEAIFM6TQQ7RL","created_at":"2026-07-05T05:51:30.805180+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BVUEAIF","created_at":"2026-07-05T05:51:30.805180+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2211.05981","citing_title":"Multiparameter persistence modules in the large scale","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527","json":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527.json","graph_json":"https://pith.science/api/pith-number/7BVUEAIFM6TQQ7RLHAA4422527/graph.json","events_json":"https://pith.science/api/pith-number/7BVUEAIFM6TQQ7RLHAA4422527/events.json","paper":"https://pith.science/paper/7BVUEAIF"},"agent_actions":{"view_html":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527","download_json":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527.json","view_paper":"https://pith.science/paper/7BVUEAIF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.08270&json=true","fetch_graph":"https://pith.science/api/pith-number/7BVUEAIFM6TQQ7RLHAA4422527/graph.json","fetch_events":"https://pith.science/api/pith-number/7BVUEAIFM6TQQ7RLHAA4422527/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527/action/storage_attestation","attest_author":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527/action/author_attestation","sign_citation":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527/action/citation_signature","submit_replication":"https://pith.science/pith/7BVUEAIFM6TQQ7RLHAA4422527/action/replication_record"}},"created_at":"2026-07-05T05:51:30.805180+00:00","updated_at":"2026-07-05T05:51:30.805180+00:00"}