{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3GTTXQES4IIFAXAVRXNY4SAXMU","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":"43bbdeab28b81318479d376a15a0fff274c2005e4251cd4825c47a67fdd89599","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T09:10:53Z","title_canon_sha256":"67906b94124da8d4d856d4400c06bae7bed8b4a66c01e7807cc44bd7357b7f18"},"schema_version":"1.0","source":{"id":"1809.06603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06603","created_at":"2026-05-18T00:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06603v1","created_at":"2026-05-18T00:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06603","created_at":"2026-05-18T00:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"3GTTXQES4IIF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3GTTXQES4IIFAXAV","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3GTTXQES","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:0278e462f6f9c8d6044b77cf312973d33d63c02aab0c535689461f43a5865bf7","target":"graph","created_at":"2026-05-18T00:05:25Z","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":"While there has been considerable interest in the problem of finding elliptic curves of high rank over $\\mathbb{Q}$, very few parametrized families of elliptic curves of generic rank $\\geq 8$ have been published. In this paper we use solutions of certain symmetric diophantine systems to construct several parametrized families of elliptic curves with their generic ranks ranging from at least 8 to at least 12. Specific numerical values of the parameters yield elliptic curves with quite large coefficients and we could therefore determine the precise rank only in a few cases where the rank of the ","authors_text":"Ajai Choudhry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T09:10:53Z","title":"Symmetric diophantine systems and families of elliptic curves of high rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06603","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":"sha256:8a58a3c44c44c616e33498a3c3cda6896962441f82be784e6399c53abdd2b689","target":"record","created_at":"2026-05-18T00:05:25Z","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":"43bbdeab28b81318479d376a15a0fff274c2005e4251cd4825c47a67fdd89599","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-18T09:10:53Z","title_canon_sha256":"67906b94124da8d4d856d4400c06bae7bed8b4a66c01e7807cc44bd7357b7f18"},"schema_version":"1.0","source":{"id":"1809.06603","kind":"arxiv","version":1}},"canonical_sha256":"d9a73bc092e210505c158ddb8e48176536fe82afe719eedd10e15eba2f7dc95b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9a73bc092e210505c158ddb8e48176536fe82afe719eedd10e15eba2f7dc95b","first_computed_at":"2026-05-18T00:05:25.207453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:25.207453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMKoPvEjqGBnTjC7Zb9O7r6BEeNA6vc3BkVIlM48RIsBzFp0Yyl608oJiXyajChrGctNF2D7P7WzR3+hPc4TBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:25.208011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a58a3c44c44c616e33498a3c3cda6896962441f82be784e6399c53abdd2b689","sha256:0278e462f6f9c8d6044b77cf312973d33d63c02aab0c535689461f43a5865bf7"],"state_sha256":"2143366c45da0dd937658bab687522b3a191cf15aa54a811e49a441312aff751"}