{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6HSECOL5FAF652GA7NLQ5POBHT","short_pith_number":"pith:6HSECOL5","canonical_record":{"source":{"id":"1309.5154","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-20T01:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"797ebbffeae37faf8fe3739accf3b4cc1734115688777ee0ca15be56ab599c31","abstract_canon_sha256":"98fbfa9ec50f52e7fd9f878769df9c6d0d96cb3813260f0c64bbf8ee2eef451e"},"schema_version":"1.0"},"canonical_sha256":"f1e441397d280beee8c0fb570ebdc13cca13e2da7fea07d0cdf783455486a483","source":{"kind":"arxiv","id":"1309.5154","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5154","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5154v2","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5154","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"6HSECOL5FAF6","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6HSECOL5FAF652GA","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6HSECOL5","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6HSECOL5FAF652GA7NLQ5POBHT","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5154","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-20T01:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"797ebbffeae37faf8fe3739accf3b4cc1734115688777ee0ca15be56ab599c31","abstract_canon_sha256":"98fbfa9ec50f52e7fd9f878769df9c6d0d96cb3813260f0c64bbf8ee2eef451e"},"schema_version":"1.0"},"canonical_sha256":"f1e441397d280beee8c0fb570ebdc13cca13e2da7fea07d0cdf783455486a483","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:57.182168Z","signature_b64":"xoAMwJvQwXcagpkIsShjh42RwKHoMZIbq5UYx1/IE9Qp6rHLH2atY6VkzbKd041DOBb28KW2MdPP1oH/jq3aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1e441397d280beee8c0fb570ebdc13cca13e2da7fea07d0cdf783455486a483","last_reissued_at":"2026-05-18T01:33:57.181603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:57.181603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5154","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZlQoJqJI75HpczfdJLP6J/9JOCXdfRL1fvoerIM6DDAj9oCW7mn+FU/Mh6DLlmBXU5qlWnXKaDa7ax6QH8rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:33:41.593224Z"},"content_sha256":"a55ff3a32474e1b0da961c5e336094d192b08dc523817d3b4330ef2ca768c414","schema_version":"1.0","event_id":"sha256:a55ff3a32474e1b0da961c5e336094d192b08dc523817d3b4330ef2ca768c414"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6HSECOL5FAF652GA7NLQ5POBHT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diophantine properties of continued fractions on the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joseph Vandehey","submitted_at":"2013-09-20T01:59:44Z","abstract_excerpt":"We provide several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem and that convergents are also best approximants up to a constant factor of the denominator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5154","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kPTppK6DabV+W8B/lXSiyH4flqMTzwPJPFk1a51iNQdctyvvawtxhlONeGlBZjvCYj+NPu1OkuUguxCYSEW+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:33:41.593683Z"},"content_sha256":"d69bc2b68be04f818f125ff6517de5b216ecceaa5d985cfc22ca94fb0647ae00","schema_version":"1.0","event_id":"sha256:d69bc2b68be04f818f125ff6517de5b216ecceaa5d985cfc22ca94fb0647ae00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HSECOL5FAF652GA7NLQ5POBHT/bundle.json","state_url":"https://pith.science/pith/6HSECOL5FAF652GA7NLQ5POBHT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HSECOL5FAF652GA7NLQ5POBHT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T02:33:41Z","links":{"resolver":"https://pith.science/pith/6HSECOL5FAF652GA7NLQ5POBHT","bundle":"https://pith.science/pith/6HSECOL5FAF652GA7NLQ5POBHT/bundle.json","state":"https://pith.science/pith/6HSECOL5FAF652GA7NLQ5POBHT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HSECOL5FAF652GA7NLQ5POBHT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6HSECOL5FAF652GA7NLQ5POBHT","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":"98fbfa9ec50f52e7fd9f878769df9c6d0d96cb3813260f0c64bbf8ee2eef451e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-20T01:59:44Z","title_canon_sha256":"797ebbffeae37faf8fe3739accf3b4cc1734115688777ee0ca15be56ab599c31"},"schema_version":"1.0","source":{"id":"1309.5154","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5154","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5154v2","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5154","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"6HSECOL5FAF6","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6HSECOL5FAF652GA","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6HSECOL5","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:d69bc2b68be04f818f125ff6517de5b216ecceaa5d985cfc22ca94fb0647ae00","target":"graph","created_at":"2026-05-18T01:33:57Z","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 several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem and that convergents are also best approximants up to a constant factor of the denominator.","authors_text":"Joseph Vandehey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-20T01:59:44Z","title":"Diophantine properties of continued fractions on the Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5154","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:a55ff3a32474e1b0da961c5e336094d192b08dc523817d3b4330ef2ca768c414","target":"record","created_at":"2026-05-18T01:33:57Z","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":"98fbfa9ec50f52e7fd9f878769df9c6d0d96cb3813260f0c64bbf8ee2eef451e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-20T01:59:44Z","title_canon_sha256":"797ebbffeae37faf8fe3739accf3b4cc1734115688777ee0ca15be56ab599c31"},"schema_version":"1.0","source":{"id":"1309.5154","kind":"arxiv","version":2}},"canonical_sha256":"f1e441397d280beee8c0fb570ebdc13cca13e2da7fea07d0cdf783455486a483","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1e441397d280beee8c0fb570ebdc13cca13e2da7fea07d0cdf783455486a483","first_computed_at":"2026-05-18T01:33:57.181603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.181603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xoAMwJvQwXcagpkIsShjh42RwKHoMZIbq5UYx1/IE9Qp6rHLH2atY6VkzbKd041DOBb28KW2MdPP1oH/jq3aCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.182168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5154","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a55ff3a32474e1b0da961c5e336094d192b08dc523817d3b4330ef2ca768c414","sha256:d69bc2b68be04f818f125ff6517de5b216ecceaa5d985cfc22ca94fb0647ae00"],"state_sha256":"0f4c427ff7b2388a7e608b0bd6d5bd9d3615d5cc02ab451aa9ed3fff5873a756"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jm0GE57e3o0uVSJX6YBmbriO08Z7HvomYgdmZ3flM6frcGZv/EBo7cDXikYcx3nzcpZwti1/4GKcrN0TuNptDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:33:41.597347Z","bundle_sha256":"60f943604f51772e73e360e5661fc5ef90e46839e54498921ec9bbee5c5486f4"}}