{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2VCQA6IHAZKRTWMT4HRFNGQYDC","short_pith_number":"pith:2VCQA6IH","schema_version":"1.0","canonical_sha256":"d545007907065519d993e1e2569a18189e14a620520f5227004cca0a3302b253","source":{"kind":"arxiv","id":"1107.1140","version":4},"attestation_state":"computed","paper":{"title":"Identifying supersingular elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew V. Sutherland","submitted_at":"2011-07-06T14:22:37Z","abstract_excerpt":"Given an elliptic curve E over a field of positive characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing algorithms and then present a new approach that exploits structural differences between ordinary and supersingular isogeny graphs. This yields a simple algorithm that, given E and a suitable non-residue in F_p^2, determines the supersingularity of E in O(n^3 log^2 n) time and O(n) space, where n=O(log p). Both these complexity bounds are significant improvements over existing methods, as we demonstrat"},"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":"1107.1140","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-06T14:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"70cfc01a4ed7eee54d2bec0a678e5cccff213048716af2f01f1c2c974f6c0630","abstract_canon_sha256":"443adff6e9b632a312c951e818de5f1a1bfd1f12e398d974199d7b5a162630ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.320900Z","signature_b64":"tSduok6K3Y69Mc41sjjqDtdc9NtuVpXCD7j6RAlgiqcTS9gM36KMdUvEtIdMjfKpMKX34klpJsrQeNOzfdLMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d545007907065519d993e1e2569a18189e14a620520f5227004cca0a3302b253","last_reissued_at":"2026-05-17T23:53:19.320278Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.320278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identifying supersingular elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew V. Sutherland","submitted_at":"2011-07-06T14:22:37Z","abstract_excerpt":"Given an elliptic curve E over a field of positive characteristic p, we consider how to efficiently determine whether E is ordinary or supersingular. We analyze the complexity of several existing algorithms and then present a new approach that exploits structural differences between ordinary and supersingular isogeny graphs. This yields a simple algorithm that, given E and a suitable non-residue in F_p^2, determines the supersingularity of E in O(n^3 log^2 n) time and O(n) space, where n=O(log p). Both these complexity bounds are significant improvements over existing methods, as we demonstrat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1140","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":"1107.1140","created_at":"2026-05-17T23:53:19.320378+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.1140v4","created_at":"2026-05-17T23:53:19.320378+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1140","created_at":"2026-05-17T23:53:19.320378+00:00"},{"alias_kind":"pith_short_12","alias_value":"2VCQA6IHAZKR","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2VCQA6IHAZKRTWMT","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2VCQA6IH","created_at":"2026-05-18T12:26:18.847500+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/2VCQA6IHAZKRTWMT4HRFNGQYDC","json":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC.json","graph_json":"https://pith.science/api/pith-number/2VCQA6IHAZKRTWMT4HRFNGQYDC/graph.json","events_json":"https://pith.science/api/pith-number/2VCQA6IHAZKRTWMT4HRFNGQYDC/events.json","paper":"https://pith.science/paper/2VCQA6IH"},"agent_actions":{"view_html":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC","download_json":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC.json","view_paper":"https://pith.science/paper/2VCQA6IH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.1140&json=true","fetch_graph":"https://pith.science/api/pith-number/2VCQA6IHAZKRTWMT4HRFNGQYDC/graph.json","fetch_events":"https://pith.science/api/pith-number/2VCQA6IHAZKRTWMT4HRFNGQYDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC/action/storage_attestation","attest_author":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC/action/author_attestation","sign_citation":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC/action/citation_signature","submit_replication":"https://pith.science/pith/2VCQA6IHAZKRTWMT4HRFNGQYDC/action/replication_record"}},"created_at":"2026-05-17T23:53:19.320378+00:00","updated_at":"2026-05-17T23:53:19.320378+00:00"}