{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3C25RNTEILPRAG54XEKWSTN5SZ","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":"a1eac7330c5afa7d4dbc114b8494f2485694b6d5eb3486284b4bbed64e1070d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-10-25T01:11:58Z","title_canon_sha256":"961d1c221a86d740a11438f3f78b095ebad40731732d33cf73b8fbde96d5b3ab"},"schema_version":"1.0","source":{"id":"1710.09035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09035","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09035v1","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09035","created_at":"2026-05-18T00:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"3C25RNTEILPR","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3C25RNTEILPRAG54","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3C25RNTE","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:3b2791a8fe4099f733b5af9dab6d63e38736e808b42faafd5d7fff73b9da13d9","target":"graph","created_at":"2026-05-18T00:32:00Z","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 geodesic $k$-center problem in a simple polygon with $n$ vertices consists in the following. Find a set $S$ of $k$ points in the polygon that minimizes the maximum geodesic distance from any point of the polygon to its closest point in $S$. In this paper, we focus on the case where $k=2$ and present an exact algorithm that returns a geodesic $2$-center in $O(n^2\\log^2 n)$ time.","authors_text":"Eunjin Oh, Hee-Kap Ahn, Jean-Lou De Carufel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-10-25T01:11:58Z","title":"The Geodesic $2$-center Problem in a Simple Polygon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09035","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":"sha256:573b9d803e426bc3d1acd792cef9ddc962873eed865114e581c0ddf2f34e6804","target":"record","created_at":"2026-05-18T00:32:00Z","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":"a1eac7330c5afa7d4dbc114b8494f2485694b6d5eb3486284b4bbed64e1070d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-10-25T01:11:58Z","title_canon_sha256":"961d1c221a86d740a11438f3f78b095ebad40731732d33cf73b8fbde96d5b3ab"},"schema_version":"1.0","source":{"id":"1710.09035","kind":"arxiv","version":1}},"canonical_sha256":"d8b5d8b66442df101bbcb915694dbd965d254d5621a20873ffd16b22d94ab7f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b5d8b66442df101bbcb915694dbd965d254d5621a20873ffd16b22d94ab7f7","first_computed_at":"2026-05-18T00:32:00.524059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:00.524059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pe3yRAIOF60ZvO5Da8WXgA/6Ui3jcQMrzPFELNYqaygUYCcAe29iZ/swzNd7eSrGNGGI4fKICSUfed+9+7pYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:00.524705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:573b9d803e426bc3d1acd792cef9ddc962873eed865114e581c0ddf2f34e6804","sha256:3b2791a8fe4099f733b5af9dab6d63e38736e808b42faafd5d7fff73b9da13d9"],"state_sha256":"62d317d00328afeda3d465d848db6210522bff641598fe592b943a6d2a8a4698"}