{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GXNI3K6M5GRPWAAN6QAPXBFVZV","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":"a164fa37d9d9c87f490549dc04e571f4751f25f011583d508805c2cdb4a0b994","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.AG","submitted_at":"2006-01-07T18:51:44Z","title_canon_sha256":"3b33c58dd809e1868f24a23f7f39ff810d16599ab6c4bea6d425b546aff53904"},"schema_version":"1.0","source":{"id":"math/0601141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601141","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601141v2","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601141","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"GXNI3K6M5GRP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"GXNI3K6M5GRPWAAN","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"GXNI3K6M","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:96deb02f8a9175703f6dfc8a6edaed0896947053ec53e9c977ec8648988f9620","target":"graph","created_at":"2026-05-18T00:47:31Z","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 k be an algebraically closed field of characteristic p. Let X(p^e;N) be the curve parameterizing elliptic curves with full level N structure (where p does not divide N) and full level p^e Igusa structure. By modular curve, we mean a quotient of any X(p^e;N) by any subgroup of ((Z/p^e Z)^* x \\SL_2(Z/NZ))/{+-1}. We prove that in any sequence of distinct modular curves over k, the k-gonality tends to infinity. This extends earlier work, in which the result was proved for particular sequences of modular curves, such as X_0(N) for p not dividing N. We give an application to the function field a","authors_text":"Bjorn Poonen","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2006-01-07T18:51:44Z","title":"Gonality of modular curves in characteristic p"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601141","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:f47f4b2ca470e803cbdbc01e71efb78edc9f740d8494a7198891caced01d4dd5","target":"record","created_at":"2026-05-18T00:47:31Z","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":"a164fa37d9d9c87f490549dc04e571f4751f25f011583d508805c2cdb4a0b994","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.AG","submitted_at":"2006-01-07T18:51:44Z","title_canon_sha256":"3b33c58dd809e1868f24a23f7f39ff810d16599ab6c4bea6d425b546aff53904"},"schema_version":"1.0","source":{"id":"math/0601141","kind":"arxiv","version":2}},"canonical_sha256":"35da8dabcce9a2fb000df400fb84b5cd634dcace861e006eceb712ba164d931e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35da8dabcce9a2fb000df400fb84b5cd634dcace861e006eceb712ba164d931e","first_computed_at":"2026-05-18T00:47:31.992463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:31.992463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sg4NHDHKe7nlszqdek7BHWzgGm9HFkSCN66RD/ZtRBhdMOKIYmp0CZgVlh4RPnrtVSOj857YNvwd7OC0FM8hCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:31.992924Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f47f4b2ca470e803cbdbc01e71efb78edc9f740d8494a7198891caced01d4dd5","sha256:96deb02f8a9175703f6dfc8a6edaed0896947053ec53e9c977ec8648988f9620"],"state_sha256":"fe0e4aea2dc35878df78a4e19c8e1411a800c0bd4ac0c1dec0771337c839eae4"}