{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YOSO6SUUJ5PNHSAGNFGQ67LRZS","short_pith_number":"pith:YOSO6SUU","schema_version":"1.0","canonical_sha256":"c3a4ef4a944f5ed3c806694d0f7d71cc9b30fb5804cc37025a8af693505fe0cf","source":{"kind":"arxiv","id":"1403.7168","version":2},"attestation_state":"computed","paper":{"title":"P-torsion monodromy representations of elliptic curves over geometric function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Benjamin Bakker, Jacob Tsimerman","submitted_at":"2014-03-27T18:46:06Z","abstract_excerpt":"Given a complex quasiprojective curve $B$ and a non-isotrivial family $\\mathcal{E}$ of elliptic curves over $B$, the $p$-torsion $\\mathcal{E}[p]$ yields a monodromy representation $\\rho_\\mathcal{E}[p]:\\pi_1(B)\\rightarrow \\mathrm{GL}_2(\\mathbb{F}_p)$. We prove that if $\\rho_{\\mathcal E}[p]\\cong \\rho_{\\mathcal E'}[p]$ then $\\mathcal{E}$ and $\\mathcal E'$ are isogenous, provided $p$ is larger than a constant depending only on the gonality of $B$. This can be viewed as a function field analog of the Frey--Mazur conjecture, which states that an elliptic curve over $\\mathbb{Q}$ is determined up to i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.7168","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-27T18:46:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"62a0c2695a17c73cb38861e61a5e8994cdc5f0098fc2009508d854f011093672","abstract_canon_sha256":"f4e58c10ed9117ce125510258fd98fdc1988bba19d5054042acb8f678bc5bb64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:53.511820Z","signature_b64":"ek7O2uWhg8VYZSy4yEE1ivUgNBymZ5a4h5ergvjXzYvLRQ3Awh9FgAF9tjpqFZf6t8ghhfdmJD/Vxe7cK/vTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3a4ef4a944f5ed3c806694d0f7d71cc9b30fb5804cc37025a8af693505fe0cf","last_reissued_at":"2026-05-18T01:15:53.511167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:53.511167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"P-torsion monodromy representations of elliptic curves over geometric function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Benjamin Bakker, Jacob Tsimerman","submitted_at":"2014-03-27T18:46:06Z","abstract_excerpt":"Given a complex quasiprojective curve $B$ and a non-isotrivial family $\\mathcal{E}$ of elliptic curves over $B$, the $p$-torsion $\\mathcal{E}[p]$ yields a monodromy representation $\\rho_\\mathcal{E}[p]:\\pi_1(B)\\rightarrow \\mathrm{GL}_2(\\mathbb{F}_p)$. We prove that if $\\rho_{\\mathcal E}[p]\\cong \\rho_{\\mathcal E'}[p]$ then $\\mathcal{E}$ and $\\mathcal E'$ are isogenous, provided $p$ is larger than a constant depending only on the gonality of $B$. This can be viewed as a function field analog of the Frey--Mazur conjecture, which states that an elliptic curve over $\\mathbb{Q}$ is determined up to i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7168","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.7168","created_at":"2026-05-18T01:15:53.511257+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7168v2","created_at":"2026-05-18T01:15:53.511257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7168","created_at":"2026-05-18T01:15:53.511257+00:00"},{"alias_kind":"pith_short_12","alias_value":"YOSO6SUUJ5PN","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YOSO6SUUJ5PNHSAG","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YOSO6SUU","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS","json":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS.json","graph_json":"https://pith.science/api/pith-number/YOSO6SUUJ5PNHSAGNFGQ67LRZS/graph.json","events_json":"https://pith.science/api/pith-number/YOSO6SUUJ5PNHSAGNFGQ67LRZS/events.json","paper":"https://pith.science/paper/YOSO6SUU"},"agent_actions":{"view_html":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS","download_json":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS.json","view_paper":"https://pith.science/paper/YOSO6SUU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7168&json=true","fetch_graph":"https://pith.science/api/pith-number/YOSO6SUUJ5PNHSAGNFGQ67LRZS/graph.json","fetch_events":"https://pith.science/api/pith-number/YOSO6SUUJ5PNHSAGNFGQ67LRZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS/action/storage_attestation","attest_author":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS/action/author_attestation","sign_citation":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS/action/citation_signature","submit_replication":"https://pith.science/pith/YOSO6SUUJ5PNHSAGNFGQ67LRZS/action/replication_record"}},"created_at":"2026-05-18T01:15:53.511257+00:00","updated_at":"2026-05-18T01:15:53.511257+00:00"}