{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GJQSZ5IDA4KYXIY4PYAGG25HUZ","short_pith_number":"pith:GJQSZ5ID","canonical_record":{"source":{"id":"1603.05748","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-18T01:55:54Z","cross_cats_sorted":[],"title_canon_sha256":"3e1ff211a9e797b4690058b6b88c575095a8ef468b4f1bb2ff4f5c4d2637d2d4","abstract_canon_sha256":"260ecfcd0ad0b5adb385366ede383653dba0e24f50b272e7b02760d3b9fa35ef"},"schema_version":"1.0"},"canonical_sha256":"32612cf50307158ba31c7e00636ba7a668e72d1f35844685cb516df93150946c","source":{"kind":"arxiv","id":"1603.05748","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GJQSZ5IDA4KYXIY4PYAGG25HUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05748","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-18T01:55:54Z","cross_cats_sorted":[],"title_canon_sha256":"3e1ff211a9e797b4690058b6b88c575095a8ef468b4f1bb2ff4f5c4d2637d2d4","abstract_canon_sha256":"260ecfcd0ad0b5adb385366ede383653dba0e24f50b272e7b02760d3b9fa35ef"},"schema_version":"1.0"},"canonical_sha256":"32612cf50307158ba31c7e00636ba7a668e72d1f35844685cb516df93150946c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:29.750530Z","signature_b64":"QZXR1091nGDU6cxdheeDEz+eI+xkpYrIhR15X2t172HAnHljlDKaVWwLMn9Lyq9+J3RX8lpOEhbiidpaTdQQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32612cf50307158ba31c7e00636ba7a668e72d1f35844685cb516df93150946c","last_reissued_at":"2026-05-18T01:12:29.750146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:29.750146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05748","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uh6omAorVRtMEmGOnd4ABDhkoUojuI4CZoBuzi7Z1JFRc1vmJNscWuEsvuWXpBqvRx1WNMopgH7jO7T0WLZRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:22:05.482760Z"},"content_sha256":"f9271eb4362144979a2ff51f32f917e2da79a8daedbc5c2a4a47a471b0533c5c","schema_version":"1.0","event_id":"sha256:f9271eb4362144979a2ff51f32f917e2da79a8daedbc5c2a4a47a471b0533c5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GJQSZ5IDA4KYXIY4PYAGG25HUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tuenter polynomials and a Catalan triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrei K. Svinin","submitted_at":"2016-03-18T01:55:54Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05748","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SW+3FuvgiwNUTmfkZ308/Qvu/w0GVXoPXD+pEuKNHRgp8dAlJeyWCLpV2PomqC2klV8GX9L6ovuKTWk3t5ZyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:22:05.483101Z"},"content_sha256":"3999da37182dfc862f21edaa3b195ab810a3ebc5ae44fcc10c27bafd943d8cd0","schema_version":"1.0","event_id":"sha256:3999da37182dfc862f21edaa3b195ab810a3ebc5ae44fcc10c27bafd943d8cd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ/bundle.json","state_url":"https://pith.science/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T18:22:05Z","links":{"resolver":"https://pith.science/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ","bundle":"https://pith.science/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ/bundle.json","state":"https://pith.science/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJQSZ5IDA4KYXIY4PYAGG25HUZ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jb/oxp4rRdc9QDZ5uE8dJy+dzf2AXOthWYe8m2cPEeb5s21TkafD+JZBI7IKY8G/3aiP9ED564cy5PJZm9EDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T18:22:05.485003Z","bundle_sha256":"c9114c41e0f8d462e0f4c50a3939cac38b066650e3a43f488efb6c4d65c4cf7a"}}