{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XZPK3SCP2PGCBDLQYXX4AWC4AR","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":"fe721f26e27ba7d7aa8453dab87c873349059067732792a744ac872fcc11c78f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-07T12:28:57Z","title_canon_sha256":"4c3fbb493acff1a1f88abae13cf8d55438bb0184e660ccd2db6d905f4cb32b96"},"schema_version":"1.0","source":{"id":"1711.02432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02432","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02432v1","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02432","created_at":"2026-05-18T00:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"XZPK3SCP2PGC","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XZPK3SCP2PGCBDLQ","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XZPK3SCP","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:acd5f4d9097ce340b809bdc81c5693e04d4a6b5fb6369bcee0388af22e21a844","target":"graph","created_at":"2026-05-18T00:31:07Z","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":"We explain a method for computing the Cassels-Tate pairing on the 3-isogeny Selmer groups of an elliptic curve. This improves the upper bound on the rank of the elliptic curve coming from a descent by 3-isogeny, to that coming from a full 3-descent. One ingredient of our work is a new algorithm for solving cubic norm equations, that avoids the need for any S-unit computations. As an application, we show that the elliptic curves with torsion subgroup of order 3 and rank at least 13, found by Eroshkin, have rank exactly 13.","authors_text":"Monique van Beek, Tom Fisher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-07T12:28:57Z","title":"Computing the Cassels-Tate pairing on 3-isogeny Selmer groups via cubic norm equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02432","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":"sha256:9660ed3d81160ff7b621607fce81c708ef983750cee498cfc0682f688d5e6591","target":"record","created_at":"2026-05-18T00:31:07Z","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":"fe721f26e27ba7d7aa8453dab87c873349059067732792a744ac872fcc11c78f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-07T12:28:57Z","title_canon_sha256":"4c3fbb493acff1a1f88abae13cf8d55438bb0184e660ccd2db6d905f4cb32b96"},"schema_version":"1.0","source":{"id":"1711.02432","kind":"arxiv","version":1}},"canonical_sha256":"be5eadc84fd3cc208d70c5efc0585c04561699cc8f0e6db8be023ce21589d552","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be5eadc84fd3cc208d70c5efc0585c04561699cc8f0e6db8be023ce21589d552","first_computed_at":"2026-05-18T00:31:07.907280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:07.907280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"imlbe7VUQO/1hQzc9d7oLgb9A6bdN3DyQ04yoCddFXdQf5J8TwW5qmr6lS69EKzs/2tuwjlRPoS+aRRuTG0cAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:07.907820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9660ed3d81160ff7b621607fce81c708ef983750cee498cfc0682f688d5e6591","sha256:acd5f4d9097ce340b809bdc81c5693e04d4a6b5fb6369bcee0388af22e21a844"],"state_sha256":"75e5e4f6769d7a83d2ebe7cf8b34d55c220f0a2947b297d85602a3b95ff9536d"}