{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XXJ7V5NDZ5X263F4WEEQGYZGLX","short_pith_number":"pith:XXJ7V5ND","schema_version":"1.0","canonical_sha256":"bdd3faf5a3cf6faf6cbcb1090363265dd412d239c19d100698d7525e1b4b3e08","source":{"kind":"arxiv","id":"1609.02513","version":2},"attestation_state":"computed","paper":{"title":"Functorial Hierarchical Clustering with Overlaps","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dan P. Guralnik, Jared Culbertson, Peter F. Stiller","submitted_at":"2016-09-08T17:52:26Z","abstract_excerpt":"This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and M\\'{e}moli to partition-based clustering, and the Isbell/Dress school's study of injective envelopes. Carlsson and M\\'{e}moli introduce the idea of viewing clustering methods as functors from a category of metric spaces to a category of clusters, with functoriality subsuming many desirable pr"},"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":"1609.02513","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.LG","submitted_at":"2016-09-08T17:52:26Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1e005bbc456664155fa89a8880d06b8ed4537c1a274e943b2f45e9a3e33908bc","abstract_canon_sha256":"8c4f2cf0dc8fc414fac1bc76f3b3e7cfc0070bf29904e673ecee95a57db41062"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:05.321101Z","signature_b64":"mrYUFMeIzXFTk30xxqDiAZYO4V5gmfwizEC8PxwfAqbDEZcwr1SaHWHs0s3WbijstovKI7EERn8/OzJ/SqeeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdd3faf5a3cf6faf6cbcb1090363265dd412d239c19d100698d7525e1b4b3e08","last_reissued_at":"2026-05-18T00:08:05.320715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:05.320715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functorial Hierarchical Clustering with Overlaps","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Dan P. Guralnik, Jared Culbertson, Peter F. Stiller","submitted_at":"2016-09-08T17:52:26Z","abstract_excerpt":"This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and M\\'{e}moli to partition-based clustering, and the Isbell/Dress school's study of injective envelopes. Carlsson and M\\'{e}moli introduce the idea of viewing clustering methods as functors from a category of metric spaces to a category of clusters, with functoriality subsuming many desirable pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02513","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1609.02513","created_at":"2026-05-18T00:08:05.320774+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.02513v2","created_at":"2026-05-18T00:08:05.320774+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02513","created_at":"2026-05-18T00:08:05.320774+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXJ7V5NDZ5X2","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXJ7V5NDZ5X263F4","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXJ7V5ND","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX","json":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX.json","graph_json":"https://pith.science/api/pith-number/XXJ7V5NDZ5X263F4WEEQGYZGLX/graph.json","events_json":"https://pith.science/api/pith-number/XXJ7V5NDZ5X263F4WEEQGYZGLX/events.json","paper":"https://pith.science/paper/XXJ7V5ND"},"agent_actions":{"view_html":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX","download_json":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX.json","view_paper":"https://pith.science/paper/XXJ7V5ND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.02513&json=true","fetch_graph":"https://pith.science/api/pith-number/XXJ7V5NDZ5X263F4WEEQGYZGLX/graph.json","fetch_events":"https://pith.science/api/pith-number/XXJ7V5NDZ5X263F4WEEQGYZGLX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX/action/storage_attestation","attest_author":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX/action/author_attestation","sign_citation":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX/action/citation_signature","submit_replication":"https://pith.science/pith/XXJ7V5NDZ5X263F4WEEQGYZGLX/action/replication_record"}},"created_at":"2026-05-18T00:08:05.320774+00:00","updated_at":"2026-05-18T00:08:05.320774+00:00"}