{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:YXPKGZXHQFYNO6MRCE5EAZTAPP","short_pith_number":"pith:YXPKGZXH","schema_version":"1.0","canonical_sha256":"c5dea366e78170d77991113a4066607bfa3d999cc35843fc4b3fe60ad406b6ec","source":{"kind":"arxiv","id":"math/0312284","version":1},"attestation_state":"computed","paper":{"title":"Determining the automorphism group of a hyperelliptic curve","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"T. Shaska","submitted_at":"2003-12-15T03:07:32Z","abstract_excerpt":"In this note we discuss techniques for determining the automorphism group of a genus $g$ hyperelliptic curve $\\X_g$ defined over an algebraically closed field $k$ of characteristic zero. The first technique uses the classical $GL_2 (k)$-invariants of binary forms. This is a practical method for curves of small genus, but has limitations as the genus increases, due to the fact that such invariants are not known for large genus.\n  The second approach, which uses dihedral invariants of hyperelliptic curves, is a very convenient method and works well in all genera. First we define the normal decom"},"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":"math/0312284","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2003-12-15T03:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"900070554341b84790e0872129ab512fcf4efd75bf1fcc4bd84292d9c4101765","abstract_canon_sha256":"567977654499e6ab405f79e10543a42ed9660f517e41c9e44d4fdf5e0620298c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.579848Z","signature_b64":"trVqt8jWPhLaDlAvwqLhKN9H5YYBktq1jtXx9U43mWq9kKk5vAd6fVcahXZzpsGU+GI3YOi+f6Nurw8lQlzQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5dea366e78170d77991113a4066607bfa3d999cc35843fc4b3fe60ad406b6ec","last_reissued_at":"2026-05-18T03:45:23.579188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.579188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determining the automorphism group of a hyperelliptic curve","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"T. Shaska","submitted_at":"2003-12-15T03:07:32Z","abstract_excerpt":"In this note we discuss techniques for determining the automorphism group of a genus $g$ hyperelliptic curve $\\X_g$ defined over an algebraically closed field $k$ of characteristic zero. The first technique uses the classical $GL_2 (k)$-invariants of binary forms. This is a practical method for curves of small genus, but has limitations as the genus increases, due to the fact that such invariants are not known for large genus.\n  The second approach, which uses dihedral invariants of hyperelliptic curves, is a very convenient method and works well in all genera. First we define the normal decom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312284","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":"math/0312284","created_at":"2026-05-18T03:45:23.579276+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0312284v1","created_at":"2026-05-18T03:45:23.579276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312284","created_at":"2026-05-18T03:45:23.579276+00:00"},{"alias_kind":"pith_short_12","alias_value":"YXPKGZXHQFYN","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"YXPKGZXHQFYNO6MR","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"YXPKGZXH","created_at":"2026-05-18T12:25:52.051335+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/YXPKGZXHQFYNO6MRCE5EAZTAPP","json":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP.json","graph_json":"https://pith.science/api/pith-number/YXPKGZXHQFYNO6MRCE5EAZTAPP/graph.json","events_json":"https://pith.science/api/pith-number/YXPKGZXHQFYNO6MRCE5EAZTAPP/events.json","paper":"https://pith.science/paper/YXPKGZXH"},"agent_actions":{"view_html":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP","download_json":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP.json","view_paper":"https://pith.science/paper/YXPKGZXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0312284&json=true","fetch_graph":"https://pith.science/api/pith-number/YXPKGZXHQFYNO6MRCE5EAZTAPP/graph.json","fetch_events":"https://pith.science/api/pith-number/YXPKGZXHQFYNO6MRCE5EAZTAPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP/action/storage_attestation","attest_author":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP/action/author_attestation","sign_citation":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP/action/citation_signature","submit_replication":"https://pith.science/pith/YXPKGZXHQFYNO6MRCE5EAZTAPP/action/replication_record"}},"created_at":"2026-05-18T03:45:23.579276+00:00","updated_at":"2026-05-18T03:45:23.579276+00:00"}