{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YY3ZHB6D4TYWUGMK5OWMXMUVQX","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":"9de35d05406e7cc69f61666e7b68746b4814f5b03e90e86d8c4c5dae57c4b5ad","cross_cats_sorted":["math.DS","math.GR","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T15:25:34Z","title_canon_sha256":"0f7db501500a6eb96f2bacf7d728f29b6d7947315e44d3a8cf2dbd7131def1f2"},"schema_version":"1.0","source":{"id":"1302.6121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6121","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6121v2","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6121","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"YY3ZHB6D4TYW","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YY3ZHB6D4TYWUGMK","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YY3ZHB6D","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:b6927e7b3c13c711541dde7c4d59fa4211dab9c094b5d388d0272641babe4be7","target":"graph","created_at":"2026-05-18T01:12:19Z","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 provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions. We then discuss dynamical properties of the associated Gauss map, comparing them with base-$b$ expansions on the Heisenberg group and continued fractions on the complex plane.","authors_text":"Anton Lukyanenko, Joseph Vandehey","cross_cats":["math.DS","math.GR","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T15:25:34Z","title":"Continued fractions on the Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6121","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":"sha256:1c5da271dd8c18dab7d0d7c0b3e4348ae8859cc81bc097ab9c80bcf8f6398d66","target":"record","created_at":"2026-05-18T01:12:19Z","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":"9de35d05406e7cc69f61666e7b68746b4814f5b03e90e86d8c4c5dae57c4b5ad","cross_cats_sorted":["math.DS","math.GR","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T15:25:34Z","title_canon_sha256":"0f7db501500a6eb96f2bacf7d728f29b6d7947315e44d3a8cf2dbd7131def1f2"},"schema_version":"1.0","source":{"id":"1302.6121","kind":"arxiv","version":2}},"canonical_sha256":"c6379387c3e4f16a198aebaccbb29585fcdcbb981601ed5bbfb226ead17b0848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6379387c3e4f16a198aebaccbb29585fcdcbb981601ed5bbfb226ead17b0848","first_computed_at":"2026-05-18T01:12:19.013222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:19.013222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D72Ej43OvC9WJkodZvHxyWP3pLt/Xv2UF5OQ7jwswpsVLjVYwNXaYzXTbT2rA7xvaTYFM9dmPGCDLsaLZzsbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:19.013572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c5da271dd8c18dab7d0d7c0b3e4348ae8859cc81bc097ab9c80bcf8f6398d66","sha256:b6927e7b3c13c711541dde7c4d59fa4211dab9c094b5d388d0272641babe4be7"],"state_sha256":"e665fa8cf59c40332194cd974486cf90c44d069f5d1c80d957b49099826e3a88"}