{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6NLAOESYAG25ORCZAP2BH5CMIE","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":"6caf57c865c1385e6d114ce65150e8ab738117f32fe017785e55f0fb8cf6c3e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-23T10:10:04Z","title_canon_sha256":"08e176e920de796084aff4fa6a33fa0b2f9db23478fd20b3c07b7e01646e87e8"},"schema_version":"1.0","source":{"id":"1201.4662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4662","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4662v2","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4662","created_at":"2026-05-18T03:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"6NLAOESYAG25","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6NLAOESYAG25ORCZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6NLAOESY","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:1c2237aaaa19d7d5b265ce00a4c158929509856e0265f3fe99d1beaf0a921b1c","target":"graph","created_at":"2026-05-18T03:59:27Z","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":"The weak-map order on the matroid base polytopes is the partial order defined by inclusion. Lucas proved that the base polytope of no binary matroid includes the base polytope of a connected matroid. A matroid base polytope is said to be decomposable when it has a polytopal decomposition which consists of at least two matroid base polytopes.\n  We shed light on the relation between the decomposability and the weak-map order of matroid base polytopes. We classify matroids into five types with respect to the weak-map order and decomposability. We give an example of a matroid in each class. Moreov","authors_text":"Kenji Kashiwabara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-23T10:10:04Z","title":"The Weak-Map Order and Polytopal Decompositions of Matroid Base Polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4662","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":"sha256:40eca3da670cbaecb8df6e08f788dbc9cd8af2ec53b61bc3038429cde499a69b","target":"record","created_at":"2026-05-18T03:59:27Z","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":"6caf57c865c1385e6d114ce65150e8ab738117f32fe017785e55f0fb8cf6c3e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-23T10:10:04Z","title_canon_sha256":"08e176e920de796084aff4fa6a33fa0b2f9db23478fd20b3c07b7e01646e87e8"},"schema_version":"1.0","source":{"id":"1201.4662","kind":"arxiv","version":2}},"canonical_sha256":"f35607125801b5d7445903f413f44c4104a91e4bea36da19f2ba2586c301d9ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f35607125801b5d7445903f413f44c4104a91e4bea36da19f2ba2586c301d9ff","first_computed_at":"2026-05-18T03:59:27.042238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:27.042238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XVBjS58KC2iN5grnZtNlNP/+BAyuntcd9ngfujgGPxKFX/cvltKpLxpZm22n0Kq1POa/cFSZWZa89mYYEVg5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:27.042975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40eca3da670cbaecb8df6e08f788dbc9cd8af2ec53b61bc3038429cde499a69b","sha256:1c2237aaaa19d7d5b265ce00a4c158929509856e0265f3fe99d1beaf0a921b1c"],"state_sha256":"ff250b64019780b2b6b0e2aa00850dca91499265dd1db964b93878495bcb9768"}