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When $d$ is divisible by $r$ and of the form $p^\\nu +1$, and $K_d := \\mathbb{F}_p(\\mu_d,t^{1/d})$, we write down explicit points in $J(K_d)$, show that t"},"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":"1505.00021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-30T20:24:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"70951c4f135233f8f035bc7ebe95eac2c63f2394a5de17a0dab3f3043811a5a4","abstract_canon_sha256":"b7a3a613d7b77b2730260249724a1e6b3164acdc1836ad0b9602f949f2e6dad8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:42.699484Z","signature_b64":"ID8+E8lD85CgHOEmpj2nveHnJYydK0uLlm6Qwf/HWq1ieAmDRzuntUXkha9j/5gQnMpkBHFHp6NpjiA58Wa7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5627d929571c694b954439071c8d21b07b7047cb3daa5cf98c5a67c4ee9b7540","last_reissued_at":"2026-05-18T00:44:42.699086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:42.699086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alice Silverberg, Chris Hall, Douglas Ulmer, Jennifer Park, Lisa Berger, Rachel Pries, Ren\\'e Pannekoek, Shahed Sharif","submitted_at":"2015-04-30T20:24:30Z","abstract_excerpt":"We study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^{r-1}(x + 1)(x + t)$ over the function field $\\mathbb{F}_p(t)$, when $p$ is prime and $r\\ge 2$ is an integer prime to $p$. 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When $d$ is divisible by $r$ and of the form $p^\\nu +1$, and $K_d := \\mathbb{F}_p(\\mu_d,t^{1/d})$, we write down explicit points in $J(K_d)$, show that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00021","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":"1505.00021","created_at":"2026-05-18T00:44:42.699151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00021v2","created_at":"2026-05-18T00:44:42.699151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00021","created_at":"2026-05-18T00:44:42.699151+00:00"},{"alias_kind":"pith_short_12","alias_value":"KYT5SKKXDRUU","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KYT5SKKXDRUUXFKE","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KYT5SKKX","created_at":"2026-05-18T12:29:29.992203+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/KYT5SKKXDRUUXFKEHEDRZDJBWB","json":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB.json","graph_json":"https://pith.science/api/pith-number/KYT5SKKXDRUUXFKEHEDRZDJBWB/graph.json","events_json":"https://pith.science/api/pith-number/KYT5SKKXDRUUXFKEHEDRZDJBWB/events.json","paper":"https://pith.science/paper/KYT5SKKX"},"agent_actions":{"view_html":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB","download_json":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB.json","view_paper":"https://pith.science/paper/KYT5SKKX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00021&json=true","fetch_graph":"https://pith.science/api/pith-number/KYT5SKKXDRUUXFKEHEDRZDJBWB/graph.json","fetch_events":"https://pith.science/api/pith-number/KYT5SKKXDRUUXFKEHEDRZDJBWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB/action/storage_attestation","attest_author":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB/action/author_attestation","sign_citation":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB/action/citation_signature","submit_replication":"https://pith.science/pith/KYT5SKKXDRUUXFKEHEDRZDJBWB/action/replication_record"}},"created_at":"2026-05-18T00:44:42.699151+00:00","updated_at":"2026-05-18T00:44:42.699151+00:00"}