{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JZOHLLCUACMOKUGW3VJVBVAEY6","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":"d9befb7b7b4acda1a6deaf8ae8f0cbb8509f86dfece10c4ba79692731c09bb1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-11T13:52:51Z","title_canon_sha256":"9ba75f6410da3b26874785ef2b590dc65e33c8a8f51755797ecabc1586e3bc5a"},"schema_version":"1.0","source":{"id":"1611.03705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03705","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03705v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03705","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"JZOHLLCUACMO","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JZOHLLCUACMOKUGW","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JZOHLLCU","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:945f96f75f82bc846bb2ff96133429b6aba0dab0fbf9f2fb253ae1ada11d4f5e","target":"graph","created_at":"2026-05-18T00:54:04Z","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 establish the asymptotic density of the Catalan numbers modulo 3 and modulo powers of 2.","authors_text":"Rob Burns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-11T13:52:51Z","title":"Asymptotic density of Catalan numbers modulo 3 and powers of 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03705","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:d7843873f0986985cd6ec0805059a6bd1154b3134d62617e35a40be2fbe72b51","target":"record","created_at":"2026-05-18T00:54:04Z","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":"d9befb7b7b4acda1a6deaf8ae8f0cbb8509f86dfece10c4ba79692731c09bb1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-11T13:52:51Z","title_canon_sha256":"9ba75f6410da3b26874785ef2b590dc65e33c8a8f51755797ecabc1586e3bc5a"},"schema_version":"1.0","source":{"id":"1611.03705","kind":"arxiv","version":2}},"canonical_sha256":"4e5c75ac540098e550d6dd5350d404c7989de5eecd96fb771516b820ef68fbb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e5c75ac540098e550d6dd5350d404c7989de5eecd96fb771516b820ef68fbb5","first_computed_at":"2026-05-18T00:54:04.599056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:04.599056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86MaKJGECdqKY4GhCAbvhaWFzZdAd4mGYmP4yfvGjUfR0qH3Cw8CiFEhS8IUtNn4IswHtfPSCwbg7HtI/Bd9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:04.599565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7843873f0986985cd6ec0805059a6bd1154b3134d62617e35a40be2fbe72b51","sha256:945f96f75f82bc846bb2ff96133429b6aba0dab0fbf9f2fb253ae1ada11d4f5e"],"state_sha256":"6fb7bd9ac48010dfd7f0c815fc258842508a3fda9206960ab5d2abaf29422142"}