{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6S2NGEEUSKRC36JGDCFWGFJCPO","short_pith_number":"pith:6S2NGEEU","schema_version":"1.0","canonical_sha256":"f4b4d3109492a22df926188b6315227b8ff4709a6dff7abb0d1d6244c0e4acb8","source":{"kind":"arxiv","id":"1505.06036","version":2},"attestation_state":"computed","paper":{"title":"VPG and EPG bend-numbers of Halin Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Abhiruk Lahiri, Mathew C. Francis","submitted_at":"2015-05-22T12:04:15Z","abstract_excerpt":"A piecewise linear curve in the plane made up of $k+1$ line segments, each of which is either horizontal or vertical, with consecutive segments being of different orientation is called a $k$-bend path. Given a graph $G$, a collection of $k$-bend paths in which each path corresponds to a vertex in $G$ and two paths have a common point if and only if the vertices corresponding to them are adjacent in $G$ is called a $B_k$-VPG representation of $G$. Similarly, a collection of $k$-bend paths each of which corresponds to a vertex in $G$ is called an $B_k$-EPG representation of $G$ if any two paths "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.06036","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-22T12:04:15Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"931ef9110a7b1a3e3a5f1b28b8ba14240bba97940f4d7cfb5dcc68853e5c86e8","abstract_canon_sha256":"17b8eebcb58828cab85b9f9296fff2cd8b605921ad445efd0e2279a84f50dc52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:58.053173Z","signature_b64":"WBc7LssxqCeCtQryfYm2Jz6KS4A3g7wkU4xxP8sxpaMLyGQv2J3F5FpUDxx7tvKo6pZrpTjJ/m+Yi9TRyYS9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4b4d3109492a22df926188b6315227b8ff4709a6dff7abb0d1d6244c0e4acb8","last_reissued_at":"2026-05-18T00:26:58.052439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:58.052439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"VPG and EPG bend-numbers of Halin Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Abhiruk Lahiri, Mathew C. Francis","submitted_at":"2015-05-22T12:04:15Z","abstract_excerpt":"A piecewise linear curve in the plane made up of $k+1$ line segments, each of which is either horizontal or vertical, with consecutive segments being of different orientation is called a $k$-bend path. Given a graph $G$, a collection of $k$-bend paths in which each path corresponds to a vertex in $G$ and two paths have a common point if and only if the vertices corresponding to them are adjacent in $G$ is called a $B_k$-VPG representation of $G$. Similarly, a collection of $k$-bend paths each of which corresponds to a vertex in $G$ is called an $B_k$-EPG representation of $G$ if any two paths "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06036","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.06036","created_at":"2026-05-18T00:26:58.052559+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06036v2","created_at":"2026-05-18T00:26:58.052559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06036","created_at":"2026-05-18T00:26:58.052559+00:00"},{"alias_kind":"pith_short_12","alias_value":"6S2NGEEUSKRC","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6S2NGEEUSKRC36JG","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6S2NGEEU","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO","json":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO.json","graph_json":"https://pith.science/api/pith-number/6S2NGEEUSKRC36JGDCFWGFJCPO/graph.json","events_json":"https://pith.science/api/pith-number/6S2NGEEUSKRC36JGDCFWGFJCPO/events.json","paper":"https://pith.science/paper/6S2NGEEU"},"agent_actions":{"view_html":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO","download_json":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO.json","view_paper":"https://pith.science/paper/6S2NGEEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06036&json=true","fetch_graph":"https://pith.science/api/pith-number/6S2NGEEUSKRC36JGDCFWGFJCPO/graph.json","fetch_events":"https://pith.science/api/pith-number/6S2NGEEUSKRC36JGDCFWGFJCPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO/action/storage_attestation","attest_author":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO/action/author_attestation","sign_citation":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO/action/citation_signature","submit_replication":"https://pith.science/pith/6S2NGEEUSKRC36JGDCFWGFJCPO/action/replication_record"}},"created_at":"2026-05-18T00:26:58.052559+00:00","updated_at":"2026-05-18T00:26:58.052559+00:00"}