{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6XZI52BOFEEOCPTBBTCYE3KUTQ","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":"7f4420b918178e8acfc444e137aaa4f81640963dcfc1ca1de182aa9d97f8f364","cross_cats_sorted":["math.AC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-04T13:15:07Z","title_canon_sha256":"1002d6ed4b0b91223451d9c29efce18a136372dc383ffe84f33f90f2bef6043b"},"schema_version":"1.0","source":{"id":"1412.1654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1654","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1654v1","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1654","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"6XZI52BOFEEO","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6XZI52BOFEEOCPTB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6XZI52BO","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:bfe2bbcaeace7743226bb64b099b6fe468f68a348348c3d2e647c7c3ca434bf8","target":"graph","created_at":"2026-05-18T02:32:06Z","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 Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Grobner basis with respect to the graded reverse lexicographic order. This solves a conjecture by Robeva, Sturmfels and the last author.","authors_text":"Emil Horobet, Kaie Kubjas, Rob H. Eggermont","cross_cats":["math.AC","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-04T13:15:07Z","title":"Algebraic boundary of matrices of nonnegative rank at most three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1654","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:aef5ae7c9bbf7f43a7949bbcffe027cdf1762a180690503b90f88b04b29acb46","target":"record","created_at":"2026-05-18T02:32:06Z","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":"7f4420b918178e8acfc444e137aaa4f81640963dcfc1ca1de182aa9d97f8f364","cross_cats_sorted":["math.AC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-04T13:15:07Z","title_canon_sha256":"1002d6ed4b0b91223451d9c29efce18a136372dc383ffe84f33f90f2bef6043b"},"schema_version":"1.0","source":{"id":"1412.1654","kind":"arxiv","version":1}},"canonical_sha256":"f5f28ee82e2908e13e610cc5826d549c0ba406797b8d73330e4de64199fffe38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5f28ee82e2908e13e610cc5826d549c0ba406797b8d73330e4de64199fffe38","first_computed_at":"2026-05-18T02:32:06.781448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:06.781448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgPqPFjHisOXIl7R+L7NDoAcajPiQ6abxmmnz9JJNw4Kk/cKTZCSqOgUi8EFKmVPqpEi7t+ROFn6rSNc7Y8EAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:06.781837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aef5ae7c9bbf7f43a7949bbcffe027cdf1762a180690503b90f88b04b29acb46","sha256:bfe2bbcaeace7743226bb64b099b6fe468f68a348348c3d2e647c7c3ca434bf8"],"state_sha256":"30191e444c5a1ded25bc7d763d81783b5b44ea08d8048cfe77d0c59f10edf7f6"}