{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:JVQ5PTGKITR2KBUO457VZDABOB","short_pith_number":"pith:JVQ5PTGK","canonical_record":{"source":{"id":"0903.4963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-28T11:32:35Z","cross_cats_sorted":[],"title_canon_sha256":"d580dfdae9cf1952f66ff5f15620e3b8ee0f7f5ee8791879c6ccba82e40c74cd","abstract_canon_sha256":"eff5c46f81d96d615b162f06afc5fca8d5302b126d3fa739e6475a6b6e77e93b"},"schema_version":"1.0"},"canonical_sha256":"4d61d7ccca44e3a5068ee77f5c8c01707f031c25fa67b28df10aed173864ff4d","source":{"kind":"arxiv","id":"0903.4963","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4963","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4963v3","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4963","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"JVQ5PTGKITR2","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JVQ5PTGKITR2KBUO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JVQ5PTGK","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:JVQ5PTGKITR2KBUO457VZDABOB","target":"record","payload":{"canonical_record":{"source":{"id":"0903.4963","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-28T11:32:35Z","cross_cats_sorted":[],"title_canon_sha256":"d580dfdae9cf1952f66ff5f15620e3b8ee0f7f5ee8791879c6ccba82e40c74cd","abstract_canon_sha256":"eff5c46f81d96d615b162f06afc5fca8d5302b126d3fa739e6475a6b6e77e93b"},"schema_version":"1.0"},"canonical_sha256":"4d61d7ccca44e3a5068ee77f5c8c01707f031c25fa67b28df10aed173864ff4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:33.369502Z","signature_b64":"ddCuSugri2eDIXR4kZcWWmrBM2Z7wrPNg6UO56r8SgnBbdSItlMkaSQnagmpONy96z8s/M9XwOQN3OPUAYeLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d61d7ccca44e3a5068ee77f5c8c01707f031c25fa67b28df10aed173864ff4d","last_reissued_at":"2026-05-18T01:37:33.368915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:33.368915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.4963","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rpm+cdJsjlzE44f8HjSny2XmdaP1HrU7oKObZNmRsof94/IYRjGD8FQLippSc+6rJzVyrKSCXbtaG4Jpt+XSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:34:42.705891Z"},"content_sha256":"bccd8104ce5af3a52a9222af0f43009a7355e19c1a6ed7567ae59821eb414060","schema_version":"1.0","event_id":"sha256:bccd8104ce5af3a52a9222af0f43009a7355e19c1a6ed7567ae59821eb414060"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:JVQ5PTGKITR2KBUO457VZDABOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elementary 3-descent with a 3-isogeny","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabien Pazuki, Henri Cohen","submitted_at":"2009-03-28T11:32:35Z","abstract_excerpt":"In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and we also give a geometric interpretation of these computations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4963","kind":"arxiv","version":3},"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":"2026-05-18T01:37:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcsIOm5+9jDdDBkEMs9lfRQMnGxAUqRHpycvwKio2yvL0n65jWhyMwSIpoYActSr3tulwglWNQzA5NPuIfcsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:34:42.706232Z"},"content_sha256":"51045dd0d943bceb2de8022fb020daee6f1f9546df21484acf72f7b9deebd5d1","schema_version":"1.0","event_id":"sha256:51045dd0d943bceb2de8022fb020daee6f1f9546df21484acf72f7b9deebd5d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVQ5PTGKITR2KBUO457VZDABOB/bundle.json","state_url":"https://pith.science/pith/JVQ5PTGKITR2KBUO457VZDABOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVQ5PTGKITR2KBUO457VZDABOB/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":"2026-06-02T07:34:42Z","links":{"resolver":"https://pith.science/pith/JVQ5PTGKITR2KBUO457VZDABOB","bundle":"https://pith.science/pith/JVQ5PTGKITR2KBUO457VZDABOB/bundle.json","state":"https://pith.science/pith/JVQ5PTGKITR2KBUO457VZDABOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVQ5PTGKITR2KBUO457VZDABOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JVQ5PTGKITR2KBUO457VZDABOB","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":"eff5c46f81d96d615b162f06afc5fca8d5302b126d3fa739e6475a6b6e77e93b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-28T11:32:35Z","title_canon_sha256":"d580dfdae9cf1952f66ff5f15620e3b8ee0f7f5ee8791879c6ccba82e40c74cd"},"schema_version":"1.0","source":{"id":"0903.4963","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4963","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4963v3","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4963","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"JVQ5PTGKITR2","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JVQ5PTGKITR2KBUO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JVQ5PTGK","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:51045dd0d943bceb2de8022fb020daee6f1f9546df21484acf72f7b9deebd5d1","target":"graph","created_at":"2026-05-18T01:37:33Z","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":"In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and we also give a geometric interpretation of these computations.","authors_text":"Fabien Pazuki, Henri Cohen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-28T11:32:35Z","title":"Elementary 3-descent with a 3-isogeny"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4963","kind":"arxiv","version":3},"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:bccd8104ce5af3a52a9222af0f43009a7355e19c1a6ed7567ae59821eb414060","target":"record","created_at":"2026-05-18T01:37:33Z","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":"eff5c46f81d96d615b162f06afc5fca8d5302b126d3fa739e6475a6b6e77e93b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-28T11:32:35Z","title_canon_sha256":"d580dfdae9cf1952f66ff5f15620e3b8ee0f7f5ee8791879c6ccba82e40c74cd"},"schema_version":"1.0","source":{"id":"0903.4963","kind":"arxiv","version":3}},"canonical_sha256":"4d61d7ccca44e3a5068ee77f5c8c01707f031c25fa67b28df10aed173864ff4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d61d7ccca44e3a5068ee77f5c8c01707f031c25fa67b28df10aed173864ff4d","first_computed_at":"2026-05-18T01:37:33.368915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:33.368915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ddCuSugri2eDIXR4kZcWWmrBM2Z7wrPNg6UO56r8SgnBbdSItlMkaSQnagmpONy96z8s/M9XwOQN3OPUAYeLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:33.369502Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4963","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bccd8104ce5af3a52a9222af0f43009a7355e19c1a6ed7567ae59821eb414060","sha256:51045dd0d943bceb2de8022fb020daee6f1f9546df21484acf72f7b9deebd5d1"],"state_sha256":"9aafcc350a0d562dfc1b9dbac46a44e23f013bde39026ac0642c01f58056d364"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vm71up8aikX8kh77tT/eZtIfeGDZspeg8+NENjbo7cRJLnDF5yU1ZVb8187xH5Aoz/LdewXklbq1xTEWUKa+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:34:42.708283Z","bundle_sha256":"cdb2aa311892721dcd3fe7dd8daeabb761214349499acae1781660d8a8b55612"}}