{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I7GKSILDUMRBCHJAWPHAJB2HMC","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":"ad5ff373a78ffe7050ec780fb205892020dc9f827fd4dcf4b2c7d5a78edff8c7","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-04T22:24:14Z","title_canon_sha256":"ca6f46b9c634a2db1f59360e4da4b81831aa3268952502e532b59cda3cf44e24"},"schema_version":"1.0","source":{"id":"1204.1086","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1086","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1086v2","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1086","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"I7GKSILDUMRB","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I7GKSILDUMRBCHJA","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I7GKSILD","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:fd80138ff3eb9813d2d12f99325d49302e03615e7a7609b5a4859a74866aef37","target":"graph","created_at":"2026-05-18T03:25:25Z","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":"One of the longest-standing open problems in computational geometry is to bound the lower envelope of $n$ univariate functions, each pair of which crosses at most $s$ times, for some fixed $s$. This problem is known to be equivalent to bounding the length of an order-$s$ Davenport-Schinzel sequence, namely a sequence over an $n$-letter alphabet that avoids alternating subsequences of the form $a \\cdots b \\cdots a \\cdots b \\cdots$ with length $s+2$. These sequences were introduced by Davenport and Schinzel in 1965 to model a certain problem in differential equations and have since been applied ","authors_text":"Seth Pettie","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-04T22:24:14Z","title":"Sharp Bounds on Davenport-Schinzel Sequences of Every Order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1086","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":"sha256:0df0d1459f733ccd54d400ad1ac2422363e91e3dc91f52d1387211d41070e238","target":"record","created_at":"2026-05-18T03:25:25Z","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":"ad5ff373a78ffe7050ec780fb205892020dc9f827fd4dcf4b2c7d5a78edff8c7","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-04T22:24:14Z","title_canon_sha256":"ca6f46b9c634a2db1f59360e4da4b81831aa3268952502e532b59cda3cf44e24"},"schema_version":"1.0","source":{"id":"1204.1086","kind":"arxiv","version":2}},"canonical_sha256":"47cca92163a322111d20b3ce04874760b0cc8e4fada18d6404703af0c76ef885","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47cca92163a322111d20b3ce04874760b0cc8e4fada18d6404703af0c76ef885","first_computed_at":"2026-05-18T03:25:25.812578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:25.812578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0NFjJVfiTrtug5UDRRptNfO0Sis/y+Evcybc2dF67eV6Z337rV7duUUosFpHUOj24rjyetxw2xmxYLzJKqvoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:25.813216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1086","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0df0d1459f733ccd54d400ad1ac2422363e91e3dc91f52d1387211d41070e238","sha256:fd80138ff3eb9813d2d12f99325d49302e03615e7a7609b5a4859a74866aef37"],"state_sha256":"3a4a6de267c3052f1cb6cce0a92c67c2a209241e61e1db0210057dcca7e79300"}