{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5V7YLIVJYFVRMBFL62SKNLGPY2","short_pith_number":"pith:5V7YLIVJ","schema_version":"1.0","canonical_sha256":"ed7f85a2a9c16b1604abf6a4a6accfc6a6cc8d0ec061e930d1773beb385564a6","source":{"kind":"arxiv","id":"1908.05268","version":2},"attestation_state":"computed","paper":{"title":"The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CO"],"primary_cat":"cs.DM","authors_text":"Daniel Neuen, Sandra Kiefer","submitted_at":"2019-08-14T17:49:29Z","abstract_excerpt":"The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which is often exploited in approaches to tackle the graph isomorphism problem, is the decomposition into 2- and 3-connected components.\n  We prove that the 2-dimensional Weisfeiler-Leman algorithm implicitly computes the decomposition of a graph into its 3-connected components. This implies that the dimension of the algorithm needed to distinguish two given non-i"},"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":"1908.05268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-08-14T17:49:29Z","cross_cats_sorted":["cs.LO","math.CO"],"title_canon_sha256":"8d4bc6adf0d204923e4485d80edff1c182d0af434d70e916cca241b9726ecfd7","abstract_canon_sha256":"166fdadd594b867e4e3c009970fb686f650a1e378a5c0315c826e338d7c1b381"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:40:41.886014Z","signature_b64":"5z9/2+vHR33PyvPh34+Bv9bGSsdxEjWjrg9Ei8v5sfCxUgobi8AKR/hnJ68nPEaDA5OWtCXXP8UrmxzgHTe5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed7f85a2a9c16b1604abf6a4a6accfc6a6cc8d0ec061e930d1773beb385564a6","last_reissued_at":"2026-07-05T04:40:41.885661Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:40:41.885661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CO"],"primary_cat":"cs.DM","authors_text":"Daniel Neuen, Sandra Kiefer","submitted_at":"2019-08-14T17:49:29Z","abstract_excerpt":"The Weisfeiler-Leman procedure is a widely-used technique for graph isomorphism testing that works by iteratively computing an isomorphism-invariant coloring of vertex tuples. Meanwhile, a fundamental tool in structural graph theory, which is often exploited in approaches to tackle the graph isomorphism problem, is the decomposition into 2- and 3-connected components.\n  We prove that the 2-dimensional Weisfeiler-Leman algorithm implicitly computes the decomposition of a graph into its 3-connected components. This implies that the dimension of the algorithm needed to distinguish two given non-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05268","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05268/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":"1908.05268","created_at":"2026-07-05T04:40:41.885722+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05268v2","created_at":"2026-07-05T04:40:41.885722+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05268","created_at":"2026-07-05T04:40:41.885722+00:00"},{"alias_kind":"pith_short_12","alias_value":"5V7YLIVJYFVR","created_at":"2026-07-05T04:40:41.885722+00:00"},{"alias_kind":"pith_short_16","alias_value":"5V7YLIVJYFVRMBFL","created_at":"2026-07-05T04:40:41.885722+00:00"},{"alias_kind":"pith_short_8","alias_value":"5V7YLIVJ","created_at":"2026-07-05T04:40:41.885722+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/5V7YLIVJYFVRMBFL62SKNLGPY2","json":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2.json","graph_json":"https://pith.science/api/pith-number/5V7YLIVJYFVRMBFL62SKNLGPY2/graph.json","events_json":"https://pith.science/api/pith-number/5V7YLIVJYFVRMBFL62SKNLGPY2/events.json","paper":"https://pith.science/paper/5V7YLIVJ"},"agent_actions":{"view_html":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2","download_json":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2.json","view_paper":"https://pith.science/paper/5V7YLIVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05268&json=true","fetch_graph":"https://pith.science/api/pith-number/5V7YLIVJYFVRMBFL62SKNLGPY2/graph.json","fetch_events":"https://pith.science/api/pith-number/5V7YLIVJYFVRMBFL62SKNLGPY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2/action/storage_attestation","attest_author":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2/action/author_attestation","sign_citation":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2/action/citation_signature","submit_replication":"https://pith.science/pith/5V7YLIVJYFVRMBFL62SKNLGPY2/action/replication_record"}},"created_at":"2026-07-05T04:40:41.885722+00:00","updated_at":"2026-07-05T04:40:41.885722+00:00"}