{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S4IW4RX7OQNF43NDCSNBP266ZX","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":"fdd76a025f526f027634c4d4e9e87f452f2ebcb00effad1424fc356bebd08362","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-14T00:34:09Z","title_canon_sha256":"7810c2668aa41b4a14d3c65924148779ae1cf11a48bed4bb18882e51a5121f95"},"schema_version":"1.0","source":{"id":"1612.04443","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04443","created_at":"2026-05-18T00:31:22Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04443v4","created_at":"2026-05-18T00:31:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04443","created_at":"2026-05-18T00:31:22Z"},{"alias_kind":"pith_short_12","alias_value":"S4IW4RX7OQNF","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"S4IW4RX7OQNF43ND","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"S4IW4RX7","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:00ca20efe70c4ebd88839527839478619036db6b5ee660646d7daf2813a475ba","target":"graph","created_at":"2026-05-18T00:31:22Z","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 quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discriminants down to -X whose class numbers are indivisible by a given prime and whose imaginary quadratic fields satisfy any given set of local conditions. This estimate matches the best results in the direction of the Cohen-Lenstra heuristics for the number of imaginary quadratic fields with class number indivisible by a given prime. This general result is applied to study rank 0 twists of certain elliptic curves.","authors_text":"Olivia Beckwith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-14T00:34:09Z","title":"Indivisibility of class numbers of imaginary quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04443","kind":"arxiv","version":4},"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":"sha256:68eb5d960cc47e4ab6c6e699fa6660416ad362f164cec4f822ecfaf11c3a6806","target":"record","created_at":"2026-05-18T00:31:22Z","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":"fdd76a025f526f027634c4d4e9e87f452f2ebcb00effad1424fc356bebd08362","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-14T00:34:09Z","title_canon_sha256":"7810c2668aa41b4a14d3c65924148779ae1cf11a48bed4bb18882e51a5121f95"},"schema_version":"1.0","source":{"id":"1612.04443","kind":"arxiv","version":4}},"canonical_sha256":"97116e46ff741a5e6da3149a17ebdecdec0cb83515928d46125e3aacaaa38dfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97116e46ff741a5e6da3149a17ebdecdec0cb83515928d46125e3aacaaa38dfb","first_computed_at":"2026-05-18T00:31:22.270085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:22.270085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcO2b2CaHfSrKO+tvnRuzZ27W76SRCB4ZiosIFPDFHOmH/QVc8Jnqm4ySwtry26LjcO6nnUqw9yDYD8nBTndDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:22.270586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04443","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68eb5d960cc47e4ab6c6e699fa6660416ad362f164cec4f822ecfaf11c3a6806","sha256:00ca20efe70c4ebd88839527839478619036db6b5ee660646d7daf2813a475ba"],"state_sha256":"7a153e784868072618f97e5259df317557e8264084ff1f2821473b69dfc5cfd8"}