{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3O4MERANCLF7Z4QD7QK6D54OZT","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":"32edb06ffdfabd431cbe9e652864235fc8b6171bf4467099f718d79df9478f89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-17T23:29:49Z","title_canon_sha256":"af553f3f90f93b99e229aa5f0414efef9921fbccbdd075693af526821a0fb44f"},"schema_version":"1.0","source":{"id":"1012.4034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4034","created_at":"2026-05-18T04:32:56Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4034v1","created_at":"2026-05-18T04:32:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4034","created_at":"2026-05-18T04:32:56Z"},{"alias_kind":"pith_short_12","alias_value":"3O4MERANCLF7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3O4MERANCLF7Z4QD","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3O4MERAN","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:afb18315788f9bdcda4b7ee90963088ab46b4d255127ae90b2aed37e78cf5668","target":"graph","created_at":"2026-05-18T04:32:56Z","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":"Let $[x]$ be the greatest integer not exceeding $x$. In the paper we introduce the sequence $\\{U_n\\}$ given by $U_0=1$ and $U_n=-2\\sum_{k=1}^{[n/2]}\\binom n{2k}U_{n-2k}\\quad(n\\ge 1)$, and establish many recursive formulas and congruences involving $\\{U_n\\}$.","authors_text":"Zhi-Hong Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-17T23:29:49Z","title":"Identities and congruences for a new sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4034","kind":"arxiv","version":1},"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:c8084698a0235f58c0ccd34d2659dd66582b2190971251931ac441bb55de5fa2","target":"record","created_at":"2026-05-18T04:32:56Z","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":"32edb06ffdfabd431cbe9e652864235fc8b6171bf4467099f718d79df9478f89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-17T23:29:49Z","title_canon_sha256":"af553f3f90f93b99e229aa5f0414efef9921fbccbdd075693af526821a0fb44f"},"schema_version":"1.0","source":{"id":"1012.4034","kind":"arxiv","version":1}},"canonical_sha256":"dbb8c2440d12cbfcf203fc15e1f78eccd611740f249c09cf4044e3844f9ffda0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbb8c2440d12cbfcf203fc15e1f78eccd611740f249c09cf4044e3844f9ffda0","first_computed_at":"2026-05-18T04:32:56.431850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:56.431850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EuzXJZQhp+lg9t95QDvOkTvALd7JI42tdb4ce4gadEPVIv7iHr8LZ/uBHPhjTGMomk6AZejiYRmw9MMj6FpiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:56.432529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8084698a0235f58c0ccd34d2659dd66582b2190971251931ac441bb55de5fa2","sha256:afb18315788f9bdcda4b7ee90963088ab46b4d255127ae90b2aed37e78cf5668"],"state_sha256":"68da0ae9865aec04680b0f40cbab27d224198e7f9a5cb707f5ee30f6edd0b7fb"}