{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:2HQTOPMX3W2BCMNOG7YPSZQ3TN","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":"37ca0a73bacf3e947b592d705b201fa8e772c6898562907ad13d9f0535034424","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-03-29T06:36:45Z","title_canon_sha256":"b15074aa1ba7aa674c43af81eb0b5782126a9d92c415d46810a98be5eb6bcc60"},"schema_version":"1.0","source":{"id":"alg-geom/9603024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9603024","created_at":"2026-07-04T15:08:05Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9603024v1","created_at":"2026-07-04T15:08:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9603024","created_at":"2026-07-04T15:08:05Z"},{"alias_kind":"pith_short_12","alias_value":"2HQTOPMX3W2B","created_at":"2026-07-04T15:08:05Z"},{"alias_kind":"pith_short_16","alias_value":"2HQTOPMX3W2BCMNO","created_at":"2026-07-04T15:08:05Z"},{"alias_kind":"pith_short_8","alias_value":"2HQTOPMX","created_at":"2026-07-04T15:08:05Z"}],"graph_snapshots":[{"event_id":"sha256:89b7b5ce10db146aade5376dd5c01779d6b85efbf8e1871b6c0ac075f0f32bb0","target":"graph","created_at":"2026-07-04T15:08:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/alg-geom/9603024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of $d$-gonality of the modular curve $X_0(N)$. As a result, we can give an upperbound of the level $N$ by means of $d$. This generalizes Ogg's result on hyperelliptic modular curves ($d = 2$). As a corollary of this result, we prove an analogue of the strong Uniform Boundedness Conjecture for elliptic curves defined over the function fields of curves. If a base curve is $d$-gonal, we can bound orders of torsions of Mordell-Weil groups in terms of $d$ uniformly.","authors_text":"Khac Viet Nguyen, Masa-Hiko Saito","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1996-03-29T06:36:45Z","title":"d-gonality of modular curves and bounding torsions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9603024","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:db62bed0962ab436cd5007361c7f72d506bcf56f8400d01543397188b0e8f582","target":"record","created_at":"2026-07-04T15:08:05Z","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":"37ca0a73bacf3e947b592d705b201fa8e772c6898562907ad13d9f0535034424","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-03-29T06:36:45Z","title_canon_sha256":"b15074aa1ba7aa674c43af81eb0b5782126a9d92c415d46810a98be5eb6bcc60"},"schema_version":"1.0","source":{"id":"alg-geom/9603024","kind":"arxiv","version":1}},"canonical_sha256":"d1e1373d97ddb41131ae37f0f9661b9b5151a35d1e3d43cb31b252acf7486fbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1e1373d97ddb41131ae37f0f9661b9b5151a35d1e3d43cb31b252acf7486fbc","first_computed_at":"2026-07-04T15:08:05.757569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:05.757569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qB0heN4fRvT8NiVcp+/WbInbA5TgjRVWJE05NupvtaaSdptUodAe9buhIpGxIwalSPVegoyBD/0XBNTO2sIaCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:05.757934Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9603024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db62bed0962ab436cd5007361c7f72d506bcf56f8400d01543397188b0e8f582","sha256:89b7b5ce10db146aade5376dd5c01779d6b85efbf8e1871b6c0ac075f0f32bb0"],"state_sha256":"6731344b4d7d29024880fde99974a69f44bb9c990ce86f83f035973e3017ee3e"}