{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RWPXCILWXSSLF4W3CTOC3RLKEY","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":"1fa23fdffe65433148e66edc2f838446423034c99335228f0a814f123f6da137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-13T20:49:16Z","title_canon_sha256":"d56c88c747b69cf2990cc029df932bcb6ec9e16fbf9e795d3ee9de180e307e48"},"schema_version":"1.0","source":{"id":"1310.3520","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3520","created_at":"2026-05-18T03:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3520v1","created_at":"2026-05-18T03:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3520","created_at":"2026-05-18T03:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"RWPXCILWXSSL","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RWPXCILWXSSLF4W3","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RWPXCILW","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:70294d9fed8b3e70438648b82c31cfc3cc63b86e40920f5ee1d054f82aa9b051","target":"graph","created_at":"2026-05-18T03:10:35Z","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":"A sign pattern matrix is a matrix whose entries are from the set $\\{+,-,0\\}$. If $A$ is an $m\\times n$ sign pattern matrix, the qualitative class of $A$, denoted $Q(A)$, is the set of all real $m\\times n$ matrices $B=[b_{i,j}]$ with $b_{i,j}$ positive (respectively, negative, zero) if $a_{i,j}$ is + (respectively, $-$, 0). The minimum rank of a sign pattern matrix $A$, denoted $\\mr(A)$, is the minimum of the ranks of the real matrices in $Q(A)$. Determination of the minimum rank of a sign pattern matrix is a longstanding open problem.\n  For the case that the sign pattern matrix has a 1-separat","authors_text":"Frank J. Hall, Hein van der Holst, Lihua Zhang, Marina Arav, Wenyan Zhou, Zhongshan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-13T20:49:16Z","title":"The minimum rank of a sign pattern matrix with a 1-separation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3520","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":"sha256:9b72345397954a276d8941db15fe54d771e121f1347307de39f3e200024a02ec","target":"record","created_at":"2026-05-18T03:10:35Z","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":"1fa23fdffe65433148e66edc2f838446423034c99335228f0a814f123f6da137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-13T20:49:16Z","title_canon_sha256":"d56c88c747b69cf2990cc029df932bcb6ec9e16fbf9e795d3ee9de180e307e48"},"schema_version":"1.0","source":{"id":"1310.3520","kind":"arxiv","version":1}},"canonical_sha256":"8d9f712176bca4b2f2db14dc2dc56a26232a4679c2286e64450ace56ed9e531d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d9f712176bca4b2f2db14dc2dc56a26232a4679c2286e64450ace56ed9e531d","first_computed_at":"2026-05-18T03:10:35.467725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:35.467725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vo3+Tj4DNI2/YzPH914Hyn/HhM8QbkhwU40iFpb/Jz7aWj8oOPPgWeos9c47WxCkhKhRDw5LG3vI8UKuJYTCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:35.468285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3520","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b72345397954a276d8941db15fe54d771e121f1347307de39f3e200024a02ec","sha256:70294d9fed8b3e70438648b82c31cfc3cc63b86e40920f5ee1d054f82aa9b051"],"state_sha256":"b16dd5f941c2f32bab9e783257bf19ed4a00862ff52c2a431b3ecee251355ad8"}