{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PM7VZD5PCGBRY53FY5IKDBKPDC","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":"1f63a0be01dbb51ed74a37216922d953019d795420a3301812e913c676fff04c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-19T14:12:38Z","title_canon_sha256":"ab0893c2faba1b67b0af37ebcb2107e7fc8bf4b5812517f654bb3b749c569aca"},"schema_version":"1.0","source":{"id":"1510.05485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05485","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05485v1","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05485","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"PM7VZD5PCGBR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PM7VZD5PCGBRY53F","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PM7VZD5P","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:3e0b6a71d92314b314c0efee53f7148b8f667273d540673cbed6272611fbea3f","target":"graph","created_at":"2026-05-18T01:29:52Z","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":"It is shown that the lattices of flats of boolean representable simplicial complexes are always atomistic, but semimodular if and only if the complex is a matroid. A canonical construction is introduced for arbitrary finite atomistic lattices, providing a characterization of the lattices of flats of boolean representable simplicial complexes and a decidability condition. We remark that every finite lattice occurs as the lattice of flats of some simplicial complex.","authors_text":"John Rhodes, Pedro V. Silva, Stuart Margolis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-19T14:12:38Z","title":"On the lattice of flats of a boolean representable simplicial complex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05485","kind":"arxiv","version":1},"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":"sha256:6c4ed4de2e39a47ad5a4e3c711c4b22dab76e895ab99c853266242e895c9926d","target":"record","created_at":"2026-05-18T01:29:52Z","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":"1f63a0be01dbb51ed74a37216922d953019d795420a3301812e913c676fff04c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-19T14:12:38Z","title_canon_sha256":"ab0893c2faba1b67b0af37ebcb2107e7fc8bf4b5812517f654bb3b749c569aca"},"schema_version":"1.0","source":{"id":"1510.05485","kind":"arxiv","version":1}},"canonical_sha256":"7b3f5c8faf11831c7765c750a1854f18b1ae8579641e9761a55903b9ffcf07b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b3f5c8faf11831c7765c750a1854f18b1ae8579641e9761a55903b9ffcf07b0","first_computed_at":"2026-05-18T01:29:52.227962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:52.227962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wHidSF31x1iLA2C9R1hNe4lp8ODVIod2b0+WoZyy8IaodxiqODadBdhsxjWgQIE9BuRS2jr7utc5I8n3OFy2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:52.228393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c4ed4de2e39a47ad5a4e3c711c4b22dab76e895ab99c853266242e895c9926d","sha256:3e0b6a71d92314b314c0efee53f7148b8f667273d540673cbed6272611fbea3f"],"state_sha256":"7bc96018b2806e5b777926aa07c190143fbbacbca8609d346331a2db72638712"}