{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z57MFWR3X23DHGZX7PJCXC3IGX","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":"183f3e2fd6f23a1691a26d19612c32343a4712e0b63adbea797d74926145b5a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-01T15:41:30Z","title_canon_sha256":"e55d6915fcfbcaefd2a9b52ddb123bfee3bc0249b0a364686bf24f14b85c6a75"},"schema_version":"1.0","source":{"id":"2505.00611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00611","created_at":"2026-07-05T10:57:22Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00611v1","created_at":"2026-07-05T10:57:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00611","created_at":"2026-07-05T10:57:22Z"},{"alias_kind":"pith_short_12","alias_value":"Z57MFWR3X23D","created_at":"2026-07-05T10:57:22Z"},{"alias_kind":"pith_short_16","alias_value":"Z57MFWR3X23DHGZX","created_at":"2026-07-05T10:57:22Z"},{"alias_kind":"pith_short_8","alias_value":"Z57MFWR3","created_at":"2026-07-05T10:57:22Z"}],"graph_snapshots":[{"event_id":"sha256:e63dedff3f6342ca97e451805d7c9874d0d75fa9f61fbb3e4eb849e6465e28a9","target":"graph","created_at":"2026-07-05T10:57:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.00611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ellenberg--Venkatesh proved in 2007 that $h_3(d) \\ll_\\epsilon |d|^{1/3 + \\epsilon}$, where $h_3(d)$ denotes the size of the $3$-torsion of the class group of $\\mathbb{Q}(\\sqrt{d})$. We improve this bound to $h_3(d) \\ll_\\epsilon |d|^{\\kappa + \\epsilon}$ with $\\kappa \\approx 0.3193 \\cdots$. We also combine our methods with work of Heath-Brown--Pierce to give new bounds for average $\\ell$-torsion of real quadratic fields.","authors_text":"Peter Koymans, Stephanie Chan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-01T15:41:30Z","title":"A new pointwise bound for $3$-torsion of class groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00611","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":"sha256:08c4d1b3b419caa272348ee2b224388e27d4a53a2f95973dd5294883aa674d7e","target":"record","created_at":"2026-07-05T10:57:22Z","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":"183f3e2fd6f23a1691a26d19612c32343a4712e0b63adbea797d74926145b5a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-05-01T15:41:30Z","title_canon_sha256":"e55d6915fcfbcaefd2a9b52ddb123bfee3bc0249b0a364686bf24f14b85c6a75"},"schema_version":"1.0","source":{"id":"2505.00611","kind":"arxiv","version":1}},"canonical_sha256":"cf7ec2da3bbeb6339b37fbd22b8b6835cbc34d9bc91313028d4ffbbdb63a69b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7ec2da3bbeb6339b37fbd22b8b6835cbc34d9bc91313028d4ffbbdb63a69b4","first_computed_at":"2026-07-05T10:57:22.962036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:57:22.962036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"axpiKrlHWHdIZFiohDzayd/ArhWXvf1oj6qGIMGhh0g3wSuN2ythZYxmtVQB9Gi+PWYeeUFkS438sGoOeX0RDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:57:22.962458Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08c4d1b3b419caa272348ee2b224388e27d4a53a2f95973dd5294883aa674d7e","sha256:e63dedff3f6342ca97e451805d7c9874d0d75fa9f61fbb3e4eb849e6465e28a9"],"state_sha256":"143c671c88dd2d78285d7f3ba71e5d6928355ce724c2c1e0c5664bd53255cb76"}