{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OL5DLKZ3VPHPXMYB6R2ANKZGL4","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":"f8b6c63f16d211f4e4dd536d9fbc28802f1d9d1f629afce5ae3a22da42e93de6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T22:51:31Z","title_canon_sha256":"76c742b0cc20155bd02049816d438a541451b9305e0f28c6f5c735fa11912651"},"schema_version":"1.0","source":{"id":"1008.2983","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2983","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2983v4","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2983","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"OL5DLKZ3VPHP","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OL5DLKZ3VPHPXMYB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OL5DLKZ3","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:30f564a34909c9d13dd9c7250575233347ef444b1e7f3e0772281f5524cdcf8b","target":"graph","created_at":"2026-05-18T03:37:42Z","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 prove results concerning the joint limiting distribution of the renewal time of denominators and consecutive digits of random irrational numbers in the case of continued fractions with even partial quotients, with odd partial quotients, and for Nakada's \\alpha-expansions.","authors_text":"Florin P. Boca, Joseph Vandehey","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T22:51:31Z","title":"On certain statistical properties of continued fractions with even and with odd partial quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2983","kind":"arxiv","version":4},"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:c4af0414531e70255bd1789c4113244897f60df7da9adeaaacee6ace4913d387","target":"record","created_at":"2026-05-18T03:37:42Z","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":"f8b6c63f16d211f4e4dd536d9fbc28802f1d9d1f629afce5ae3a22da42e93de6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-17T22:51:31Z","title_canon_sha256":"76c742b0cc20155bd02049816d438a541451b9305e0f28c6f5c735fa11912651"},"schema_version":"1.0","source":{"id":"1008.2983","kind":"arxiv","version":4}},"canonical_sha256":"72fa35ab3babcefbb301f47406ab265f2d08525f4a6c1f722b1d9e9964d3bc69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72fa35ab3babcefbb301f47406ab265f2d08525f4a6c1f722b1d9e9964d3bc69","first_computed_at":"2026-05-18T03:37:42.025443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:42.025443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uVmW7HDsDDBxNAa5R4TWgQOUaWDM2hASVWoMcRD7na0fBeupHxY3nDNZYgB4vzhggusXhhDFT6hLUE8DwwY+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:42.026281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2983","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4af0414531e70255bd1789c4113244897f60df7da9adeaaacee6ace4913d387","sha256:30f564a34909c9d13dd9c7250575233347ef444b1e7f3e0772281f5524cdcf8b"],"state_sha256":"47aa9e1a1601cc842ec0cb2e82a1e3831e7258786407d1f04af2b86b0f6ef772"}