{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:72XZXQ2J7MW7QFMNLCZWX6BOWT","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":"c300131de9259fa2312f2b38c5e8878d2a95be5a1d31b713e58d1c88b9114366","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T01:23:14Z","title_canon_sha256":"a6620143cb77d6af99f5f7ac5227a24400ba1f13bb623cd8364e2e94eb7e495b"},"schema_version":"1.0","source":{"id":"1109.6070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6070","created_at":"2026-05-18T04:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6070v2","created_at":"2026-05-18T04:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6070","created_at":"2026-05-18T04:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"72XZXQ2J7MW7","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"72XZXQ2J7MW7QFMN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"72XZXQ2J","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:bc1739c86c86854ead34b8ed280c08e3681a43524902ec415e071b6008d03ae9","target":"graph","created_at":"2026-05-18T04:00:51Z","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":"It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k, one can effectively compute the set of isomorphism classes of hyperelliptic curves over k with good reduction outside S. We show here that an extension of this result to an effective Shafarevich conjecture for Jacobians of hyperelliptic curves of genus g would imply an effective version of Siegel's theorem for integral points on hyperelliptic curves of genus g.","authors_text":"Aaron Levin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T01:23:14Z","title":"Siegel's Theorem and the Shafarevich Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6070","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":"sha256:06536135d578c4c9276868a38e6423a8ba98248f097c0a8d5e9576d50e6cde48","target":"record","created_at":"2026-05-18T04:00:51Z","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":"c300131de9259fa2312f2b38c5e8878d2a95be5a1d31b713e58d1c88b9114366","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-09-28T01:23:14Z","title_canon_sha256":"a6620143cb77d6af99f5f7ac5227a24400ba1f13bb623cd8364e2e94eb7e495b"},"schema_version":"1.0","source":{"id":"1109.6070","kind":"arxiv","version":2}},"canonical_sha256":"feaf9bc349fb2df8158d58b36bf82eb4f6c08ac2080734dc6c24c7402c2b5fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feaf9bc349fb2df8158d58b36bf82eb4f6c08ac2080734dc6c24c7402c2b5fa6","first_computed_at":"2026-05-18T04:00:51.985072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:51.985072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+aInAU5U1n8Kgz0xsORoYhET/evTqn4yj0blUQxjFqktDcYNHW/SvkONMbJ3ropI+yw+qfC3z/ktxvv5p8ozDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:51.985851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06536135d578c4c9276868a38e6423a8ba98248f097c0a8d5e9576d50e6cde48","sha256:bc1739c86c86854ead34b8ed280c08e3681a43524902ec415e071b6008d03ae9"],"state_sha256":"97f80814fe13d02c12b066a8e6695463ed611ae1b4f991bb54c7bdb5df3aa4e8"}