{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RBZKZTDPHVKNCNDYMM3PRVVVP2","short_pith_number":"pith:RBZKZTDP","canonical_record":{"source":{"id":"1704.00473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-03T08:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"441342aba3b39b545c465473273f2b99bbb3f415156eee3de53c4b16982fb9c2","abstract_canon_sha256":"7a6a00a1a8f844027c877c6af768e8c42c9f5f4a41eeb759bbfd769ab62cb026"},"schema_version":"1.0"},"canonical_sha256":"8872accc6f3d54d134786336f8d6b57e981798bac985396f9617ffd13107d554","source":{"kind":"arxiv","id":"1704.00473","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00473","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00473v1","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00473","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"RBZKZTDPHVKN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBZKZTDPHVKNCNDY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBZKZTDP","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RBZKZTDPHVKNCNDYMM3PRVVVP2","target":"record","payload":{"canonical_record":{"source":{"id":"1704.00473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-03T08:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"441342aba3b39b545c465473273f2b99bbb3f415156eee3de53c4b16982fb9c2","abstract_canon_sha256":"7a6a00a1a8f844027c877c6af768e8c42c9f5f4a41eeb759bbfd769ab62cb026"},"schema_version":"1.0"},"canonical_sha256":"8872accc6f3d54d134786336f8d6b57e981798bac985396f9617ffd13107d554","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:22.238801Z","signature_b64":"sYczijGWGuBxO/lanQmGZ8mp0SBWujVhn02kaT9WI26szMxgDV/Jx3zCP53E5NkVSxv7ADTiUjTxU0jiYtZ/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8872accc6f3d54d134786336f8d6b57e981798bac985396f9617ffd13107d554","last_reissued_at":"2026-05-18T00:47:22.238203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:22.238203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.00473","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":"2026-05-18T00:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLA5mD88UTU4jqRSslDdzYDPCqUqa0l/epYKEx0Vdq8n5VnWWabRu8z3nOTmMGv83if3++kK932zOZukZBZcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:09:41.481693Z"},"content_sha256":"a86d792e553e5f8854aa08c0a6d91221ad97b2286b2e3f6ab64276d257abd26f","schema_version":"1.0","event_id":"sha256:a86d792e553e5f8854aa08c0a6d91221ad97b2286b2e3f6ab64276d257abd26f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RBZKZTDPHVKNCNDYMM3PRVVVP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic Chabauty for Modular Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samir Siksek","submitted_at":"2017-04-03T08:44:50Z","abstract_excerpt":"Let $X/\\mathbb{Q}$ be a curve of genus $g \\ge 2$ with Jacobian $J$ and let $\\ell$ be a prime of good reduction. Using Selmer varieties, Kim defines a decreasing sequence \\[ X(\\mathbb{Q}_\\ell) \\supseteq X(\\mathbb{Q}_\\ell)_1 \\supseteq X(\\mathbb{Q}_\\ell)_2 \\supseteq \\cdots \\] all containing the rational points of $X$. Thanks to the work of Coleman, the `Chabauty set' $X(\\mathbb{Q}_\\ell)_1$ is known to be finite provided the Mordell--Weil rank of $J$ is smaller than $g$. In this case one has a practical strategy that often succeeds in computing the set of rational points of $X$. Balakrishnan and D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00473","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":"2026-05-18T00:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jz3dwAWZkBSwx6a6o/HGgcFFHNN30/n7vicNvZrqOqvHx8I0zvbXUrX4ql1BZOKovzmtudle5j+/aA5rb+wYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:09:41.482308Z"},"content_sha256":"1d65f828208d243d2e0cb6f2ec4ea213496eef95188a5b8b23866a2657c8a91c","schema_version":"1.0","event_id":"sha256:1d65f828208d243d2e0cb6f2ec4ea213496eef95188a5b8b23866a2657c8a91c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2/bundle.json","state_url":"https://pith.science/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2/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":"2026-08-18T05:09:41Z","links":{"resolver":"https://pith.science/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2","bundle":"https://pith.science/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2/bundle.json","state":"https://pith.science/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBZKZTDPHVKNCNDYMM3PRVVVP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RBZKZTDPHVKNCNDYMM3PRVVVP2","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":"7a6a00a1a8f844027c877c6af768e8c42c9f5f4a41eeb759bbfd769ab62cb026","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-03T08:44:50Z","title_canon_sha256":"441342aba3b39b545c465473273f2b99bbb3f415156eee3de53c4b16982fb9c2"},"schema_version":"1.0","source":{"id":"1704.00473","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00473","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00473v1","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00473","created_at":"2026-05-18T00:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"RBZKZTDPHVKN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBZKZTDPHVKNCNDY","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBZKZTDP","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:1d65f828208d243d2e0cb6f2ec4ea213496eef95188a5b8b23866a2657c8a91c","target":"graph","created_at":"2026-05-18T00:47:22Z","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":"Let $X/\\mathbb{Q}$ be a curve of genus $g \\ge 2$ with Jacobian $J$ and let $\\ell$ be a prime of good reduction. Using Selmer varieties, Kim defines a decreasing sequence \\[ X(\\mathbb{Q}_\\ell) \\supseteq X(\\mathbb{Q}_\\ell)_1 \\supseteq X(\\mathbb{Q}_\\ell)_2 \\supseteq \\cdots \\] all containing the rational points of $X$. Thanks to the work of Coleman, the `Chabauty set' $X(\\mathbb{Q}_\\ell)_1$ is known to be finite provided the Mordell--Weil rank of $J$ is smaller than $g$. In this case one has a practical strategy that often succeeds in computing the set of rational points of $X$. Balakrishnan and D","authors_text":"Samir Siksek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-03T08:44:50Z","title":"Quadratic Chabauty for Modular Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00473","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:a86d792e553e5f8854aa08c0a6d91221ad97b2286b2e3f6ab64276d257abd26f","target":"record","created_at":"2026-05-18T00:47:22Z","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":"7a6a00a1a8f844027c877c6af768e8c42c9f5f4a41eeb759bbfd769ab62cb026","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-03T08:44:50Z","title_canon_sha256":"441342aba3b39b545c465473273f2b99bbb3f415156eee3de53c4b16982fb9c2"},"schema_version":"1.0","source":{"id":"1704.00473","kind":"arxiv","version":1}},"canonical_sha256":"8872accc6f3d54d134786336f8d6b57e981798bac985396f9617ffd13107d554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8872accc6f3d54d134786336f8d6b57e981798bac985396f9617ffd13107d554","first_computed_at":"2026-05-18T00:47:22.238203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:22.238203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sYczijGWGuBxO/lanQmGZ8mp0SBWujVhn02kaT9WI26szMxgDV/Jx3zCP53E5NkVSxv7ADTiUjTxU0jiYtZ/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:22.238801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00473","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a86d792e553e5f8854aa08c0a6d91221ad97b2286b2e3f6ab64276d257abd26f","sha256:1d65f828208d243d2e0cb6f2ec4ea213496eef95188a5b8b23866a2657c8a91c"],"state_sha256":"a8ad039b1e2e48aa79146fa579b4c022d2bff0b6c39df5cddb8521e01a6c9b9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GeXRc/aN0LNOlM/kXwgmkKNMMdgWT+9FDpr9dNwsOkwCVxrNpzCidKDHZ2ZAG/yJEY4+CVTe+2xEGO+cEBpAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T05:09:41.490090Z","bundle_sha256":"ac3e00088e7ebfaa23e9efe8b037687dc1eb38790d7e78b8b48f203e92a5fc7f"}}