{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UTM7RF3I2V7CG6WR7UVAEDFJRJ","short_pith_number":"pith:UTM7RF3I","schema_version":"1.0","canonical_sha256":"a4d9f89768d57e237ad1fd2a020ca98a5f658272a8979b827ec0a08b50707b34","source":{"kind":"arxiv","id":"1308.0611","version":2},"attestation_state":"computed","paper":{"title":"The 1-2-3 Conjecture for Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florian Pfender, Maciej Kalkowski, Micha{\\l} Karo\\'nski","submitted_at":"2013-08-02T20:14:52Z","abstract_excerpt":"A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper we show that such a weighting is possible from the weight set {1,2,...,r+1} for all hypergraphs with maximum edge size r>3 and not containing edges solely consisting of identical vertices. The number r+1 is best possible for this statement.\n  Further, the weight set {1,2,3,4,5} is sufficient for all hypergraphs with maximum edge size 3, up to some trivial ex"},"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":"1308.0611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-02T20:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"9b2603b9f9999a5f1989f2a3efc3db2042d6a301e34f4aaa83933c9aa58b6f71","abstract_canon_sha256":"6d0abd9ad1d936f577af25fc277ab5c06d0cc2f9efcf5762d7a294aa40217052"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:29.795161Z","signature_b64":"AAFy81WssE3b0oDxxM5eODfoKPe7lhKD6mM+rDl7G0QBFjgKswXf+s4AXYGdcLLSL8O3ok6dtpjLKY4f+znMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4d9f89768d57e237ad1fd2a020ca98a5f658272a8979b827ec0a08b50707b34","last_reissued_at":"2026-05-18T01:14:29.794559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:29.794559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The 1-2-3 Conjecture for Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florian Pfender, Maciej Kalkowski, Micha{\\l} Karo\\'nski","submitted_at":"2013-08-02T20:14:52Z","abstract_excerpt":"A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper we show that such a weighting is possible from the weight set {1,2,...,r+1} for all hypergraphs with maximum edge size r>3 and not containing edges solely consisting of identical vertices. The number r+1 is best possible for this statement.\n  Further, the weight set {1,2,3,4,5} is sufficient for all hypergraphs with maximum edge size 3, up to some trivial ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0611","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":"1308.0611","created_at":"2026-05-18T01:14:29.794647+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.0611v2","created_at":"2026-05-18T01:14:29.794647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0611","created_at":"2026-05-18T01:14:29.794647+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTM7RF3I2V7C","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTM7RF3I2V7CG6WR","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTM7RF3I","created_at":"2026-05-18T12:28:02.375192+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/UTM7RF3I2V7CG6WR7UVAEDFJRJ","json":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ.json","graph_json":"https://pith.science/api/pith-number/UTM7RF3I2V7CG6WR7UVAEDFJRJ/graph.json","events_json":"https://pith.science/api/pith-number/UTM7RF3I2V7CG6WR7UVAEDFJRJ/events.json","paper":"https://pith.science/paper/UTM7RF3I"},"agent_actions":{"view_html":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ","download_json":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ.json","view_paper":"https://pith.science/paper/UTM7RF3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.0611&json=true","fetch_graph":"https://pith.science/api/pith-number/UTM7RF3I2V7CG6WR7UVAEDFJRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/UTM7RF3I2V7CG6WR7UVAEDFJRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ/action/storage_attestation","attest_author":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ/action/author_attestation","sign_citation":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ/action/citation_signature","submit_replication":"https://pith.science/pith/UTM7RF3I2V7CG6WR7UVAEDFJRJ/action/replication_record"}},"created_at":"2026-05-18T01:14:29.794647+00:00","updated_at":"2026-05-18T01:14:29.794647+00:00"}