{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NV73FJCKGM6675IK2YZFKADAT7","short_pith_number":"pith:NV73FJCK","canonical_record":{"source":{"id":"1702.01985","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-07T12:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"abd2dd269e9a10eace1bf6cb68a0519e28fc4ee28aa20965bf62a43c9612a07b","abstract_canon_sha256":"ec83e633dd401d1f0880ed0c7260f81390e1f7439ea35d16f6e12465d2679c09"},"schema_version":"1.0"},"canonical_sha256":"6d7fb2a44a333deff50ad6325500609fcf662f6b67d893944d26645563080505","source":{"kind":"arxiv","id":"1702.01985","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01985","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01985v2","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01985","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"NV73FJCKGM66","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NV73FJCKGM6675IK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NV73FJCK","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NV73FJCKGM6675IK2YZFKADAT7","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01985","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-07T12:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"abd2dd269e9a10eace1bf6cb68a0519e28fc4ee28aa20965bf62a43c9612a07b","abstract_canon_sha256":"ec83e633dd401d1f0880ed0c7260f81390e1f7439ea35d16f6e12465d2679c09"},"schema_version":"1.0"},"canonical_sha256":"6d7fb2a44a333deff50ad6325500609fcf662f6b67d893944d26645563080505","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:06.268034Z","signature_b64":"fXGxQh6UEYKAlVZMBHi8n2k4+Om0LOmID+aLA1apJE0LGRRW14o/3FS96v5EOIj7MUCYmdPg7uOxZKASAwF4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d7fb2a44a333deff50ad6325500609fcf662f6b67d893944d26645563080505","last_reissued_at":"2026-05-18T00:49:06.267610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:06.267610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01985","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1OaVxixU3rwuvtJPoyiAQ8uXjNNcSuO2b5n4XYsoiOUWcN3l2aO54WD428veyE4ZBLjQ915Dr2cZUWkVhcdhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:32:19.103833Z"},"content_sha256":"81755a8daa090070fc241fd2f01f23eb8be27a92f06ae70582341d747b57fdc3","schema_version":"1.0","event_id":"sha256:81755a8daa090070fc241fd2f01f23eb8be27a92f06ae70582341d747b57fdc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NV73FJCKGM6675IK2YZFKADAT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Serre's Uniformity Conjecture for Elliptic Curves with Rational Cyclic Isogenies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pedro Lemos","submitted_at":"2017-02-07T12:42:24Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ such that $\\mathrm{End}_{\\bar{\\mathbb{Q}}}(E)=\\mathbb{Z}$ and which admits a non-trivial cyclic $\\mathbb{Q}$-isogeny. We prove that, for $p>37$, the residual mod $p$ Galois representation $\\bar{\\rho}_{E,p}:G_{\\mathbb{Q}}\\rightarrow\\mathrm{GL}_2(\\mathbb{F}_p)$ is surjective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01985","kind":"arxiv","version":2},"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":"2026-05-18T00:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjszOLBy12fJ8ZFiyV8rKGpuLV1oIxDoe2bxEuMaW9ndZHoaNQqOiRQuGf+h986cjwBpO+tAYJPsAp8aBzWfAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:32:19.104443Z"},"content_sha256":"fa4c9cf720832bba16f1bf563afdc19cd3ec07c3cdfe3f44739dc329dd643435","schema_version":"1.0","event_id":"sha256:fa4c9cf720832bba16f1bf563afdc19cd3ec07c3cdfe3f44739dc329dd643435"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NV73FJCKGM6675IK2YZFKADAT7/bundle.json","state_url":"https://pith.science/pith/NV73FJCKGM6675IK2YZFKADAT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NV73FJCKGM6675IK2YZFKADAT7/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":"2026-06-30T23:32:19Z","links":{"resolver":"https://pith.science/pith/NV73FJCKGM6675IK2YZFKADAT7","bundle":"https://pith.science/pith/NV73FJCKGM6675IK2YZFKADAT7/bundle.json","state":"https://pith.science/pith/NV73FJCKGM6675IK2YZFKADAT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NV73FJCKGM6675IK2YZFKADAT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NV73FJCKGM6675IK2YZFKADAT7","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":"ec83e633dd401d1f0880ed0c7260f81390e1f7439ea35d16f6e12465d2679c09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-07T12:42:24Z","title_canon_sha256":"abd2dd269e9a10eace1bf6cb68a0519e28fc4ee28aa20965bf62a43c9612a07b"},"schema_version":"1.0","source":{"id":"1702.01985","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01985","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01985v2","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01985","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"NV73FJCKGM66","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NV73FJCKGM6675IK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NV73FJCK","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:fa4c9cf720832bba16f1bf563afdc19cd3ec07c3cdfe3f44739dc329dd643435","target":"graph","created_at":"2026-05-18T00:49:06Z","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 $E$ be an elliptic curve over $\\mathbb{Q}$ such that $\\mathrm{End}_{\\bar{\\mathbb{Q}}}(E)=\\mathbb{Z}$ and which admits a non-trivial cyclic $\\mathbb{Q}$-isogeny. We prove that, for $p>37$, the residual mod $p$ Galois representation $\\bar{\\rho}_{E,p}:G_{\\mathbb{Q}}\\rightarrow\\mathrm{GL}_2(\\mathbb{F}_p)$ is surjective.","authors_text":"Pedro Lemos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-07T12:42:24Z","title":"Serre's Uniformity Conjecture for Elliptic Curves with Rational Cyclic Isogenies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01985","kind":"arxiv","version":2},"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":"sha256:81755a8daa090070fc241fd2f01f23eb8be27a92f06ae70582341d747b57fdc3","target":"record","created_at":"2026-05-18T00:49:06Z","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":"ec83e633dd401d1f0880ed0c7260f81390e1f7439ea35d16f6e12465d2679c09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-07T12:42:24Z","title_canon_sha256":"abd2dd269e9a10eace1bf6cb68a0519e28fc4ee28aa20965bf62a43c9612a07b"},"schema_version":"1.0","source":{"id":"1702.01985","kind":"arxiv","version":2}},"canonical_sha256":"6d7fb2a44a333deff50ad6325500609fcf662f6b67d893944d26645563080505","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d7fb2a44a333deff50ad6325500609fcf662f6b67d893944d26645563080505","first_computed_at":"2026-05-18T00:49:06.267610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:06.267610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fXGxQh6UEYKAlVZMBHi8n2k4+Om0LOmID+aLA1apJE0LGRRW14o/3FS96v5EOIj7MUCYmdPg7uOxZKASAwF4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:06.268034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01985","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81755a8daa090070fc241fd2f01f23eb8be27a92f06ae70582341d747b57fdc3","sha256:fa4c9cf720832bba16f1bf563afdc19cd3ec07c3cdfe3f44739dc329dd643435"],"state_sha256":"830a0768d359cc4996f7c60229a9938d13431ef082a79fdb8d4d760477724bbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GD6FXagIaui6JVb+Rp3tCDnO8h3H/EPn+m5auieewhQw7yDnaOmfL4Zy6DFGurV/NRn0R4UgF4dRLyPU/+RnCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:32:19.107543Z","bundle_sha256":"a7c2d1128bdad8a3c6228f8aa480225dae941fba167a0c2139b7eb3436dfa5c9"}}