{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:H426LYZVAR2UN35DQ7VJXXFKDD","short_pith_number":"pith:H426LYZV","schema_version":"1.0","canonical_sha256":"3f35e5e335047546efa387ea9bdcaa18d4287745b881b613936258d6b8d9395b","source":{"kind":"arxiv","id":"1409.5451","version":1},"attestation_state":"computed","paper":{"title":"On Hilbert bases of cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luis Goddyn, Tanmay Deshpande, Tony Huynh","submitted_at":"2014-09-18T20:13:34Z","abstract_excerpt":"A Hilbert basis is a set of vectors X such that the integer cone (semigroup) generated by X is the intersection of the lattice generated by X with the cone generated by X. Define a graph to be (cut) Hilbert if its set of cuts forms a Hilbert basis. We show that the Hilbert property is not closed under edge deletions, subdivisions, nor 2-sums. Furthermore, no graph having K_6-e as a minor is Hilbert. This corrects an error in [M. Laurent. Hilbert bases of cuts. Discrete Math., 150(1-3):257-279 (1996)]. For positive results, we give conditions under which the 2-sum of two graphs produces a Hilbe"},"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":"1409.5451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-18T20:13:34Z","cross_cats_sorted":[],"title_canon_sha256":"39cc7b2cb5ad4cda087db5795b0d8e49e2f48a6fe6016ae90f7d483d70d63f7b","abstract_canon_sha256":"6af6800f6ed4d77b22624eabfd1bf24bfdbe5aa05a440159ae5f8161ff734880"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:27.605761Z","signature_b64":"zyb/uGkyuSkOJkmYo9JDSyhesQBbmUXR1dPj16rAMa4s+9tZulcZ1GafpniNk1KrVAOwGKk7sxrSIie4MideDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f35e5e335047546efa387ea9bdcaa18d4287745b881b613936258d6b8d9395b","last_reissued_at":"2026-05-18T02:42:27.604668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:27.604668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hilbert bases of cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Luis Goddyn, Tanmay Deshpande, Tony Huynh","submitted_at":"2014-09-18T20:13:34Z","abstract_excerpt":"A Hilbert basis is a set of vectors X such that the integer cone (semigroup) generated by X is the intersection of the lattice generated by X with the cone generated by X. Define a graph to be (cut) Hilbert if its set of cuts forms a Hilbert basis. We show that the Hilbert property is not closed under edge deletions, subdivisions, nor 2-sums. Furthermore, no graph having K_6-e as a minor is Hilbert. This corrects an error in [M. Laurent. Hilbert bases of cuts. Discrete Math., 150(1-3):257-279 (1996)]. For positive results, we give conditions under which the 2-sum of two graphs produces a Hilbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5451","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":"1409.5451","created_at":"2026-05-18T02:42:27.604819+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5451v1","created_at":"2026-05-18T02:42:27.604819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5451","created_at":"2026-05-18T02:42:27.604819+00:00"},{"alias_kind":"pith_short_12","alias_value":"H426LYZVAR2U","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"H426LYZVAR2UN35D","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"H426LYZV","created_at":"2026-05-18T12:28:30.664211+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/H426LYZVAR2UN35DQ7VJXXFKDD","json":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD.json","graph_json":"https://pith.science/api/pith-number/H426LYZVAR2UN35DQ7VJXXFKDD/graph.json","events_json":"https://pith.science/api/pith-number/H426LYZVAR2UN35DQ7VJXXFKDD/events.json","paper":"https://pith.science/paper/H426LYZV"},"agent_actions":{"view_html":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD","download_json":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD.json","view_paper":"https://pith.science/paper/H426LYZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5451&json=true","fetch_graph":"https://pith.science/api/pith-number/H426LYZVAR2UN35DQ7VJXXFKDD/graph.json","fetch_events":"https://pith.science/api/pith-number/H426LYZVAR2UN35DQ7VJXXFKDD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD/action/storage_attestation","attest_author":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD/action/author_attestation","sign_citation":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD/action/citation_signature","submit_replication":"https://pith.science/pith/H426LYZVAR2UN35DQ7VJXXFKDD/action/replication_record"}},"created_at":"2026-05-18T02:42:27.604819+00:00","updated_at":"2026-05-18T02:42:27.604819+00:00"}