{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:SZI3ZJEVH52Z67PLEMMZCCYC6W","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":"70a5c82688d59b36e1f34d220558aa754e38c10d4e7ce17df20e27183e3e44a6","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2008-06-02T18:01:35Z","title_canon_sha256":"a65aff66ff7c0d471e19eaafcd4fe2b95406e2016461e9039b71a5559e0d25c2"},"schema_version":"1.0","source":{"id":"0806.0253","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0806.0253","created_at":"2026-05-18T04:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"0806.0253v5","created_at":"2026-05-18T04:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.0253","created_at":"2026-05-18T04:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"SZI3ZJEVH52Z","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SZI3ZJEVH52Z67PL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SZI3ZJEV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:346bc2295baf4ae95a9d9d14af7f24cbe364dbd0eac94a2c6c7f7e92788c6ed5","target":"graph","created_at":"2026-05-18T04:08:33Z","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 consider straight line drawings of a planar graph $G$ with possible edge crossings. The \\emph{untangling problem} is to eliminate all edge crossings by moving as few vertices as possible to new positions. Let $fix(G)$ denote the maximum number of vertices that can be left fixed in the worst case. In the \\emph{allocation problem}, we are given a planar graph $G$ on $n$ vertices together with an $n$-point set $X$ in the plane and have to draw $G$ without edge crossings so that as many vertices as possible are located in $X$. Let $fit(G)$ denote the maximum number of points fitting this purpos","authors_text":"Alexander Ravsky, Oleg Verbitsky","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2008-06-02T18:01:35Z","title":"On collinear sets in straight line drawings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0253","kind":"arxiv","version":5},"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":"sha256:52392323e0d49f459acc3af3bbecd5a44ec08c51014e115040e762beff16a4ba","target":"record","created_at":"2026-05-18T04:08:33Z","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":"70a5c82688d59b36e1f34d220558aa754e38c10d4e7ce17df20e27183e3e44a6","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2008-06-02T18:01:35Z","title_canon_sha256":"a65aff66ff7c0d471e19eaafcd4fe2b95406e2016461e9039b71a5559e0d25c2"},"schema_version":"1.0","source":{"id":"0806.0253","kind":"arxiv","version":5}},"canonical_sha256":"9651bca4953f759f7deb2319910b02f59b94c06c945618631ede597cb32b88ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9651bca4953f759f7deb2319910b02f59b94c06c945618631ede597cb32b88ea","first_computed_at":"2026-05-18T04:08:33.759760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:33.759760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VB6m1/nr3m3YWRxdV16s2O0l/guUlUpEQTkjxrDXY1Su8mfjUBDzAUp/HWg8qPsXhJ7KkhnjANNbhbJGfNazAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:33.760447Z","signed_message":"canonical_sha256_bytes"},"source_id":"0806.0253","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52392323e0d49f459acc3af3bbecd5a44ec08c51014e115040e762beff16a4ba","sha256:346bc2295baf4ae95a9d9d14af7f24cbe364dbd0eac94a2c6c7f7e92788c6ed5"],"state_sha256":"4e2bc16f41dec812a16f72df5d5fbe91a12e66dca4ab72c0dd4fad7c55af1c52"}