{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FDW3PWNOL6366CDRAJPOTFDST4","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":"1ce918a054626dffcb264a23710b50c77737835b71e474d67f56a19843896173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-28T21:25:14Z","title_canon_sha256":"95af47e516046c32acc7904ff2db0999fc02499e32abb0449a18fd080ec9ccb7"},"schema_version":"1.0","source":{"id":"1812.11221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11221","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11221v1","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11221","created_at":"2026-05-17T23:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"FDW3PWNOL636","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FDW3PWNOL6366CDR","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FDW3PWNO","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:9b56bc96f0b6b8739db6255444354fc25fc545f650595dd03ad8f4528ca54b3a","target":"graph","created_at":"2026-05-17T23:57:14Z","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":"In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a wider class of $q$-continued fractions, a class which includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fractions. We show, for each $q$-continued fraction, $G(q)$, in this class, that there is an uncountable set of points, $Y_{G}$, on the unit circle such that if $y \\in Y_{G}$ then $G(y)$ does not converge to a finite va","authors_text":"Douglas Bowman, James Mc Laughlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-28T21:25:14Z","title":"The Convergence Behavior of $q$-Continued Fractions on the Unit Circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11221","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":"sha256:76117318d882301cce5712662022fde95fcd8a2336c979f369e4a8dac0aa5233","target":"record","created_at":"2026-05-17T23:57:14Z","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":"1ce918a054626dffcb264a23710b50c77737835b71e474d67f56a19843896173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-28T21:25:14Z","title_canon_sha256":"95af47e516046c32acc7904ff2db0999fc02499e32abb0449a18fd080ec9ccb7"},"schema_version":"1.0","source":{"id":"1812.11221","kind":"arxiv","version":1}},"canonical_sha256":"28edb7d9ae5fb7ef0871025ee994729f0e036a1119575dd273d656839847c46e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28edb7d9ae5fb7ef0871025ee994729f0e036a1119575dd273d656839847c46e","first_computed_at":"2026-05-17T23:57:14.367224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:14.367224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QUI393Zh4nBDRGJlsyP42VqhSE7fWKLtTPkmdCuav+V0Tl1FgfIZ8Cl71vqx/5M+2kQlpWeXglUvNhTLx7ifBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:14.367926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76117318d882301cce5712662022fde95fcd8a2336c979f369e4a8dac0aa5233","sha256:9b56bc96f0b6b8739db6255444354fc25fc545f650595dd03ad8f4528ca54b3a"],"state_sha256":"77edd10b74542c4ce91f73ed43a25fb052844487089a839512e7663d191553db"}