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We denote by $\\delta(C)$ (resp. $\\delta'(C)$) the number of Galois points contained in $C$ (resp. in $\\mathbb P^2 \\setminus C$). In this article, we determine the numbers $\\delta(C)$ and $\\delta'(C)$ in any remaining open cases. Summarizing results obtained by now, we will have a complete classification theorem of smooth plane curves by the number $\\delta(C)$ or $\\delta'(C)$. In particular, we give ne"},"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":"1011.3648","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-16T11:01:54Z","cross_cats_sorted":[],"title_canon_sha256":"63c495968166f9f96e88b3cd2f18c01b0ed80d4491d8d7f60ce2e8117b460826","abstract_canon_sha256":"f93df204617d779ac7e4f01980255758cf72a3c4698c33f76ae691eea0626299"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:38.863043Z","signature_b64":"b+RLbh2Uf5ki9I1p4TmbO64D76NWl+mTQXW1c69/7RTE7/8NIuzcC3QcdO6OguARp6ecUjsndVmsyNglPBPRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be7881fbd530742aeef7b806b9d4a3c3d033037a821409a646c8754e9e7e013b","last_reissued_at":"2026-05-18T03:16:38.862533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:38.862533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete determination of the number of Galois points for a smooth plane curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Satoru Fukasawa","submitted_at":"2010-11-16T11:01:54Z","abstract_excerpt":"Let $C$ be a smooth plane curve. A point $P$ in the projective plane is said to be Galois with respect to $C$ if the function field extension induced from the point projection from $P$ is Galois. We denote by $\\delta(C)$ (resp. $\\delta'(C)$) the number of Galois points contained in $C$ (resp. in $\\mathbb P^2 \\setminus C$). In this article, we determine the numbers $\\delta(C)$ and $\\delta'(C)$ in any remaining open cases. Summarizing results obtained by now, we will have a complete classification theorem of smooth plane curves by the number $\\delta(C)$ or $\\delta'(C)$. 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