{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YNXPZGNI4Q6ETS23MIKFZSV5QP","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":"89645bcb2cf0dd9d47278c948cb160657574905a068fb15635d14dc94d9a4a6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-24T03:05:29Z","title_canon_sha256":"13ea496a8debef48f04878fac79a1642a13da95666c2640490813bd505e11e80"},"schema_version":"1.0","source":{"id":"1703.08275","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08275","created_at":"2026-05-18T00:19:19Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08275v3","created_at":"2026-05-18T00:19:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08275","created_at":"2026-05-18T00:19:19Z"},{"alias_kind":"pith_short_12","alias_value":"YNXPZGNI4Q6E","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YNXPZGNI4Q6ETS23","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YNXPZGNI","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:217040e858f8b56ec013e397d83df35ec0d22f17070ead2a8c3affdc64fc03bc","target":"graph","created_at":"2026-05-18T00:19:19Z","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":"Using the rank of the Mordell-Weil group $E(\\mathbb{Q})$ of an elliptic curve $E$ over $\\mathbb{Q}$, we give a lower bound of the class number of the number field $\\mathbb{Q}(E[p^n])$ generated by $p^n$-division points of $E$ when the curve $E$ does not possess a $p$-adic point of order $p$: $E(\\mathbb{Q}_p)[p] =0$.","authors_text":"Toshiro Hiranouchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-24T03:05:29Z","title":"Local torsion primes and the class numbers associated to an elliptic curve over $\\mathbb{Q}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08275","kind":"arxiv","version":3},"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:b1327a537ad5fc970ce32872a0c7dc2cc4b4c0437eea62b748126b78e90f18e2","target":"record","created_at":"2026-05-18T00:19:19Z","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":"89645bcb2cf0dd9d47278c948cb160657574905a068fb15635d14dc94d9a4a6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-24T03:05:29Z","title_canon_sha256":"13ea496a8debef48f04878fac79a1642a13da95666c2640490813bd505e11e80"},"schema_version":"1.0","source":{"id":"1703.08275","kind":"arxiv","version":3}},"canonical_sha256":"c36efc99a8e43c49cb5b62145ccabd83f2a80340dd199e4085b5cd34a0f87545","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c36efc99a8e43c49cb5b62145ccabd83f2a80340dd199e4085b5cd34a0f87545","first_computed_at":"2026-05-18T00:19:19.421057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:19.421057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RldL0TOZ2tCrvLgYpCSG2e5wjVcYbnxtERqHbxnlr85yKoL9kLCMnHRtNi57uRbNd4tJlTo/1ZFHOSx3L+MRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:19.421795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08275","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1327a537ad5fc970ce32872a0c7dc2cc4b4c0437eea62b748126b78e90f18e2","sha256:217040e858f8b56ec013e397d83df35ec0d22f17070ead2a8c3affdc64fc03bc"],"state_sha256":"1881dcb49ff8ce3ac47a44a5fed89756fcca36e6f79ad4550bb7d957a6930736"}