{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6KOAQ4XIS7PBDD3MFBDYQYRI3V","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":"123eb1d8770d3982b42f213cfc3aa605a5201a4e73214fd4c5e7c3834322c3f7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-26T10:20:20Z","title_canon_sha256":"438aa2708ef7f6cf87eb2f40b804c22b5143981c4b18edb91406560d5ea3a215"},"schema_version":"1.0","source":{"id":"1902.09841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09841","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09841v1","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09841","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"6KOAQ4XIS7PB","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6KOAQ4XIS7PBDD3M","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6KOAQ4XI","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:d4c58d5c3c9a7a268bd3e040dc55717cca82fcb2a436c145ff78c370bf3545a1","target":"graph","created_at":"2026-05-17T23:52:35Z","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 use the concept of production matrices to show that there exist sets of $n$ points in the plane that admit $\\Omega(42.11^n)$ crossing-free geometric graphs. This improves the previously best known bound of $\\Omega(41.18^n)$ by Aichholzer et al. (2007).","authors_text":"Alexander Pilz, Clemens Huemer, Rodrigo I. Silveira","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-26T10:20:20Z","title":"A new lower bound on the maximum number of plane graphs using production matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09841","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":"sha256:62633af96c57496110fa428aaf3b749edc59f7893d4c0597a7780f46ef7f035d","target":"record","created_at":"2026-05-17T23:52:35Z","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":"123eb1d8770d3982b42f213cfc3aa605a5201a4e73214fd4c5e7c3834322c3f7","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-02-26T10:20:20Z","title_canon_sha256":"438aa2708ef7f6cf87eb2f40b804c22b5143981c4b18edb91406560d5ea3a215"},"schema_version":"1.0","source":{"id":"1902.09841","kind":"arxiv","version":1}},"canonical_sha256":"f29c0872e897de118f6c2847886228dd70cc7ab59097ae483551ab62fbf146d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f29c0872e897de118f6c2847886228dd70cc7ab59097ae483551ab62fbf146d8","first_computed_at":"2026-05-17T23:52:35.207116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:35.207116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Vor4F+9fKI0D7BGDe8zkCtGTt//hhn4goJ1kyysdFuEaUf6G+G23q6Hi9C8NNx9gtwAm071W5oNuZGcsXv0AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:35.207597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62633af96c57496110fa428aaf3b749edc59f7893d4c0597a7780f46ef7f035d","sha256:d4c58d5c3c9a7a268bd3e040dc55717cca82fcb2a436c145ff78c370bf3545a1"],"state_sha256":"b45760436a7e01797213b8778dc291abaf3d10c49284923b38f7716b7e2072c4"}