{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EGAIBPXPHRBQYCZKPTNNK5SH4F","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":"bc1e06bddcc470aaf9365502592960ac3ea2bf62268b7168a7e7abea6beb132b","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-06T19:11:36Z","title_canon_sha256":"b5e006077839070807ff57655ffc4b667faa9e325a87c8937754690cdbc2414e"},"schema_version":"1.0","source":{"id":"1803.02385","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02385","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02385v2","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02385","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"EGAIBPXPHRBQ","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EGAIBPXPHRBQYCZK","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EGAIBPXP","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:a2965ba532c2bfcfda43a75dc23acc5117b1b7bc71e47d4d303993f9a7db56ba","target":"graph","created_at":"2026-05-17T23:52:53Z","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":"Let $P$ be a set of $n$ points in the plane in general position. We show that at least $\\lfloor n/3\\rfloor$ plane spanning trees can be packed into the complete geometric graph on $P$. This improves the previous best known lower bound $\\Omega\\left(\\sqrt{n}\\right)$. Towards our proof of this lower bound we show that the center of a set of points, in the $d$-dimensional space in general position, is of dimension either $0$ or $d$.","authors_text":"Ahmad Biniaz, Alfredo Garc\\'ia","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-06T19:11:36Z","title":"Packing Plane Spanning Trees into a Point Set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02385","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":"sha256:44cbfa599b79c2675af6cddb4f658e47dd1c9b6fa3477c7f061676226e97c68c","target":"record","created_at":"2026-05-17T23:52:53Z","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":"bc1e06bddcc470aaf9365502592960ac3ea2bf62268b7168a7e7abea6beb132b","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-03-06T19:11:36Z","title_canon_sha256":"b5e006077839070807ff57655ffc4b667faa9e325a87c8937754690cdbc2414e"},"schema_version":"1.0","source":{"id":"1803.02385","kind":"arxiv","version":2}},"canonical_sha256":"218080beef3c430c0b2a7cdad57647e15acf976b92006b2c03695634ae1fb851","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"218080beef3c430c0b2a7cdad57647e15acf976b92006b2c03695634ae1fb851","first_computed_at":"2026-05-17T23:52:53.336105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:53.336105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WP0wWXrwPZ3dSezfb1oBDmcNAWH+bzvhIoK40Ll7yvQDqH/L7l6FFoSIW2sojJuGxMVeRlaUaa4Lgf9xf0/mBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:53.336974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02385","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44cbfa599b79c2675af6cddb4f658e47dd1c9b6fa3477c7f061676226e97c68c","sha256:a2965ba532c2bfcfda43a75dc23acc5117b1b7bc71e47d4d303993f9a7db56ba"],"state_sha256":"ae21b2c582c60928eaa6aa4789ff931961f62ae6050549f7579f940642daf547"}