{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KYYLFG443D34U5YTBYBBPUV7LH","short_pith_number":"pith:KYYLFG44","schema_version":"1.0","canonical_sha256":"5630b29b9cd8f7ca77130e0217d2bf59d3957a7e1385c26a5e54e001c0dead0a","source":{"kind":"arxiv","id":"1605.08382","version":4},"attestation_state":"computed","paper":{"title":"Rank parity for congruent supersingular elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeffrey Hatley","submitted_at":"2016-05-26T17:53:44Z","abstract_excerpt":"A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and $E_2$ for which there is an isomorphism $E_1[p] \\simeq E_2[p]$ as $\\mathrm{Gal}(\\bar{\\mathbf{Q}}/\\mathbf{Q})$-modules, where $p$ is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where $p$ is a prime of good supersingular reduction."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.08382","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-26T17:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"b141d4d911743a43435fc30bf648593ba9f969b817d57702c3a586a5a6055756","abstract_canon_sha256":"971acb26dd4dd9fb5390560ea13ae8e75bd77b465ca4cc6780690dffa956b573"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:17.867028Z","signature_b64":"BpX4aPv0rnAcOkgnPkXZRlfYWpjjLZYS3dOusyj6fKeN1Q9rceIRlrx0QVnNr2ljD27z8f2PF7hoPxiiWV4EBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5630b29b9cd8f7ca77130e0217d2bf59d3957a7e1385c26a5e54e001c0dead0a","last_reissued_at":"2026-05-18T00:42:17.866356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:17.866356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank parity for congruent supersingular elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeffrey Hatley","submitted_at":"2016-05-26T17:53:44Z","abstract_excerpt":"A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and $E_2$ for which there is an isomorphism $E_1[p] \\simeq E_2[p]$ as $\\mathrm{Gal}(\\bar{\\mathbf{Q}}/\\mathbf{Q})$-modules, where $p$ is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where $p$ is a prime of good supersingular reduction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08382","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.08382","created_at":"2026-05-18T00:42:17.866465+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.08382v4","created_at":"2026-05-18T00:42:17.866465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08382","created_at":"2026-05-18T00:42:17.866465+00:00"},{"alias_kind":"pith_short_12","alias_value":"KYYLFG443D34","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"KYYLFG443D34U5YT","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"KYYLFG44","created_at":"2026-05-18T12:30:29.479603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH","json":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH.json","graph_json":"https://pith.science/api/pith-number/KYYLFG443D34U5YTBYBBPUV7LH/graph.json","events_json":"https://pith.science/api/pith-number/KYYLFG443D34U5YTBYBBPUV7LH/events.json","paper":"https://pith.science/paper/KYYLFG44"},"agent_actions":{"view_html":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH","download_json":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH.json","view_paper":"https://pith.science/paper/KYYLFG44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.08382&json=true","fetch_graph":"https://pith.science/api/pith-number/KYYLFG443D34U5YTBYBBPUV7LH/graph.json","fetch_events":"https://pith.science/api/pith-number/KYYLFG443D34U5YTBYBBPUV7LH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH/action/storage_attestation","attest_author":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH/action/author_attestation","sign_citation":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH/action/citation_signature","submit_replication":"https://pith.science/pith/KYYLFG443D34U5YTBYBBPUV7LH/action/replication_record"}},"created_at":"2026-05-18T00:42:17.866465+00:00","updated_at":"2026-05-18T00:42:17.866465+00:00"}