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We prove that if $\\mathcal{X}$ is an algebraic curve of genus $g=(p-1)^2$ such that $\\mbox{Aut}_{\\mathbb{F}_p}(\\mathcal{X})$ contains a subgroup isomorphic to $H$ then $\\mathcal{X}$ is birationally equivalent over $\\mathbb{F}_p$ to the Artin-Mumford curve $\\mathcal{M}$."},"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":"1501.02616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-12T12:23:34Z","cross_cats_sorted":["math.CO","math.NT"],"title_canon_sha256":"e0c2f379d82126baa0123d1cba43a65ca93d061b2eadb50b9eb3ee0f225c8766","abstract_canon_sha256":"a327e36da35363502c78eb32cc39518756e4da92c7a4c9489d00d43d8c5930b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:37.621102Z","signature_b64":"vk/I9Muc8VR/9mGpLRdpHMASrNL1wyLzcFsOx0LcjXi8gq6gYkZOlx6J7gzJbLfaVhoD+O8VzH3qVMGiZ0hYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"882a8d8cbedfefc1296a68bd9fac44b623311287dbdbe4625c09a628c7c8d545","last_reissued_at":"2026-05-18T02:29:37.620721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:37.620721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of the Artin-Mumford curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.AG","authors_text":"G\\'abor Korchm\\'aros, Nazar Arakelian","submitted_at":"2015-01-12T12:23:34Z","abstract_excerpt":"Let $\\mathcal{M}$ be the Artin-Mumford curve over the finite prime field $\\mathbb{F}_p$ with $p>2$. By a result of Valentini and Madan, $\\mbox{Aut}_{\\mathbb{F}_p}(\\mathcal{M})\\cong H$ with $H=(C_p\\times C_p)\\rtimes D_{p-1}$. We prove that if $\\mathcal{X}$ is an algebraic curve of genus $g=(p-1)^2$ such that $\\mbox{Aut}_{\\mathbb{F}_p}(\\mathcal{X})$ contains a subgroup isomorphic to $H$ then $\\mathcal{X}$ is birationally equivalent over $\\mathbb{F}_p$ to the Artin-Mumford curve $\\mathcal{M}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02616","kind":"arxiv","version":1},"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":"1501.02616","created_at":"2026-05-18T02:29:37.620776+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02616v1","created_at":"2026-05-18T02:29:37.620776+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02616","created_at":"2026-05-18T02:29:37.620776+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAVI3DF637X4","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAVI3DF637X4CKLK","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAVI3DF6","created_at":"2026-05-18T12:29:39.896362+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/RAVI3DF637X4CKLKNC6Z7LCEWY","json":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY.json","graph_json":"https://pith.science/api/pith-number/RAVI3DF637X4CKLKNC6Z7LCEWY/graph.json","events_json":"https://pith.science/api/pith-number/RAVI3DF637X4CKLKNC6Z7LCEWY/events.json","paper":"https://pith.science/paper/RAVI3DF6"},"agent_actions":{"view_html":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY","download_json":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY.json","view_paper":"https://pith.science/paper/RAVI3DF6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02616&json=true","fetch_graph":"https://pith.science/api/pith-number/RAVI3DF637X4CKLKNC6Z7LCEWY/graph.json","fetch_events":"https://pith.science/api/pith-number/RAVI3DF637X4CKLKNC6Z7LCEWY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY/action/storage_attestation","attest_author":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY/action/author_attestation","sign_citation":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY/action/citation_signature","submit_replication":"https://pith.science/pith/RAVI3DF637X4CKLKNC6Z7LCEWY/action/replication_record"}},"created_at":"2026-05-18T02:29:37.620776+00:00","updated_at":"2026-05-18T02:29:37.620776+00:00"}