{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BSNUXKZW4CKVSHIETPDRVSRR2Q","short_pith_number":"pith:BSNUXKZW","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"},"canonical_sha256":"0c9b4bab36e095591d049bc71aca31d408499b1d8bda11cc02bf2f9b28cc3aa1","source":{"kind":"arxiv","id":"1212.6879","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6879","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6879v2","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6879","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"BSNUXKZW4CKV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BSNUXKZW4CKVSHIE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BSNUXKZW","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BSNUXKZW4CKVSHIETPDRVSRR2Q","target":"record","payload":{"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"},"canonical_sha256":"0c9b4bab36e095591d049bc71aca31d408499b1d8bda11cc02bf2f9b28cc3aa1","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"},"source_kind":"arxiv","source_id":"1212.6879","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/yFD3FP3r5TF1eACarV8IstP0HyFDQpkO2oUNpEIrM2TIHozsD4Wre8zLvkSFl1mtoXkb4XjGmTYpH2+cAPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:33:39.062168Z"},"content_sha256":"43b201c115f2c71cce6524873eba89b6cb7835af60aeddf28c742c64fa953313","schema_version":"1.0","event_id":"sha256:43b201c115f2c71cce6524873eba89b6cb7835af60aeddf28c742c64fa953313"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BSNUXKZW4CKVSHIETPDRVSRR2Q","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRIIvDXnRHWgB2un/U/zfbQNDzI8mLPan1l1ZmyN6SGTlJkJUOrYXdlYZj4BCWZiXv4LBNrSwD8Yz5k1as8ZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:33:39.062544Z"},"content_sha256":"de10fb8178409b7f5d4be01f16f4d2339a3a4ef489d26c92faae101f69ba5e70","schema_version":"1.0","event_id":"sha256:de10fb8178409b7f5d4be01f16f4d2339a3a4ef489d26c92faae101f69ba5e70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/bundle.json","state_url":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T05:33:39Z","links":{"resolver":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q","bundle":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/bundle.json","state":"https://pith.science/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSNUXKZW4CKVSHIETPDRVSRR2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BSNUXKZW4CKVSHIETPDRVSRR2Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"31ffa90f97988395fc0830559d6ffd7edca9a111386fda5a7b4e9dcc197dc025","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-31T12:34:54Z","title_canon_sha256":"e5f490576274fd58c0b7bce8c59c9269ea88653bf6f70f6af8c5b4ead4e41a6f"},"schema_version":"1.0","source":{"id":"1212.6879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6879","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6879v2","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6879","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"BSNUXKZW4CKV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BSNUXKZW4CKVSHIE","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BSNUXKZW","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:de10fb8178409b7f5d4be01f16f4d2339a3a4ef489d26c92faae101f69ba5e70","target":"graph","created_at":"2026-05-17T23:58:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Damian Osajda, J\\'er\\'emie Chalopin, Victor Chepoi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-31T12:34:54Z","title":"On two conjectures of Maurer concerning basis graphs of matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6879","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:43b201c115f2c71cce6524873eba89b6cb7835af60aeddf28c742c64fa953313","target":"record","created_at":"2026-05-17T23:58:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"31ffa90f97988395fc0830559d6ffd7edca9a111386fda5a7b4e9dcc197dc025","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-31T12:34:54Z","title_canon_sha256":"e5f490576274fd58c0b7bce8c59c9269ea88653bf6f70f6af8c5b4ead4e41a6f"},"schema_version":"1.0","source":{"id":"1212.6879","kind":"arxiv","version":2}},"canonical_sha256":"0c9b4bab36e095591d049bc71aca31d408499b1d8bda11cc02bf2f9b28cc3aa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c9b4bab36e095591d049bc71aca31d408499b1d8bda11cc02bf2f9b28cc3aa1","first_computed_at":"2026-05-17T23:58:55.014178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:55.014178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OGsxtKHftdksBLypvnP1EVL008UqD3Rks2q4ccRaeJw4FE9koNBRAo0U5rPZ6i8oMAPkT+B962gA7pSDhIBiCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:55.014602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43b201c115f2c71cce6524873eba89b6cb7835af60aeddf28c742c64fa953313","sha256:de10fb8178409b7f5d4be01f16f4d2339a3a4ef489d26c92faae101f69ba5e70"],"state_sha256":"5fed672e2a162e7f0cb3f3b5a512fe4d8b7a9c33f7ea3f4ff7d82dbe4f0e3430"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vnKBqYFLJsbT3KKCKhl/5gya/o1fhizJRwhvivR3/L/l6eXeRhM8nEeae8pF5tI0vmmxzmoV+XG4IHYsSHmmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:33:39.064664Z","bundle_sha256":"13e6d0884527061cfce91e345903aaa171c3d83effa459119a1f9f9bfa483496"}}