{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:77EQQBFJCBQINXGWEPDCRSMKLD","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":"0781515ee1a70313a4402fd6c49f875da768e66a4a2da16b075d30bbf726c8bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","title_canon_sha256":"28f1e2967cb1f023ddc9fa3684681aea88f01c3d2d4136c6fea8c56e8a2f82e0"},"schema_version":"1.0","source":{"id":"1611.04910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04910","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04910v2","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04910","created_at":"2026-05-18T00:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"77EQQBFJCBQI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"77EQQBFJCBQINXGW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"77EQQBFJ","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:a095e5aa01a58e6eb503bb7934bc58f6053ac838ef7a91ba4beea2a4efd61cdc","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 Motzkin numbers modulo small primes.","authors_text":"Rob Burns","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","title":"Asymptotic density of Motzkin numbers modulo small primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04910","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:e1a9db6a3c945fc27f39c8ed755795528fea019d667c88b71e5917caeffaf4e9","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":"0781515ee1a70313a4402fd6c49f875da768e66a4a2da16b075d30bbf726c8bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-15T16:06:40Z","title_canon_sha256":"28f1e2967cb1f023ddc9fa3684681aea88f01c3d2d4136c6fea8c56e8a2f82e0"},"schema_version":"1.0","source":{"id":"1611.04910","kind":"arxiv","version":2}},"canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc90804a9106086dcd623c628c98a58d15310733655c7f4f29213b9378ff866","first_computed_at":"2026-05-18T00:54:04.591833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:04.591833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LdgyRKG0r6eefd6eZCVD5iHhT/CZo2FjAZdrQ80oNWMt9nI2no68G6OnyWoEq9BLYCJZlYOM2iDtCm56ARlZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:04.592311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1a9db6a3c945fc27f39c8ed755795528fea019d667c88b71e5917caeffaf4e9","sha256:a095e5aa01a58e6eb503bb7934bc58f6053ac838ef7a91ba4beea2a4efd61cdc"],"state_sha256":"95c0e50b7d74a34308dd4df20f33c51fe7bfbcd24d1683dba0d2f6a9ab556cb9"}