{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:37FMX6VGR3RBDOSNYVXSO2I3K2","short_pith_number":"pith:37FMX6VG","schema_version":"1.0","canonical_sha256":"dfcacbfaa68ee211ba4dc56f27691b56a897bfc476745868776a171ca9fcd918","source":{"kind":"arxiv","id":"1702.08812","version":2},"attestation_state":"computed","paper":{"title":"Algebraic curves with many automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2017-02-28T15:06:21Z","abstract_excerpt":"Let $X$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \\ge 2$ defined over an algebraically closed field $K$ of odd characteristic $p$. Let $Aut(X)$ be the group of all automorphisms of $X$ which fix $K$ element-wise. It is known that if $|Aut(X)|\\geq 8g^3$ then the $p$-rank (equivalently, the Hasse-Witt invariant) of $X$ is zero. This raises the problem of determining the (minimum-value) function $f(g)$ such that whenever $|Aut(X)|\\geq f(g)$ then $X$ has zero $p$-rank. For {\\em{even}} $g$ we prove that $f(g)\\leq 900 g^2$. The {\\em{odd}} genus case appear"},"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":"1702.08812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-28T15:06:21Z","cross_cats_sorted":[],"title_canon_sha256":"0ac2fbb979a94307772cddb3ae800004b5f0745e7585f969baf8115c37cc8156","abstract_canon_sha256":"e1d4fc323fcffbbe059cdc91fbc182f8efa141df866d6f0fc4e0b1abc295e83a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.258054Z","signature_b64":"sj6Z3kAbGj3G37LG9tLy3UPRaxOZm55ip0OAmZ6QWp4JKDnJyP4UmcCYLIBuMpYwbRRZH4En8boufVwQYQZGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfcacbfaa68ee211ba4dc56f27691b56a897bfc476745868776a171ca9fcd918","last_reissued_at":"2026-05-18T00:16:03.257707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.257707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic curves with many automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2017-02-28T15:06:21Z","abstract_excerpt":"Let $X$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \\ge 2$ defined over an algebraically closed field $K$ of odd characteristic $p$. Let $Aut(X)$ be the group of all automorphisms of $X$ which fix $K$ element-wise. It is known that if $|Aut(X)|\\geq 8g^3$ then the $p$-rank (equivalently, the Hasse-Witt invariant) of $X$ is zero. This raises the problem of determining the (minimum-value) function $f(g)$ such that whenever $|Aut(X)|\\geq f(g)$ then $X$ has zero $p$-rank. For {\\em{even}} $g$ we prove that $f(g)\\leq 900 g^2$. The {\\em{odd}} genus case appear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08812","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":"1702.08812","created_at":"2026-05-18T00:16:03.257762+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08812v2","created_at":"2026-05-18T00:16:03.257762+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08812","created_at":"2026-05-18T00:16:03.257762+00:00"},{"alias_kind":"pith_short_12","alias_value":"37FMX6VGR3RB","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"37FMX6VGR3RBDOSN","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"37FMX6VG","created_at":"2026-05-18T12:30:58.224056+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/37FMX6VGR3RBDOSNYVXSO2I3K2","json":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2.json","graph_json":"https://pith.science/api/pith-number/37FMX6VGR3RBDOSNYVXSO2I3K2/graph.json","events_json":"https://pith.science/api/pith-number/37FMX6VGR3RBDOSNYVXSO2I3K2/events.json","paper":"https://pith.science/paper/37FMX6VG"},"agent_actions":{"view_html":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2","download_json":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2.json","view_paper":"https://pith.science/paper/37FMX6VG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08812&json=true","fetch_graph":"https://pith.science/api/pith-number/37FMX6VGR3RBDOSNYVXSO2I3K2/graph.json","fetch_events":"https://pith.science/api/pith-number/37FMX6VGR3RBDOSNYVXSO2I3K2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2/action/storage_attestation","attest_author":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2/action/author_attestation","sign_citation":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2/action/citation_signature","submit_replication":"https://pith.science/pith/37FMX6VGR3RBDOSNYVXSO2I3K2/action/replication_record"}},"created_at":"2026-05-18T00:16:03.257762+00:00","updated_at":"2026-05-18T00:16:03.257762+00:00"}