{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:U5YMHCM7YBYMW5R3FXFVL6IAE4","short_pith_number":"pith:U5YMHCM7","schema_version":"1.0","canonical_sha256":"a770c3899fc070cb763b2dcb55f90027331e6cf869d37ee2e90ade8f37744001","source":{"kind":"arxiv","id":"1209.2938","version":1},"attestation_state":"computed","paper":{"title":"Hyperelliptic curves of genus 3 with prescribed automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. Sevilla, J. Gutierrez, T. Shaska","submitted_at":"2012-09-13T15:50:44Z","abstract_excerpt":"We study genus 3 hyperelliptic curves which have an extra involution. The locus $\\L_3$ of these curves is a 3-dimensional subvariety in the genus 3 hyperelliptic moduli $\\H_3$. We find a birational parametrization of this locus by affine 3-space. For every moduli point $\\p \\in \\H_3$ such that $|\\Aut (\\p)|>2$, the field of moduli is a field of definition. We provide a rational model of the curve over its field of moduli for all moduli points $\\p \\in \\H_3$ such that $|\\Aut(\\p)|>4$. This is the first time that such a rational model of these curves appears in the literature."},"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":"1209.2938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-13T15:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"92a453715a318078ac3bbdd0bb80ae3cba4aa4dfccb4ec55ee96b03c3bfee9a5","abstract_canon_sha256":"6d049c1c9d4f8d7a0c31741a109ff58ab1b3a8743ea99c05dd4dc4f728d026c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:40.573811Z","signature_b64":"LJZMavOpJX4SYc+ETeG7jGRW1+mPWiu4Jv1/z3qBb1FNqNGNDTgX7rKJhqbUaVdALaP5+d4kfRI6wpqAPXP5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a770c3899fc070cb763b2dcb55f90027331e6cf869d37ee2e90ade8f37744001","last_reissued_at":"2026-05-18T03:45:40.573255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:40.573255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperelliptic curves of genus 3 with prescribed automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. Sevilla, J. Gutierrez, T. Shaska","submitted_at":"2012-09-13T15:50:44Z","abstract_excerpt":"We study genus 3 hyperelliptic curves which have an extra involution. The locus $\\L_3$ of these curves is a 3-dimensional subvariety in the genus 3 hyperelliptic moduli $\\H_3$. We find a birational parametrization of this locus by affine 3-space. For every moduli point $\\p \\in \\H_3$ such that $|\\Aut (\\p)|>2$, the field of moduli is a field of definition. We provide a rational model of the curve over its field of moduli for all moduli points $\\p \\in \\H_3$ such that $|\\Aut(\\p)|>4$. This is the first time that such a rational model of these curves appears in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2938","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":"1209.2938","created_at":"2026-05-18T03:45:40.573347+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.2938v1","created_at":"2026-05-18T03:45:40.573347+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2938","created_at":"2026-05-18T03:45:40.573347+00:00"},{"alias_kind":"pith_short_12","alias_value":"U5YMHCM7YBYM","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"U5YMHCM7YBYMW5R3","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"U5YMHCM7","created_at":"2026-05-18T12:27:23.164592+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/U5YMHCM7YBYMW5R3FXFVL6IAE4","json":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4.json","graph_json":"https://pith.science/api/pith-number/U5YMHCM7YBYMW5R3FXFVL6IAE4/graph.json","events_json":"https://pith.science/api/pith-number/U5YMHCM7YBYMW5R3FXFVL6IAE4/events.json","paper":"https://pith.science/paper/U5YMHCM7"},"agent_actions":{"view_html":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4","download_json":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4.json","view_paper":"https://pith.science/paper/U5YMHCM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.2938&json=true","fetch_graph":"https://pith.science/api/pith-number/U5YMHCM7YBYMW5R3FXFVL6IAE4/graph.json","fetch_events":"https://pith.science/api/pith-number/U5YMHCM7YBYMW5R3FXFVL6IAE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4/action/storage_attestation","attest_author":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4/action/author_attestation","sign_citation":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4/action/citation_signature","submit_replication":"https://pith.science/pith/U5YMHCM7YBYMW5R3FXFVL6IAE4/action/replication_record"}},"created_at":"2026-05-18T03:45:40.573347+00:00","updated_at":"2026-05-18T03:45:40.573347+00:00"}