{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5NK6W3LMOC4TVGAZZX7CSBPSDI","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":"fa046c4cb734d9045f92c42b34017ecefaf9e57d625782c566af66b069637be9","cross_cats_sorted":["math.AC","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-18T11:51:54Z","title_canon_sha256":"bf8536728988a4add9ee23a574535784fcb73e2a0e00212b3001b2b308b68b29"},"schema_version":"1.0","source":{"id":"1010.3566","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3566","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3566v3","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3566","created_at":"2026-05-18T04:17:15Z"},{"alias_kind":"pith_short_12","alias_value":"5NK6W3LMOC4T","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5NK6W3LMOC4TVGAZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5NK6W3LM","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:1144e7a0bd3c6eb7f0c6fd335158cfdf599bd1dd6e19f9fa35290de9291b230a","target":"graph","created_at":"2026-05-18T04:17:15Z","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":"In this paper we study how perturbing a matrix changes its non-negative rank. We prove that the non-negative rank is upper-semicontinuos and we describe some special families of perturbations. We show how our results relate to Statistics in terms of the study of Maximum Likelihood Estimation for mixture models.","authors_text":"Cristiano Bocci, Enrico Carlini, Fabio Rapallo","cross_cats":["math.AC","math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-18T11:51:54Z","title":"Perturbation of matrices and non-negative rank with a view toward statistical models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3566","kind":"arxiv","version":3},"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":"sha256:563565ce3d377ba33302654fe3bc91d04b75d16bcc28435473b86b3644a4c8ed","target":"record","created_at":"2026-05-18T04:17:15Z","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":"fa046c4cb734d9045f92c42b34017ecefaf9e57d625782c566af66b069637be9","cross_cats_sorted":["math.AC","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-18T11:51:54Z","title_canon_sha256":"bf8536728988a4add9ee23a574535784fcb73e2a0e00212b3001b2b308b68b29"},"schema_version":"1.0","source":{"id":"1010.3566","kind":"arxiv","version":3}},"canonical_sha256":"eb55eb6d6c70b93a9819cdfe2905f21a35ea66c202c8afe09ad5200a8fb8fd61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb55eb6d6c70b93a9819cdfe2905f21a35ea66c202c8afe09ad5200a8fb8fd61","first_computed_at":"2026-05-18T04:17:15.182031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:15.182031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mkuy7IEhN6TWzfZF8c9ST/82ozRyKsTmWP74cqoyqlGxTOvtowRVzOAKRzb+L9o+X+6+GoeSyDxhfXhAOWdvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:15.183055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3566","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:563565ce3d377ba33302654fe3bc91d04b75d16bcc28435473b86b3644a4c8ed","sha256:1144e7a0bd3c6eb7f0c6fd335158cfdf599bd1dd6e19f9fa35290de9291b230a"],"state_sha256":"1ce07f1a7075fe94f635286c2c33ce44bbc49ca6ca0e9a4223c60678a290e003"}