{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BSNUXKZW4CKVSHIETPDRVSRR2Q","short_pith_number":"pith:BSNUXKZW","schema_version":"1.0","canonical_sha256":"0c9b4bab36e095591d049bc71aca31d408499b1d8bda11cc02bf2f9b28cc3aa1","source":{"kind":"arxiv","id":"1212.6879","version":2},"attestation_state":"computed","paper":{"title":"On two conjectures of Maurer concerning basis graphs of matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Damian Osajda, J\\'er\\'emie Chalopin, Victor Chepoi","submitted_at":"2012-12-31T12:34:54Z","abstract_excerpt":"We characterize 2-dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer (Conjecture 3 of S. Maurer, Matroid basis graphs I, JCTB 14 (1973), 216-240). We also establish Conjecture 1 from the same paper about the redundancy of the conditions in the characterization of basis graphs. We indicate positive-curvature-like aspects of the local properties of the studied complexes. We characterize similarly the corresponding 2-dimensiona"},"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":"1212.6879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-31T12:34:54Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"e5f490576274fd58c0b7bce8c59c9269ea88653bf6f70f6af8c5b4ead4e41a6f","abstract_canon_sha256":"31ffa90f97988395fc0830559d6ffd7edca9a111386fda5a7b4e9dcc197dc025"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.014602Z","signature_b64":"OGsxtKHftdksBLypvnP1EVL008UqD3Rks2q4ccRaeJw4FE9koNBRAo0U5rPZ6i8oMAPkT+B962gA7pSDhIBiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c9b4bab36e095591d049bc71aca31d408499b1d8bda11cc02bf2f9b28cc3aa1","last_reissued_at":"2026-05-17T23:58:55.014178Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.014178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On two conjectures of Maurer concerning basis graphs of matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Damian Osajda, J\\'er\\'emie Chalopin, Victor Chepoi","submitted_at":"2012-12-31T12:34:54Z","abstract_excerpt":"We characterize 2-dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer (Conjecture 3 of S. Maurer, Matroid basis graphs I, JCTB 14 (1973), 216-240). We also establish Conjecture 1 from the same paper about the redundancy of the conditions in the characterization of basis graphs. We indicate positive-curvature-like aspects of the local properties of the studied complexes. We characterize similarly the corresponding 2-dimensiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6879","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":"1212.6879","created_at":"2026-05-17T23:58:55.014238+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6879v2","created_at":"2026-05-17T23:58:55.014238+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6879","created_at":"2026-05-17T23:58:55.014238+00:00"},{"alias_kind":"pith_short_12","alias_value":"BSNUXKZW4CKV","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BSNUXKZW4CKVSHIE","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BSNUXKZW","created_at":"2026-05-18T12:27:01.376967+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/BSNUXKZW4CKVSHIETPDRVSRR2Q","json":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q.json","graph_json":"https://pith.science/api/pith-number/BSNUXKZW4CKVSHIETPDRVSRR2Q/graph.json","events_json":"https://pith.science/api/pith-number/BSNUXKZW4CKVSHIETPDRVSRR2Q/events.json","paper":"https://pith.science/paper/BSNUXKZW"},"agent_actions":{"view_html":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q","download_json":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q.json","view_paper":"https://pith.science/paper/BSNUXKZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6879&json=true","fetch_graph":"https://pith.science/api/pith-number/BSNUXKZW4CKVSHIETPDRVSRR2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/BSNUXKZW4CKVSHIETPDRVSRR2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/action/storage_attestation","attest_author":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/action/author_attestation","sign_citation":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/action/citation_signature","submit_replication":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/action/replication_record"}},"created_at":"2026-05-17T23:58:55.014238+00:00","updated_at":"2026-05-17T23:58:55.014238+00:00"}