{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XLXUR3XULKGTYWMF2TWAYNPANQ","short_pith_number":"pith:XLXUR3XU","schema_version":"1.0","canonical_sha256":"baef48eef45a8d3c5985d4ec0c35e06c3c0f68c41e7859acfccf90432292e2fd","source":{"kind":"arxiv","id":"1608.02635","version":2},"attestation_state":"computed","paper":{"title":"Matroid basis graph: Counting Hamiltonian cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\'esar Hern\\'andez-V\\'elez, Cristina G. Fernandes, Jorge Luis Ram\\'irez Alfons\\'in, Jos\\'e C. de Pina","submitted_at":"2016-08-08T21:52:53Z","abstract_excerpt":"We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform matroids. All lower bounds were obtained by a common general strategy based on counting appropriated cycles of length four in the corresponding matroid basis graph."},"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":"1608.02635","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-08T21:52:53Z","cross_cats_sorted":[],"title_canon_sha256":"2c43e44c435aff91aa80b30c34e0357a87af5fbe699b33adada8d895c08a4760","abstract_canon_sha256":"c8cb371df2aaa80aa7f04e756efe376035050846cef9b594dd115b25d9717397"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:44.614580Z","signature_b64":"bvelI8kp/bfMo+/PxDb6ySFGGRBYySUIimR6bIPWbcU7uiQfyGgFuzcgNK3FTWVkF4BM1XbS+wErn4JRbUO8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baef48eef45a8d3c5985d4ec0c35e06c3c0f68c41e7859acfccf90432292e2fd","last_reissued_at":"2026-05-17T23:47:44.614011Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:44.614011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matroid basis graph: Counting Hamiltonian cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\'esar Hern\\'andez-V\\'elez, Cristina G. Fernandes, Jorge Luis Ram\\'irez Alfons\\'in, Jos\\'e C. de Pina","submitted_at":"2016-08-08T21:52:53Z","abstract_excerpt":"We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform matroids. All lower bounds were obtained by a common general strategy based on counting appropriated cycles of length four in the corresponding matroid basis graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02635","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":"1608.02635","created_at":"2026-05-17T23:47:44.614085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.02635v2","created_at":"2026-05-17T23:47:44.614085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02635","created_at":"2026-05-17T23:47:44.614085+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLXUR3XULKGT","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLXUR3XULKGTYWMF","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLXUR3XU","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/XLXUR3XULKGTYWMF2TWAYNPANQ","json":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ.json","graph_json":"https://pith.science/api/pith-number/XLXUR3XULKGTYWMF2TWAYNPANQ/graph.json","events_json":"https://pith.science/api/pith-number/XLXUR3XULKGTYWMF2TWAYNPANQ/events.json","paper":"https://pith.science/paper/XLXUR3XU"},"agent_actions":{"view_html":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ","download_json":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ.json","view_paper":"https://pith.science/paper/XLXUR3XU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.02635&json=true","fetch_graph":"https://pith.science/api/pith-number/XLXUR3XULKGTYWMF2TWAYNPANQ/graph.json","fetch_events":"https://pith.science/api/pith-number/XLXUR3XULKGTYWMF2TWAYNPANQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ/action/storage_attestation","attest_author":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ/action/author_attestation","sign_citation":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ/action/citation_signature","submit_replication":"https://pith.science/pith/XLXUR3XULKGTYWMF2TWAYNPANQ/action/replication_record"}},"created_at":"2026-05-17T23:47:44.614085+00:00","updated_at":"2026-05-17T23:47:44.614085+00:00"}