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Let $X$ be an irreducible quasi-projective $n$-dimensional variety such that $\\mathrm{Aut}(X)$ and $\\mathrm{Aut}(\\mathbb{A}^n)$ are isomorphic as abstract groups. If $X$ is either quasi-affine and toric or $X$ is smooth with Euler characteristic $\\chi(X) \\neq 0$ and finite Picard group $\\mathrm{Pic}(X)$, then $X$ is isomorphic to $\\mathbb{A}^n$.\n  The main ingredient is the following result. Let $X$ be a smooth irreducible quasi-projective variety of d"},"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":"1707.06883","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-21T13:12:58Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f3845d1369da5ef10b566247361a085a0836a71dc60baf27dc40648a00584ef1","abstract_canon_sha256":"d1af5c83dc8a8ac8f2eff44fe6dd9203e4ddf4b50e07e0120134c6d81a499ff9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:22.128464Z","signature_b64":"dgg7PKkcwMnA4DajWRTHj9FQkJm4Lf27m+piCYjSidTOjwWfEr0QwxghlQvWo3T1o6Xc18eGEK984cuLZfBRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a9c6e32c7f0b99c7eb4f793fbe6d633735f0dcd23d0a24317165a81ddfefc9d","last_reissued_at":"2026-05-18T00:20:22.127752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:22.127752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Is the affine space determined by its automorphism group?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Andriy Regeta, Hanspeter Kraft, Immanuel van Santen n\\'e Stampfli","submitted_at":"2017-07-21T13:12:58Z","abstract_excerpt":"In this note we study the problem of characterizing the complex affine space $\\mathbb{A}^n$ via its automorphism group. We prove the following. Let $X$ be an irreducible quasi-projective $n$-dimensional variety such that $\\mathrm{Aut}(X)$ and $\\mathrm{Aut}(\\mathbb{A}^n)$ are isomorphic as abstract groups. If $X$ is either quasi-affine and toric or $X$ is smooth with Euler characteristic $\\chi(X) \\neq 0$ and finite Picard group $\\mathrm{Pic}(X)$, then $X$ is isomorphic to $\\mathbb{A}^n$.\n  The main ingredient is the following result. Let $X$ be a smooth irreducible quasi-projective variety of d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06883","kind":"arxiv","version":3},"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":"1707.06883","created_at":"2026-05-18T00:20:22.127872+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06883v3","created_at":"2026-05-18T00:20:22.127872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06883","created_at":"2026-05-18T00:20:22.127872+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKOG4MWH6C4Z","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKOG4MWH6C4ZY7VU","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKOG4MWH","created_at":"2026-05-18T12:31:28.150371+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/LKOG4MWH6C4ZY7VU66J7XZWWGN","json":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN.json","graph_json":"https://pith.science/api/pith-number/LKOG4MWH6C4ZY7VU66J7XZWWGN/graph.json","events_json":"https://pith.science/api/pith-number/LKOG4MWH6C4ZY7VU66J7XZWWGN/events.json","paper":"https://pith.science/paper/LKOG4MWH"},"agent_actions":{"view_html":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN","download_json":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN.json","view_paper":"https://pith.science/paper/LKOG4MWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06883&json=true","fetch_graph":"https://pith.science/api/pith-number/LKOG4MWH6C4ZY7VU66J7XZWWGN/graph.json","fetch_events":"https://pith.science/api/pith-number/LKOG4MWH6C4ZY7VU66J7XZWWGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN/action/storage_attestation","attest_author":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN/action/author_attestation","sign_citation":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN/action/citation_signature","submit_replication":"https://pith.science/pith/LKOG4MWH6C4ZY7VU66J7XZWWGN/action/replication_record"}},"created_at":"2026-05-18T00:20:22.127872+00:00","updated_at":"2026-05-18T00:20:22.127872+00:00"}