{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:46JHAIKU3BOPB34TUSZ6EH5EE4","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":"b55d95f718d682aa37ddd96368e75cc994711275402fdab9db977b7b68753595","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-03T17:31:51Z","title_canon_sha256":"86b7d8c632397cadcd2e49970fa9e14ed36a6cece8f17854ff7ff84f73364edc"},"schema_version":"1.0","source":{"id":"2409.02080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.02080","created_at":"2026-07-05T09:47:34Z"},{"alias_kind":"arxiv_version","alias_value":"2409.02080v1","created_at":"2026-07-05T09:47:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.02080","created_at":"2026-07-05T09:47:34Z"},{"alias_kind":"pith_short_12","alias_value":"46JHAIKU3BOP","created_at":"2026-07-05T09:47:34Z"},{"alias_kind":"pith_short_16","alias_value":"46JHAIKU3BOPB34T","created_at":"2026-07-05T09:47:34Z"},{"alias_kind":"pith_short_8","alias_value":"46JHAIKU","created_at":"2026-07-05T09:47:34Z"}],"graph_snapshots":[{"event_id":"sha256:95d0062fbdec8e721256e77f9cee4fa9ecd457ecfa29205c851dd702585c27bf","target":"graph","created_at":"2026-07-05T09:47:34Z","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/2409.02080/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the order of magnitude for all exponential moments of the rank in a broad class of elliptic fibrations and for the $3 \\cdot 2^k$-torsion in the class group of quadratic fields.","authors_text":"Carlo Pagano, Efthymios Sofos, Peter Koymans","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-03T17:31:51Z","title":"Elliptic fibrations and $3 \\cdot 2^k$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02080","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":"sha256:6c6fb3c8b4214bf460eaa355f02bd4f3227f7ecc80ba538166836be73ea40f54","target":"record","created_at":"2026-07-05T09:47:34Z","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":"b55d95f718d682aa37ddd96368e75cc994711275402fdab9db977b7b68753595","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-03T17:31:51Z","title_canon_sha256":"86b7d8c632397cadcd2e49970fa9e14ed36a6cece8f17854ff7ff84f73364edc"},"schema_version":"1.0","source":{"id":"2409.02080","kind":"arxiv","version":1}},"canonical_sha256":"e792702154d85cf0ef93a4b3e21fa4273e492923013d1b78d17dbbbcf758ed3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e792702154d85cf0ef93a4b3e21fa4273e492923013d1b78d17dbbbcf758ed3c","first_computed_at":"2026-07-05T09:47:34.499125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:47:34.499125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GYiETFYVWFyb/ipt9xRR3uePsxGnoRbygLbbD6Rqrvm3tc19OYck+CTXgSn1d+nFEuJePVczh+orR7/QQEGbCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:47:34.499642Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.02080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c6fb3c8b4214bf460eaa355f02bd4f3227f7ecc80ba538166836be73ea40f54","sha256:95d0062fbdec8e721256e77f9cee4fa9ecd457ecfa29205c851dd702585c27bf"],"state_sha256":"fcea78bf26bf8e47332cee4fe66cacff299824249d1c7edeeee7838430bd18c3"}