{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CW6CKQFCYYUVKI7TH2VZTLUYPK","short_pith_number":"pith:CW6CKQFC","schema_version":"1.0","canonical_sha256":"15bc2540a2c6295523f33eab99ae987a9aa582c90cfe3ec98a305050a50a145e","source":{"kind":"arxiv","id":"1706.07064","version":2},"attestation_state":"computed","paper":{"title":"A New Quantity Counted by OEIS Sequence A006012","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yonah Biers-Ariel","submitted_at":"2017-06-21T18:00:38Z","abstract_excerpt":"We prove an existing conjecture that the sequence defined recursively by $a_1=1, a_2=2, a_n=4a_{n-1}-2a_{n-2}$ counts the number of length-$n$ permutations avoiding the four generalized permutation patterns 1-32-4, 1-42-3, 2-31-4, and 2-41-3."},"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":"1706.07064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-21T18:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"a2dc62aece1cee43b1e63534e566ceb62f6225914fd62e945ee74695def353e2","abstract_canon_sha256":"8f5b67b9edf65a715a5fac98879170792e659cc71a97b2c77d21f63ca07c49d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:31.858624Z","signature_b64":"roOQa8eNbs8ARrm6FddYzJCvd7l1PTrhQR5vvMfLvLH1xtWp5aj0/HLLRe9jAlJJfZlwaEFZrQxLnWJg4csSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15bc2540a2c6295523f33eab99ae987a9aa582c90cfe3ec98a305050a50a145e","last_reissued_at":"2026-05-18T00:41:31.858186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:31.858186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Quantity Counted by OEIS Sequence A006012","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yonah Biers-Ariel","submitted_at":"2017-06-21T18:00:38Z","abstract_excerpt":"We prove an existing conjecture that the sequence defined recursively by $a_1=1, a_2=2, a_n=4a_{n-1}-2a_{n-2}$ counts the number of length-$n$ permutations avoiding the four generalized permutation patterns 1-32-4, 1-42-3, 2-31-4, and 2-41-3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07064","kind":"arxiv","version":2},"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":"1706.07064","created_at":"2026-05-18T00:41:31.858249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07064v2","created_at":"2026-05-18T00:41:31.858249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07064","created_at":"2026-05-18T00:41:31.858249+00:00"},{"alias_kind":"pith_short_12","alias_value":"CW6CKQFCYYUV","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CW6CKQFCYYUVKI7T","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CW6CKQFC","created_at":"2026-05-18T12:31:10.602751+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/CW6CKQFCYYUVKI7TH2VZTLUYPK","json":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK.json","graph_json":"https://pith.science/api/pith-number/CW6CKQFCYYUVKI7TH2VZTLUYPK/graph.json","events_json":"https://pith.science/api/pith-number/CW6CKQFCYYUVKI7TH2VZTLUYPK/events.json","paper":"https://pith.science/paper/CW6CKQFC"},"agent_actions":{"view_html":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK","download_json":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK.json","view_paper":"https://pith.science/paper/CW6CKQFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07064&json=true","fetch_graph":"https://pith.science/api/pith-number/CW6CKQFCYYUVKI7TH2VZTLUYPK/graph.json","fetch_events":"https://pith.science/api/pith-number/CW6CKQFCYYUVKI7TH2VZTLUYPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK/action/storage_attestation","attest_author":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK/action/author_attestation","sign_citation":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK/action/citation_signature","submit_replication":"https://pith.science/pith/CW6CKQFCYYUVKI7TH2VZTLUYPK/action/replication_record"}},"created_at":"2026-05-18T00:41:31.858249+00:00","updated_at":"2026-05-18T00:41:31.858249+00:00"}