{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MI6SU7FB4C5ABVXAQPRJXMCBYU","short_pith_number":"pith:MI6SU7FB","canonical_record":{"source":{"id":"1611.02424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-08T08:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"94e0f7a4b7dfbfb7da721276b0bcf662c468ce1ebe2cfca36590d69332197baa","abstract_canon_sha256":"1b3c342904f1c2aee795fa32ecdafc94e428be77c2e8a45b93cb5c22bc4d368d"},"schema_version":"1.0"},"canonical_sha256":"623d2a7ca1e0ba00d6e083e29bb041c50b01fc312d378f807c867a425ef245aa","source":{"kind":"arxiv","id":"1611.02424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02424","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02424v1","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02424","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"MI6SU7FB4C5A","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MI6SU7FB4C5ABVXA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MI6SU7FB","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MI6SU7FB4C5ABVXAQPRJXMCBYU","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-08T08:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"94e0f7a4b7dfbfb7da721276b0bcf662c468ce1ebe2cfca36590d69332197baa","abstract_canon_sha256":"1b3c342904f1c2aee795fa32ecdafc94e428be77c2e8a45b93cb5c22bc4d368d"},"schema_version":"1.0"},"canonical_sha256":"623d2a7ca1e0ba00d6e083e29bb041c50b01fc312d378f807c867a425ef245aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.766610Z","signature_b64":"akqH0HpxjGvaUYWEMv8weOSGSrEWjV/vR0XyzajdsCHvkJPks7WwcMYIFrRCoAC0zc1YnkXD9kclejA1glIqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"623d2a7ca1e0ba00d6e083e29bb041c50b01fc312d378f807c867a425ef245aa","last_reissued_at":"2026-05-17T23:58:19.766207Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.766207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02424","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBlUGdz6UsSdTYHeOfi9c0J+Tzz6kt4RmxcOkrKm/9Lms49Xb2fYHQHFBX0tvgE7VeMXJx0EQCYBrFaM8MN2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:30:56.055753Z"},"content_sha256":"a9b2658fa683939beca47f10bbf62d4287889bb2cd5f0e4f0709df3e8b5578a8","schema_version":"1.0","event_id":"sha256:a9b2658fa683939beca47f10bbf62d4287889bb2cd5f0e4f0709df3e8b5578a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MI6SU7FB4C5ABVXAQPRJXMCBYU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of class numbers in continued fraction families of real quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Dahl, V\\'it\\v{e}zslav Kala","submitted_at":"2016-11-08T08:26:09Z","abstract_excerpt":"We construct a random model to study the distribution of class numbers in special families of real quadratic fields $\\mathbb Q(\\sqrt d)$ arising from continued fractions. These families are obtained by considering periodic continued fraction expansions of the form $\\sqrt {D(n)}=[f(n), [u_1, u_2, \\dots, u_{s-1}, 2f(n)]]$ with fixed coefficients $u_1, \\dots, u_{s-1}$ and generalize well-known families such as Chowla's $4n^2+1$, for which analogous results were recently proved by Dahl and Lamzouri."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02424","kind":"arxiv","version":1},"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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p8+B3x/6NOvoX4mnItb03SX6qavtbE8yQWrndElm38Lui3rF0hf7YvQL8zCbhviXAUqUUCKnOnVDXwfrjlR+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:30:56.056508Z"},"content_sha256":"c8761288cd40fdd8f7af8fb9664f1de187f186683587e927c2ea75883c8a6d02","schema_version":"1.0","event_id":"sha256:c8761288cd40fdd8f7af8fb9664f1de187f186683587e927c2ea75883c8a6d02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU/bundle.json","state_url":"https://pith.science/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU/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":"2026-06-10T10:30:56Z","links":{"resolver":"https://pith.science/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU","bundle":"https://pith.science/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU/bundle.json","state":"https://pith.science/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MI6SU7FB4C5ABVXAQPRJXMCBYU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MI6SU7FB4C5ABVXAQPRJXMCBYU","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":"1b3c342904f1c2aee795fa32ecdafc94e428be77c2e8a45b93cb5c22bc4d368d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-08T08:26:09Z","title_canon_sha256":"94e0f7a4b7dfbfb7da721276b0bcf662c468ce1ebe2cfca36590d69332197baa"},"schema_version":"1.0","source":{"id":"1611.02424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02424","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02424v1","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02424","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"MI6SU7FB4C5A","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MI6SU7FB4C5ABVXA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MI6SU7FB","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:c8761288cd40fdd8f7af8fb9664f1de187f186683587e927c2ea75883c8a6d02","target":"graph","created_at":"2026-05-17T23:58:19Z","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 construct a random model to study the distribution of class numbers in special families of real quadratic fields $\\mathbb Q(\\sqrt d)$ arising from continued fractions. These families are obtained by considering periodic continued fraction expansions of the form $\\sqrt {D(n)}=[f(n), [u_1, u_2, \\dots, u_{s-1}, 2f(n)]]$ with fixed coefficients $u_1, \\dots, u_{s-1}$ and generalize well-known families such as Chowla's $4n^2+1$, for which analogous results were recently proved by Dahl and Lamzouri.","authors_text":"Alexander Dahl, V\\'it\\v{e}zslav Kala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-08T08:26:09Z","title":"Distribution of class numbers in continued fraction families of real quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02424","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:a9b2658fa683939beca47f10bbf62d4287889bb2cd5f0e4f0709df3e8b5578a8","target":"record","created_at":"2026-05-17T23:58:19Z","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":"1b3c342904f1c2aee795fa32ecdafc94e428be77c2e8a45b93cb5c22bc4d368d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-08T08:26:09Z","title_canon_sha256":"94e0f7a4b7dfbfb7da721276b0bcf662c468ce1ebe2cfca36590d69332197baa"},"schema_version":"1.0","source":{"id":"1611.02424","kind":"arxiv","version":1}},"canonical_sha256":"623d2a7ca1e0ba00d6e083e29bb041c50b01fc312d378f807c867a425ef245aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"623d2a7ca1e0ba00d6e083e29bb041c50b01fc312d378f807c867a425ef245aa","first_computed_at":"2026-05-17T23:58:19.766207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.766207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"akqH0HpxjGvaUYWEMv8weOSGSrEWjV/vR0XyzajdsCHvkJPks7WwcMYIFrRCoAC0zc1YnkXD9kclejA1glIqDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.766610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9b2658fa683939beca47f10bbf62d4287889bb2cd5f0e4f0709df3e8b5578a8","sha256:c8761288cd40fdd8f7af8fb9664f1de187f186683587e927c2ea75883c8a6d02"],"state_sha256":"3a9398e80abd5f34dc230c991a00b01f839495e3722befc40c5755948c113f97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w9gHLn7IlVPNMpJRYHbeaWY+ziRCK7EQm4x0eDBPHoNem6pIu22jZ7574Vm4Vk+Nd80Zzs9qVozGkSozZRFBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:30:56.060623Z","bundle_sha256":"cd86b753e6fff41066521cbab21d610ea00069f56c7a43c39a435de073aac8ad"}}