{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GJQSZ5IDA4KYXIY4PYAGG25HUZ","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":"260ecfcd0ad0b5adb385366ede383653dba0e24f50b272e7b02760d3b9fa35ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-18T01:55:54Z","title_canon_sha256":"3e1ff211a9e797b4690058b6b88c575095a8ef468b4f1bb2ff4f5c4d2637d2d4"},"schema_version":"1.0","source":{"id":"1603.05748","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05748","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05748v2","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05748","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"pith_short_12","alias_value":"GJQSZ5IDA4KY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GJQSZ5IDA4KYXIY4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GJQSZ5ID","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3999da37182dfc862f21edaa3b195ab810a3ebc5ae44fcc10c27bafd943d8cd0","target":"graph","created_at":"2026-05-18T01:12:29Z","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 consider Tuenter polynomials as linear combinations of descending factorials and show that coefficients of these linear combinations are expressed via a Catalan triangle of numbers. We also describe a triangle of coefficients in terms of some polynomials.","authors_text":"Andrei K. Svinin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-18T01:55:54Z","title":"Tuenter polynomials and a Catalan triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05748","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:f9271eb4362144979a2ff51f32f917e2da79a8daedbc5c2a4a47a471b0533c5c","target":"record","created_at":"2026-05-18T01:12:29Z","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":"260ecfcd0ad0b5adb385366ede383653dba0e24f50b272e7b02760d3b9fa35ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-18T01:55:54Z","title_canon_sha256":"3e1ff211a9e797b4690058b6b88c575095a8ef468b4f1bb2ff4f5c4d2637d2d4"},"schema_version":"1.0","source":{"id":"1603.05748","kind":"arxiv","version":2}},"canonical_sha256":"32612cf50307158ba31c7e00636ba7a668e72d1f35844685cb516df93150946c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32612cf50307158ba31c7e00636ba7a668e72d1f35844685cb516df93150946c","first_computed_at":"2026-05-18T01:12:29.750146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:29.750146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZXR1091nGDU6cxdheeDEz+eI+xkpYrIhR15X2t172HAnHljlDKaVWwLMn9Lyq9+J3RX8lpOEhbiidpaTdQQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:29.750530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05748","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9271eb4362144979a2ff51f32f917e2da79a8daedbc5c2a4a47a471b0533c5c","sha256:3999da37182dfc862f21edaa3b195ab810a3ebc5ae44fcc10c27bafd943d8cd0"],"state_sha256":"3ae042f08ff640ddbd7303220d5e8adaca23b70ebe607c1c09198a4ca53c6fb4"}