{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7EOK5CVBIPYYBNYDPWF5HIQ3OX","short_pith_number":"pith:7EOK5CVB","schema_version":"1.0","canonical_sha256":"f91cae8aa143f180b7037d8bd3a21b75e4ed49d062838cff240cdc9547547598","source":{"kind":"arxiv","id":"1409.3063","version":2},"attestation_state":"computed","paper":{"title":"Automorphisms of the Generalized Fermat curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Aristides Kontogeorgis, Maximiliano Leyton-\\'Alvarez, Panagiotis Paramantzoglou, Rub\\'en A. Hidalgo","submitted_at":"2014-09-10T13:36:19Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic $p \\geq 0$. A generalized Fermat curve of type $(k,n)$, where $k,n \\geq 2$ are integers (for $p \\neq 0$ we also assume that $k$ is relatively prime to $p$), is a non-singular irreducible projective algebraic curve $F_{k,n}$ defined over $K$ admitting a group of automorphisms $H \\cong {\\mathbb Z}_{k}^{n}$ so that $F_{k,n}/H$ is the projective line with exactly $(n+1)$ cone points, each one of order $k$. Such a group $H$ is called a generalized Fermat group of type $(k,n)$. If $(n-1)(k-1)>2$, then $F_{k,n}$ has genus $g_{n,k}>1$ and it 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":"1409.3063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-10T13:36:19Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d740aa69412745e132681b9cfca60256d9af32797fd2c133a8ae677c41dd1059","abstract_canon_sha256":"9aed9cc0219daa7ef3a33b7e54039681ad4851a2baab9101641749cd8e7c4afd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:39.836544Z","signature_b64":"kIKmafAOICyCoX4kOmGy/T7orN6K4vJMwjsj7aisrleX80QZj0/Wa/ZBqGqfBA7mdQ1U7tlOd7Z/Lf3p4x6UDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f91cae8aa143f180b7037d8bd3a21b75e4ed49d062838cff240cdc9547547598","last_reissued_at":"2026-05-18T02:30:39.836047Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:39.836047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the Generalized Fermat curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Aristides Kontogeorgis, Maximiliano Leyton-\\'Alvarez, Panagiotis Paramantzoglou, Rub\\'en A. Hidalgo","submitted_at":"2014-09-10T13:36:19Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic $p \\geq 0$. A generalized Fermat curve of type $(k,n)$, where $k,n \\geq 2$ are integers (for $p \\neq 0$ we also assume that $k$ is relatively prime to $p$), is a non-singular irreducible projective algebraic curve $F_{k,n}$ defined over $K$ admitting a group of automorphisms $H \\cong {\\mathbb Z}_{k}^{n}$ so that $F_{k,n}/H$ is the projective line with exactly $(n+1)$ cone points, each one of order $k$. Such a group $H$ is called a generalized Fermat group of type $(k,n)$. If $(n-1)(k-1)>2$, then $F_{k,n}$ has genus $g_{n,k}>1$ and it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3063","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":"1409.3063","created_at":"2026-05-18T02:30:39.836129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.3063v2","created_at":"2026-05-18T02:30:39.836129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3063","created_at":"2026-05-18T02:30:39.836129+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EOK5CVBIPYY","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EOK5CVBIPYYBNYD","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EOK5CVB","created_at":"2026-05-18T12:28:16.859392+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/7EOK5CVBIPYYBNYDPWF5HIQ3OX","json":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX.json","graph_json":"https://pith.science/api/pith-number/7EOK5CVBIPYYBNYDPWF5HIQ3OX/graph.json","events_json":"https://pith.science/api/pith-number/7EOK5CVBIPYYBNYDPWF5HIQ3OX/events.json","paper":"https://pith.science/paper/7EOK5CVB"},"agent_actions":{"view_html":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX","download_json":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX.json","view_paper":"https://pith.science/paper/7EOK5CVB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.3063&json=true","fetch_graph":"https://pith.science/api/pith-number/7EOK5CVBIPYYBNYDPWF5HIQ3OX/graph.json","fetch_events":"https://pith.science/api/pith-number/7EOK5CVBIPYYBNYDPWF5HIQ3OX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX/action/storage_attestation","attest_author":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX/action/author_attestation","sign_citation":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX/action/citation_signature","submit_replication":"https://pith.science/pith/7EOK5CVBIPYYBNYDPWF5HIQ3OX/action/replication_record"}},"created_at":"2026-05-18T02:30:39.836129+00:00","updated_at":"2026-05-18T02:30:39.836129+00:00"}