{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QW5OFQUZMR5TDX3AB64RPRNFXY","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":"2b692bc01286b30f8dd5d84acc028993930c0978eb632ad511cc76266ffa671d","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-01T15:53:50Z","title_canon_sha256":"b993fbdd03b67d019c829f57f3918a438b1b5ca2d4201cd23cc2040b445e2c46"},"schema_version":"1.0","source":{"id":"1112.0217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0217","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0217v1","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0217","created_at":"2026-05-18T04:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"QW5OFQUZMR5T","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QW5OFQUZMR5TDX3A","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QW5OFQUZ","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:d246d6cc988843c1565861decf7f3f3f3b266e441f53c596f1ac6dcfa8d0c64c","target":"graph","created_at":"2026-05-18T04:07:16Z","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":"We give a polynomial-time dynamic programming algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. We briefly review three known tractable matrix classes and show that none of them contains all tridiagonal P-matrices.","authors_text":"Bernd G\\\"artner, Markus Sprecher","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-01T15:53:50Z","title":"A Polynomial-Time Algorithm for the Tridiagonal and Hessenberg P-Matrix Linear Complementarity Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0217","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:f0cc64f15ff89e5b762acb6beb93d74b6c6e194efccf25b880ac172584a57b75","target":"record","created_at":"2026-05-18T04:07:16Z","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":"2b692bc01286b30f8dd5d84acc028993930c0978eb632ad511cc76266ffa671d","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-01T15:53:50Z","title_canon_sha256":"b993fbdd03b67d019c829f57f3918a438b1b5ca2d4201cd23cc2040b445e2c46"},"schema_version":"1.0","source":{"id":"1112.0217","kind":"arxiv","version":1}},"canonical_sha256":"85bae2c299647b31df600fb917c5a5be33c67d97e3fd2cf741d3c295f0980a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85bae2c299647b31df600fb917c5a5be33c67d97e3fd2cf741d3c295f0980a43","first_computed_at":"2026-05-18T04:07:16.528374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:16.528374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Agr2/7V1Tp1gmLeW5CZbxtrcz7Nju/S7vYJNS6RXbBaxbe5bSTwj3nwF2AHl01/HgqBbfJaU6/gnu555QAGGDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:16.529353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0cc64f15ff89e5b762acb6beb93d74b6c6e194efccf25b880ac172584a57b75","sha256:d246d6cc988843c1565861decf7f3f3f3b266e441f53c596f1ac6dcfa8d0c64c"],"state_sha256":"e9c33d4db37eec71d7cf535f2d7cce4c2b9a2ec13b51fed6eb701eba769f6c93"}