{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FD4BOHEYYLB2ZA4GVN45N4KKHX","short_pith_number":"pith:FD4BOHEY","schema_version":"1.0","canonical_sha256":"28f8171c98c2c3ac8386ab79d6f14a3df3abf80847c28dbac342a30cf140720f","source":{"kind":"arxiv","id":"1508.07181","version":1},"attestation_state":"computed","paper":{"title":"Fast Factorization of Cartesian products of Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Florian Lehner, Marc Hellmuth","submitted_at":"2015-08-28T12:32:56Z","abstract_excerpt":"Cartesian products of graphs and hypergraphs have been studied since the 1960s. For (un)directed hypergraphs, unique \\emph{prime factor decomposition (PFD)} results with respect to the Cartesian product are known. However, there is still a lack of algorithms, that compute the PFD of directed hypergraphs with respect to the Cartesian product.\n  In this contribution, we focus on the algorithmic aspects for determining the Cartesian prime factors of a finite, connected, directed hypergraph and present a first polynomial time algorithm to compute its PFD. In particular, the algorithm has time comp"},"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":"1508.07181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-08-28T12:32:56Z","cross_cats_sorted":[],"title_canon_sha256":"e0d267d8afaff74abc91325fed9b24673ea09182f1ffe170ab39113858873808","abstract_canon_sha256":"4c4a3116b08d41b124af6c3076968ccd058d13299d27202a7979dfd743fd9e33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:36.665499Z","signature_b64":"H5HTbVPl/hVhrudoI+J8Lx8dTUVJ06MHecENWgxoljogAZ8y/ny5AGVgqOaJT7tapbk1ICleBP2zZxdx4pHBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28f8171c98c2c3ac8386ab79d6f14a3df3abf80847c28dbac342a30cf140720f","last_reissued_at":"2026-05-18T01:34:36.665003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:36.665003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Factorization of Cartesian products of Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Florian Lehner, Marc Hellmuth","submitted_at":"2015-08-28T12:32:56Z","abstract_excerpt":"Cartesian products of graphs and hypergraphs have been studied since the 1960s. For (un)directed hypergraphs, unique \\emph{prime factor decomposition (PFD)} results with respect to the Cartesian product are known. However, there is still a lack of algorithms, that compute the PFD of directed hypergraphs with respect to the Cartesian product.\n  In this contribution, we focus on the algorithmic aspects for determining the Cartesian prime factors of a finite, connected, directed hypergraph and present a first polynomial time algorithm to compute its PFD. In particular, the algorithm has time comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07181","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":""},"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":"1508.07181","created_at":"2026-05-18T01:34:36.665079+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07181v1","created_at":"2026-05-18T01:34:36.665079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07181","created_at":"2026-05-18T01:34:36.665079+00:00"},{"alias_kind":"pith_short_12","alias_value":"FD4BOHEYYLB2","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FD4BOHEYYLB2ZA4G","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FD4BOHEY","created_at":"2026-05-18T12:29:19.899920+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/FD4BOHEYYLB2ZA4GVN45N4KKHX","json":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX.json","graph_json":"https://pith.science/api/pith-number/FD4BOHEYYLB2ZA4GVN45N4KKHX/graph.json","events_json":"https://pith.science/api/pith-number/FD4BOHEYYLB2ZA4GVN45N4KKHX/events.json","paper":"https://pith.science/paper/FD4BOHEY"},"agent_actions":{"view_html":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX","download_json":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX.json","view_paper":"https://pith.science/paper/FD4BOHEY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07181&json=true","fetch_graph":"https://pith.science/api/pith-number/FD4BOHEYYLB2ZA4GVN45N4KKHX/graph.json","fetch_events":"https://pith.science/api/pith-number/FD4BOHEYYLB2ZA4GVN45N4KKHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX/action/storage_attestation","attest_author":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX/action/author_attestation","sign_citation":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX/action/citation_signature","submit_replication":"https://pith.science/pith/FD4BOHEYYLB2ZA4GVN45N4KKHX/action/replication_record"}},"created_at":"2026-05-18T01:34:36.665079+00:00","updated_at":"2026-05-18T01:34:36.665079+00:00"}