{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BA465EC6J7NXKVYUBLRGPEIIUW","short_pith_number":"pith:BA465EC6","canonical_record":{"source":{"id":"1811.08166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-20T10:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"6b5587ba80351ba6f6624aa3913ecbe8f321f3b497231bf5b98dd83b44e1390b","abstract_canon_sha256":"63f2ea06a13706bad4fc1a4ad9c1f077cefb80a38c0b832f9a54aca964f9f6bf"},"schema_version":"1.0"},"canonical_sha256":"0839ee905e4fdb7557140ae2679108a5a152d9595497c67c5802b48a5c85c96b","source":{"kind":"arxiv","id":"1811.08166","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08166","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08166v2","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08166","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"BA465EC6J7NX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BA465EC6J7NXKVYU","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BA465EC6","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BA465EC6J7NXKVYUBLRGPEIIUW","target":"record","payload":{"canonical_record":{"source":{"id":"1811.08166","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-20T10:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"6b5587ba80351ba6f6624aa3913ecbe8f321f3b497231bf5b98dd83b44e1390b","abstract_canon_sha256":"63f2ea06a13706bad4fc1a4ad9c1f077cefb80a38c0b832f9a54aca964f9f6bf"},"schema_version":"1.0"},"canonical_sha256":"0839ee905e4fdb7557140ae2679108a5a152d9595497c67c5802b48a5c85c96b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:57.905923Z","signature_b64":"xX6MbJJj2bbwbY752Pl69DSBeXzzo2brJjOi+ZQGLganYgcAhEcOiKlZvwHrLLbVtVjmIcuVR7dzBJ2HNpUECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0839ee905e4fdb7557140ae2679108a5a152d9595497c67c5802b48a5c85c96b","last_reissued_at":"2026-05-17T23:45:57.905288Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:57.905288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.08166","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":"2026-05-17T23:45:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jFMgoxHHZSYDSLjyBZRCqQ4aatuWtDImVWLAHizF49xk3qvipPQ9cHeeFK83iAExTwJEZ81RnysleO5xUlYJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:34:49.328841Z"},"content_sha256":"a84b25d3f167e76fcc15d2d73488bc8adaa4be91510e82a62b068678d782b4ad","schema_version":"1.0","event_id":"sha256:a84b25d3f167e76fcc15d2d73488bc8adaa4be91510e82a62b068678d782b4ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BA465EC6J7NXKVYUBLRGPEIIUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic surfaces over $\\mathbb{P}^1$ and large class groups of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aaron Levin, Jean Gillibert","submitted_at":"2018-11-20T10:27:12Z","abstract_excerpt":"Given a non-isotrivial elliptic curve over $\\mathbb{Q}(t)$ with large Mordell-Weil rank, we explain how one can build, for suitable small primes $p$, infinitely many fields of degree $p^2-1$ whose ideal class group has a large $p$-torsion subgroup. As an example, we show the existence of infinitely many cubic fields whose ideal class group contains a subgroup isomorphic to $(\\mathbb{Z}/2\\mathbb{Z})^{11}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08166","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":"2026-05-17T23:45:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLSHfMf8YZ189pAIK9H9sbrPl7qcNBbOWHOmCu211Ot+XwGDVYlb2spo31yOORwcb/C0CDOWd4+pQW34afi3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:34:49.329178Z"},"content_sha256":"2c75fb6d762ee5290da916f15700d9fd9054dfe1e174d4c41c838f4c7c34ce48","schema_version":"1.0","event_id":"sha256:2c75fb6d762ee5290da916f15700d9fd9054dfe1e174d4c41c838f4c7c34ce48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BA465EC6J7NXKVYUBLRGPEIIUW/bundle.json","state_url":"https://pith.science/pith/BA465EC6J7NXKVYUBLRGPEIIUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BA465EC6J7NXKVYUBLRGPEIIUW/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":"2026-06-20T03:34:49Z","links":{"resolver":"https://pith.science/pith/BA465EC6J7NXKVYUBLRGPEIIUW","bundle":"https://pith.science/pith/BA465EC6J7NXKVYUBLRGPEIIUW/bundle.json","state":"https://pith.science/pith/BA465EC6J7NXKVYUBLRGPEIIUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BA465EC6J7NXKVYUBLRGPEIIUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BA465EC6J7NXKVYUBLRGPEIIUW","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":"63f2ea06a13706bad4fc1a4ad9c1f077cefb80a38c0b832f9a54aca964f9f6bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-20T10:27:12Z","title_canon_sha256":"6b5587ba80351ba6f6624aa3913ecbe8f321f3b497231bf5b98dd83b44e1390b"},"schema_version":"1.0","source":{"id":"1811.08166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08166","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08166v2","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08166","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"BA465EC6J7NX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BA465EC6J7NXKVYU","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BA465EC6","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:2c75fb6d762ee5290da916f15700d9fd9054dfe1e174d4c41c838f4c7c34ce48","target":"graph","created_at":"2026-05-17T23:45:57Z","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":"Given a non-isotrivial elliptic curve over $\\mathbb{Q}(t)$ with large Mordell-Weil rank, we explain how one can build, for suitable small primes $p$, infinitely many fields of degree $p^2-1$ whose ideal class group has a large $p$-torsion subgroup. As an example, we show the existence of infinitely many cubic fields whose ideal class group contains a subgroup isomorphic to $(\\mathbb{Z}/2\\mathbb{Z})^{11}$.","authors_text":"Aaron Levin, Jean Gillibert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-20T10:27:12Z","title":"Elliptic surfaces over $\\mathbb{P}^1$ and large class groups of number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08166","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:a84b25d3f167e76fcc15d2d73488bc8adaa4be91510e82a62b068678d782b4ad","target":"record","created_at":"2026-05-17T23:45:57Z","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":"63f2ea06a13706bad4fc1a4ad9c1f077cefb80a38c0b832f9a54aca964f9f6bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-20T10:27:12Z","title_canon_sha256":"6b5587ba80351ba6f6624aa3913ecbe8f321f3b497231bf5b98dd83b44e1390b"},"schema_version":"1.0","source":{"id":"1811.08166","kind":"arxiv","version":2}},"canonical_sha256":"0839ee905e4fdb7557140ae2679108a5a152d9595497c67c5802b48a5c85c96b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0839ee905e4fdb7557140ae2679108a5a152d9595497c67c5802b48a5c85c96b","first_computed_at":"2026-05-17T23:45:57.905288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:57.905288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xX6MbJJj2bbwbY752Pl69DSBeXzzo2brJjOi+ZQGLganYgcAhEcOiKlZvwHrLLbVtVjmIcuVR7dzBJ2HNpUECA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:57.905923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a84b25d3f167e76fcc15d2d73488bc8adaa4be91510e82a62b068678d782b4ad","sha256:2c75fb6d762ee5290da916f15700d9fd9054dfe1e174d4c41c838f4c7c34ce48"],"state_sha256":"3a3a4924ea84d72fa9904505176b87aba9dd039dc9907a1fa2b5b63aca0ee55a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EvxiDnYPzRjSwXJ7muPmO1hf7n1+ngj6NxNuaowObo0ihk73pkqybkEpBrzGskFCLleZzKu0zQfmRvEzct9MAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:34:49.331037Z","bundle_sha256":"9fd5102895fab12b1505c4f03457b037137ca7c2061b574eaaf699cc5dd33581"}}