{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ONIRCZH7IRNY2B62W5DOL3AEWG","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":"876302db914b04e67b8f17a64806bb5bbf83064be95fb207c0db3e83fb6e3aa0","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-10-16T10:53:54Z","title_canon_sha256":"a15a6b09c87a4c9d439184147d5ba16f89fac10ca00aa5f146691d447a832139"},"schema_version":"1.0","source":{"id":"1210.4352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4352","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4352v2","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4352","created_at":"2026-05-18T03:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"ONIRCZH7IRNY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ONIRCZH7IRNY2B62","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ONIRCZH7","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:35bfee1f124bd6aac96ba1ae93af5e91ce739926001789c1fc275e56726f0240","target":"graph","created_at":"2026-05-18T03:00:59Z","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":"Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a natural graph class that generalizes both interval and permutation graphs, namely \\emph{simple-triangle} graphs. Simple-triangle graphs - also known as \\emph{PI} graphs (for Point-Interval) - are the intersection graphs of triangles that are defined by a point on a line $L_{1}$ and an interval on a parallel line $L_{2}$. They lie naturally between permutation a","authors_text":"George B. Mertzios","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-10-16T10:53:54Z","title":"The Recognition of Simple-Triangle Graphs and of Linear-Interval Orders is Polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4352","kind":"arxiv","version":2},"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:bc5400691e7fc9f94d0213bbb793b559412ccc66b87ee857fb27734e616445e8","target":"record","created_at":"2026-05-18T03:00:59Z","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":"876302db914b04e67b8f17a64806bb5bbf83064be95fb207c0db3e83fb6e3aa0","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-10-16T10:53:54Z","title_canon_sha256":"a15a6b09c87a4c9d439184147d5ba16f89fac10ca00aa5f146691d447a832139"},"schema_version":"1.0","source":{"id":"1210.4352","kind":"arxiv","version":2}},"canonical_sha256":"73511164ff445b8d07dab746e5ec04b1b9bb949bb02bfd088b448ce10388e15b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73511164ff445b8d07dab746e5ec04b1b9bb949bb02bfd088b448ce10388e15b","first_computed_at":"2026-05-18T03:00:59.175873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:59.175873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+PWdNsva4wfTtpMy8YS2rnkafXFehLLvBWG1QllrU1rJIfafdI21LKdfPFchhasc5G5XFmxn96+1MhfaafKfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:59.176351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc5400691e7fc9f94d0213bbb793b559412ccc66b87ee857fb27734e616445e8","sha256:35bfee1f124bd6aac96ba1ae93af5e91ce739926001789c1fc275e56726f0240"],"state_sha256":"1dc7d9ff481196641fe1299030e0ddabaa19ebdf0a880a8179016f11d88fb482"}