{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7AE3KYVV7XQFMC6THZFFRHVBBS","short_pith_number":"pith:7AE3KYVV","canonical_record":{"source":{"id":"1603.00889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-02T21:09:35Z","cross_cats_sorted":[],"title_canon_sha256":"f1b83bbe5c74640dcea5de4b2ad8781ea82ea54c8db8724e938be1f0d66063bc","abstract_canon_sha256":"e3af9133162413481886676eac929855fc11da565b9f7d7992140588974f1a0c"},"schema_version":"1.0"},"canonical_sha256":"f809b562b5fde0560bd33e4a589ea10cb2e7508bd422f7cca8750116c80eee9d","source":{"kind":"arxiv","id":"1603.00889","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00889","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00889v2","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00889","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"7AE3KYVV7XQF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AE3KYVV7XQFMC6T","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AE3KYVV","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7AE3KYVV7XQFMC6THZFFRHVBBS","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-02T21:09:35Z","cross_cats_sorted":[],"title_canon_sha256":"f1b83bbe5c74640dcea5de4b2ad8781ea82ea54c8db8724e938be1f0d66063bc","abstract_canon_sha256":"e3af9133162413481886676eac929855fc11da565b9f7d7992140588974f1a0c"},"schema_version":"1.0"},"canonical_sha256":"f809b562b5fde0560bd33e4a589ea10cb2e7508bd422f7cca8750116c80eee9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:25.782144Z","signature_b64":"0j4LTL3X1mSUe2FX+Uu9bVlWtLIsFGbBFlvM8JS7rnAnaUX6ZRVGhE0yqxfljyBlm7SOjWqT6YXSOAajQVkjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f809b562b5fde0560bd33e4a589ea10cb2e7508bd422f7cca8750116c80eee9d","last_reissued_at":"2026-05-18T00:59:25.781504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:25.781504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00889","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":"2026-05-18T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xe2RxUqGq2E0BKwvcTofmLyCELvFWWtLXQBZSHx0/QBZ4iB+C/BLlfZIlsVcFa0smsLXAm14Uu2byvxznLsSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:37:48.669135Z"},"content_sha256":"879128f1cb1a21ce82bab7f7e3ef9771743a02ef198e2bb8c96735f0adce4454","schema_version":"1.0","event_id":"sha256:879128f1cb1a21ce82bab7f7e3ef9771743a02ef198e2bb8c96735f0adce4454"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7AE3KYVV7XQFMC6THZFFRHVBBS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of class numbers in a special family of real quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Dahl, Youness Lamzouri","submitted_at":"2016-03-02T21:09:35Z","abstract_excerpt":"We investigate the distribution of class numbers in the family of real quadratic fields $\\mathbb{Q}(\\sqrt{d})$ corresponding to fundamental discriminants of the form $d=4m^2+1$, which we refer to as Chowla's family. Our results show a strong similarity between the distribution of class numbers in this family and that of class numbers of imaginary quadratic fields. As an application of our results, we prove that the average order of the number of quadratic fields in Chowla's family with class number $h$ is $(\\log h)/2G$, where $G$ is Catalan's constant. With minor modifications, one can obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00889","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":"2026-05-18T00:59:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEVCaxHAuhESDphd8JgEzlTxqX8jJFGWI/woQGGYHEnxnsseQizpsIdz3gQZFD4oWQh7JuSn/LTSjEq+1yNdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:37:48.669807Z"},"content_sha256":"1b3a7c448f1dcc97db6c02b7459e716ede98de146e615b215f929623f6fa3050","schema_version":"1.0","event_id":"sha256:1b3a7c448f1dcc97db6c02b7459e716ede98de146e615b215f929623f6fa3050"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AE3KYVV7XQFMC6THZFFRHVBBS/bundle.json","state_url":"https://pith.science/pith/7AE3KYVV7XQFMC6THZFFRHVBBS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AE3KYVV7XQFMC6THZFFRHVBBS/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":"2026-05-26T09:37:48Z","links":{"resolver":"https://pith.science/pith/7AE3KYVV7XQFMC6THZFFRHVBBS","bundle":"https://pith.science/pith/7AE3KYVV7XQFMC6THZFFRHVBBS/bundle.json","state":"https://pith.science/pith/7AE3KYVV7XQFMC6THZFFRHVBBS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AE3KYVV7XQFMC6THZFFRHVBBS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7AE3KYVV7XQFMC6THZFFRHVBBS","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":"e3af9133162413481886676eac929855fc11da565b9f7d7992140588974f1a0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-02T21:09:35Z","title_canon_sha256":"f1b83bbe5c74640dcea5de4b2ad8781ea82ea54c8db8724e938be1f0d66063bc"},"schema_version":"1.0","source":{"id":"1603.00889","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00889","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00889v2","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00889","created_at":"2026-05-18T00:59:25Z"},{"alias_kind":"pith_short_12","alias_value":"7AE3KYVV7XQF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AE3KYVV7XQFMC6T","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AE3KYVV","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:1b3a7c448f1dcc97db6c02b7459e716ede98de146e615b215f929623f6fa3050","target":"graph","created_at":"2026-05-18T00:59:25Z","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 investigate the distribution of class numbers in the family of real quadratic fields $\\mathbb{Q}(\\sqrt{d})$ corresponding to fundamental discriminants of the form $d=4m^2+1$, which we refer to as Chowla's family. Our results show a strong similarity between the distribution of class numbers in this family and that of class numbers of imaginary quadratic fields. As an application of our results, we prove that the average order of the number of quadratic fields in Chowla's family with class number $h$ is $(\\log h)/2G$, where $G$ is Catalan's constant. With minor modifications, one can obtain ","authors_text":"Alexander Dahl, Youness Lamzouri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-02T21:09:35Z","title":"The distribution of class numbers in a special family of real quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00889","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":"sha256:879128f1cb1a21ce82bab7f7e3ef9771743a02ef198e2bb8c96735f0adce4454","target":"record","created_at":"2026-05-18T00:59:25Z","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":"e3af9133162413481886676eac929855fc11da565b9f7d7992140588974f1a0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-02T21:09:35Z","title_canon_sha256":"f1b83bbe5c74640dcea5de4b2ad8781ea82ea54c8db8724e938be1f0d66063bc"},"schema_version":"1.0","source":{"id":"1603.00889","kind":"arxiv","version":2}},"canonical_sha256":"f809b562b5fde0560bd33e4a589ea10cb2e7508bd422f7cca8750116c80eee9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f809b562b5fde0560bd33e4a589ea10cb2e7508bd422f7cca8750116c80eee9d","first_computed_at":"2026-05-18T00:59:25.781504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:25.781504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0j4LTL3X1mSUe2FX+Uu9bVlWtLIsFGbBFlvM8JS7rnAnaUX6ZRVGhE0yqxfljyBlm7SOjWqT6YXSOAajQVkjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:25.782144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00889","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:879128f1cb1a21ce82bab7f7e3ef9771743a02ef198e2bb8c96735f0adce4454","sha256:1b3a7c448f1dcc97db6c02b7459e716ede98de146e615b215f929623f6fa3050"],"state_sha256":"d9d09666583837d2acfaaa787485bd8e4eed386d900cf4d12406770100d4a2f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MUid1wdmGwv80L6Z8lJ4Vk5b7rK2PEmgpwQCr1siOlhhzMS9hYtgUhHzS7tcbCHn+B8XL5ymj89nfbbBiVpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:37:48.673642Z","bundle_sha256":"4b560e35bbba725658d03ed2eedfb848364f6e11164d0da39c8c334102abe194"}}