{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z3XMCORC5UNSMT7UFAAIMNSMBR","short_pith_number":"pith:Z3XMCORC","schema_version":"1.0","canonical_sha256":"ceeec13a22ed1b264ff4280086364c0c7b1fd5eb75eb99c6953ec7955fa8d171","source":{"kind":"arxiv","id":"1401.5709","version":1},"attestation_state":"computed","paper":{"title":"Three Generalizations of Davenport-Schinzel Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Seth Pettie","submitted_at":"2014-01-22T15:53:21Z","abstract_excerpt":"We present new, and mostly sharp, bounds on the maximum length of certain generalizations of Davenport-Schinzel sequences. Among the results are sharp bounds on order-$s$ {\\em double DS} sequences, for all $s$, sharp bounds on sequences avoiding {\\em catenated permutations} (aka formation free sequences), and new lower bounds on sequences avoiding {\\em zig-zagging} patterns."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.5709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-22T15:53:21Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c2c073dbbf1f0742300411eac89a1a3fe004784eceaee9d6cce9b26173d6d8c6","abstract_canon_sha256":"f2ef54725659e0365f2011c6456b545f476347bfe1fd566ef4c6cb50f610c88f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:24.880181Z","signature_b64":"H4/xUSYix6SmCvZfiNzGozMPkBVSfySaVQWA9KB7Zbhv7Yif+vvn7wIEeBqrbv1olcCr3xWOGC2fbOVJEICSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceeec13a22ed1b264ff4280086364c0c7b1fd5eb75eb99c6953ec7955fa8d171","last_reissued_at":"2026-05-18T03:01:24.879525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:24.879525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Three Generalizations of Davenport-Schinzel Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Seth Pettie","submitted_at":"2014-01-22T15:53:21Z","abstract_excerpt":"We present new, and mostly sharp, bounds on the maximum length of certain generalizations of Davenport-Schinzel sequences. Among the results are sharp bounds on order-$s$ {\\em double DS} sequences, for all $s$, sharp bounds on sequences avoiding {\\em catenated permutations} (aka formation free sequences), and new lower bounds on sequences avoiding {\\em zig-zagging} patterns."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5709","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.5709","created_at":"2026-05-18T03:01:24.879605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.5709v1","created_at":"2026-05-18T03:01:24.879605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5709","created_at":"2026-05-18T03:01:24.879605+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z3XMCORC5UNS","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z3XMCORC5UNSMT7U","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z3XMCORC","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR","json":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR.json","graph_json":"https://pith.science/api/pith-number/Z3XMCORC5UNSMT7UFAAIMNSMBR/graph.json","events_json":"https://pith.science/api/pith-number/Z3XMCORC5UNSMT7UFAAIMNSMBR/events.json","paper":"https://pith.science/paper/Z3XMCORC"},"agent_actions":{"view_html":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR","download_json":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR.json","view_paper":"https://pith.science/paper/Z3XMCORC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.5709&json=true","fetch_graph":"https://pith.science/api/pith-number/Z3XMCORC5UNSMT7UFAAIMNSMBR/graph.json","fetch_events":"https://pith.science/api/pith-number/Z3XMCORC5UNSMT7UFAAIMNSMBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR/action/storage_attestation","attest_author":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR/action/author_attestation","sign_citation":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR/action/citation_signature","submit_replication":"https://pith.science/pith/Z3XMCORC5UNSMT7UFAAIMNSMBR/action/replication_record"}},"created_at":"2026-05-18T03:01:24.879605+00:00","updated_at":"2026-05-18T03:01:24.879605+00:00"}