{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:7VRLYWKGBYL6CNOYCFCYXQU66A","short_pith_number":"pith:7VRLYWKG","canonical_record":{"source":{"id":"math/0610318","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-10-10T12:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"e0a70f1f71469e0e4d14dc65ec57d499b965d8679350798037035d43e0ac3594","abstract_canon_sha256":"7a37099681eb23948ad6c43044da82a981c3ba5b95559b7592b9ed1716b364fd"},"schema_version":"1.0"},"canonical_sha256":"fd62bc59460e17e135d811458bc29ef00f208e27bc6be2c3f91cbe1a0f328607","source":{"kind":"arxiv","id":"math/0610318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610318","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610318v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610318","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"7VRLYWKGBYL6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7VRLYWKGBYL6CNOY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7VRLYWKG","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:7VRLYWKGBYL6CNOYCFCYXQU66A","target":"record","payload":{"canonical_record":{"source":{"id":"math/0610318","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-10-10T12:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"e0a70f1f71469e0e4d14dc65ec57d499b965d8679350798037035d43e0ac3594","abstract_canon_sha256":"7a37099681eb23948ad6c43044da82a981c3ba5b95559b7592b9ed1716b364fd"},"schema_version":"1.0"},"canonical_sha256":"fd62bc59460e17e135d811458bc29ef00f208e27bc6be2c3f91cbe1a0f328607","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.476941Z","signature_b64":"4xa8IfjKSz6mH9D28iISjX3mUVU10AQOxZBXZU+lWDZj9+pET3XKCUE7z/Tcy4c9NZDOUVBTmjDhs9YtwqkLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd62bc59460e17e135d811458bc29ef00f208e27bc6be2c3f91cbe1a0f328607","last_reissued_at":"2026-05-18T02:57:45.476341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.476341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0610318","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4kS7JGEYLQhpSt3eE7uxEu37DlUtpPRB2pjC37LeqNfkJEiMCR6qelM5vF6GH+KfFrLhYFsfGoCXlLY5BZhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:57:47.813079Z"},"content_sha256":"443a07f165909bf4b3935c5519e00c6271e294259d8c36533454dddd7518fae2","schema_version":"1.0","event_id":"sha256:443a07f165909bf4b3935c5519e00c6271e294259d8c36533454dddd7518fae2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:7VRLYWKGBYL6CNOYCFCYXQU66A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The invariants of a genus one curve","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tom Fisher","submitted_at":"2006-10-10T12:46:35Z","abstract_excerpt":"It was first pointed out by Weil that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n = 2,3,4 were already known to the nineteenth centuary invariant theorists. We have succeeded in extending these methods to curves of degree n = 5, where although the invariants are too large to write down as explicit polynomials, we have found a practical algorithm for evaluating them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610318","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qvKzSMaLYzkU3QnhQSif68vH805rXErZ4hCtA9kzFOWB9WnGIK3T7tLSQQoNaekJYMe0xC1EqdB93UDoPVh1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:57:47.813426Z"},"content_sha256":"38953020d8532ee14ade0b6a9681a342f5852d7b41ab9ab9114f1df79f93c69f","schema_version":"1.0","event_id":"sha256:38953020d8532ee14ade0b6a9681a342f5852d7b41ab9ab9114f1df79f93c69f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VRLYWKGBYL6CNOYCFCYXQU66A/bundle.json","state_url":"https://pith.science/pith/7VRLYWKGBYL6CNOYCFCYXQU66A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VRLYWKGBYL6CNOYCFCYXQU66A/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T02:57:47Z","links":{"resolver":"https://pith.science/pith/7VRLYWKGBYL6CNOYCFCYXQU66A","bundle":"https://pith.science/pith/7VRLYWKGBYL6CNOYCFCYXQU66A/bundle.json","state":"https://pith.science/pith/7VRLYWKGBYL6CNOYCFCYXQU66A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VRLYWKGBYL6CNOYCFCYXQU66A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:7VRLYWKGBYL6CNOYCFCYXQU66A","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":"7a37099681eb23948ad6c43044da82a981c3ba5b95559b7592b9ed1716b364fd","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-10-10T12:46:35Z","title_canon_sha256":"e0a70f1f71469e0e4d14dc65ec57d499b965d8679350798037035d43e0ac3594"},"schema_version":"1.0","source":{"id":"math/0610318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0610318","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0610318v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610318","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"7VRLYWKGBYL6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"7VRLYWKGBYL6CNOY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"7VRLYWKG","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:38953020d8532ee14ade0b6a9681a342f5852d7b41ab9ab9114f1df79f93c69f","target":"graph","created_at":"2026-05-18T02:57:45Z","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 was first pointed out by Weil that we can use classical invariant theory to compute the Jacobian of a genus one curve. The invariants required for curves of degree n = 2,3,4 were already known to the nineteenth centuary invariant theorists. We have succeeded in extending these methods to curves of degree n = 5, where although the invariants are too large to write down as explicit polynomials, we have found a practical algorithm for evaluating them.","authors_text":"Tom Fisher","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-10-10T12:46:35Z","title":"The invariants of a genus one curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610318","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":"sha256:443a07f165909bf4b3935c5519e00c6271e294259d8c36533454dddd7518fae2","target":"record","created_at":"2026-05-18T02:57:45Z","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":"7a37099681eb23948ad6c43044da82a981c3ba5b95559b7592b9ed1716b364fd","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-10-10T12:46:35Z","title_canon_sha256":"e0a70f1f71469e0e4d14dc65ec57d499b965d8679350798037035d43e0ac3594"},"schema_version":"1.0","source":{"id":"math/0610318","kind":"arxiv","version":1}},"canonical_sha256":"fd62bc59460e17e135d811458bc29ef00f208e27bc6be2c3f91cbe1a0f328607","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd62bc59460e17e135d811458bc29ef00f208e27bc6be2c3f91cbe1a0f328607","first_computed_at":"2026-05-18T02:57:45.476341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.476341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4xa8IfjKSz6mH9D28iISjX3mUVU10AQOxZBXZU+lWDZj9+pET3XKCUE7z/Tcy4c9NZDOUVBTmjDhs9YtwqkLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.476941Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0610318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:443a07f165909bf4b3935c5519e00c6271e294259d8c36533454dddd7518fae2","sha256:38953020d8532ee14ade0b6a9681a342f5852d7b41ab9ab9114f1df79f93c69f"],"state_sha256":"6d088cfc977ca074cc4f311bacb434039b83bb01fa9cd4643d7eb7ae42b96cc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8K+s3eJL2/6OB49H+0lc6tqMpPLYHmSjhBNeWSn1v0Atg72BQpxFJQ4NWZ2/1FPVdyPeR7pDQfWMRPYUgjlSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:57:47.815331Z","bundle_sha256":"04c517e014ca7ea0e4ef85fd29b5ee45e54c6c13db90a7400347d75727e5909f"}}