{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:5QRULDYNRHZ356SR67WS4DNVEF","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":"bcebc4c1fdedd217905f1ce3359637cc1f5d76793eae36b1bf680b048a2481b4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-06-06T04:14:02Z","title_canon_sha256":"9e55919fe8633cd222acd07287b7f6197279479ddac5edddb6bdc55f09e5a772"},"schema_version":"1.0","source":{"id":"0806.1088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.1088","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"0806.1088v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1088","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"5QRULDYNRHZ3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"5QRULDYNRHZ356SR","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"5QRULDYN","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:a2b7adc32413b33b2755b1454e2bc4996bd6fbbba4c46fc4c7da25effd843b05","target":"graph","created_at":"2026-05-17T23:56:39Z","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 correspondence between unmixed bipartite graphs and sublattices of the oolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of toric ideals arising from minimal vertex covers of unmixed bipartite graphs.","authors_text":"Hidefumi Ohsugi, Juergen Herzog, Takayuki Hibi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-06-06T04:14:02Z","title":"Unmixed bipartite graphs and sublattices of the Boolean lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1088","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":"sha256:9d149fb83aa4de6c970fd27fcdd4f0424db42270754ba8746c99c62c4097f0af","target":"record","created_at":"2026-05-17T23:56:39Z","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":"bcebc4c1fdedd217905f1ce3359637cc1f5d76793eae36b1bf680b048a2481b4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-06-06T04:14:02Z","title_canon_sha256":"9e55919fe8633cd222acd07287b7f6197279479ddac5edddb6bdc55f09e5a772"},"schema_version":"1.0","source":{"id":"0806.1088","kind":"arxiv","version":1}},"canonical_sha256":"ec23458f0d89f3befa51f7ed2e0db52175774f7746f679956737038c514b5884","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec23458f0d89f3befa51f7ed2e0db52175774f7746f679956737038c514b5884","first_computed_at":"2026-05-17T23:56:39.285290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:39.285290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ulj9FD8G0BUejSm13xmm5FL+K7iNAOyXXwTuzlV0lcIjlAtp+a0Shr37Jy+fNTacHdSCsqj6+x0nXfb84E2XCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:39.285848Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.1088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d149fb83aa4de6c970fd27fcdd4f0424db42270754ba8746c99c62c4097f0af","sha256:a2b7adc32413b33b2755b1454e2bc4996bd6fbbba4c46fc4c7da25effd843b05"],"state_sha256":"98fbfa78b569d160d7e8b403cad3fd85c502e6f3caa92ceabfd1d11e3390a821"}