{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QARZK3TCOEF3GA26SDT5UK3UB5","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":"e53e2818cdaca0bf1cbf05a712640eff2dacf5c674fcd86fc046df680c1a8572","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-10T22:39:07Z","title_canon_sha256":"0bb90e1ff23d0ed6cd7291b1c3f1c88b41183a3dc6f1c2669a6775c0f93996ba"},"schema_version":"1.0","source":{"id":"1809.03619","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03619","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03619v2","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03619","created_at":"2026-05-17T23:58:52Z"},{"alias_kind":"pith_short_12","alias_value":"QARZK3TCOEF3","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QARZK3TCOEF3GA26","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QARZK3TC","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:33c1325f7c2ae25bb3631411d9a25ac49a8abfc573b6ad8903b6f525db40ed9c","target":"graph","created_at":"2026-05-17T23:58:52Z","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":"Arrangements of lines and pseudolines are fundamental objects in discrete and computational geometry. They also appear in other areas of computer science, such as the study of sorting networks. Let $B_n$ be the number of nonisomorphic arrangements of $n$ pseudolines and let $b_n=\\log_2{B_n}$. The problem of estimating $B_n$ was posed by Knuth in 1992. Knuth conjectured that $b_n \\leq {n \\choose 2} + o(n^2)$ and also derived the first upper and lower bounds: $b_n \\leq 0.7924 (n^2 +n)$ and $b_n \\geq n^2/6 -O(n)$. The upper bound underwent several improvements, $b_n \\leq 0.6988\\, n^2$ (Felsner, 1","authors_text":"Adrian Dumitrescu, Ritankar Mandal","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-10T22:39:07Z","title":"New Lower Bounds for the Number of Pseudoline Arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03619","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:c5b5a3be5464fcc03bea2887ae020efee3863c6df700599617469ec6f93391c0","target":"record","created_at":"2026-05-17T23:58:52Z","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":"e53e2818cdaca0bf1cbf05a712640eff2dacf5c674fcd86fc046df680c1a8572","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-10T22:39:07Z","title_canon_sha256":"0bb90e1ff23d0ed6cd7291b1c3f1c88b41183a3dc6f1c2669a6775c0f93996ba"},"schema_version":"1.0","source":{"id":"1809.03619","kind":"arxiv","version":2}},"canonical_sha256":"8023956e62710bb3035e90e7da2b740f538ca75214fa721e4e139ac1c19a669f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8023956e62710bb3035e90e7da2b740f538ca75214fa721e4e139ac1c19a669f","first_computed_at":"2026-05-17T23:58:52.554350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:52.554350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g55CALunKkOZ6cZYjmFCtdRO7Lw5B3rzcgxUkQ/GxSMg7GgMLu/rEL4gm2UeOUOWn12580AptFiIsHtKqeXxBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:52.554945Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03619","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5b5a3be5464fcc03bea2887ae020efee3863c6df700599617469ec6f93391c0","sha256:33c1325f7c2ae25bb3631411d9a25ac49a8abfc573b6ad8903b6f525db40ed9c"],"state_sha256":"3f04f57af885d19299345a3ff676782cd7576c8cf6b1c4eeb1cc25b7bf7352ed"}