{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LKOG4MWH6C4ZY7VU66J7XZWWGN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d1af5c83dc8a8ac8f2eff44fe6dd9203e4ddf4b50e07e0120134c6d81a499ff9","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-21T13:12:58Z","title_canon_sha256":"f3845d1369da5ef10b566247361a085a0836a71dc60baf27dc40648a00584ef1"},"schema_version":"1.0","source":{"id":"1707.06883","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06883","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06883v3","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06883","created_at":"2026-05-18T00:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"LKOG4MWH6C4Z","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LKOG4MWH6C4ZY7VU","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LKOG4MWH","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:1590ecb62bfbe7d9125f2f0b71955b39e9c5dd5035597764952d2a3554c6b735","target":"graph","created_at":"2026-05-18T00:20:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Andriy Regeta, Hanspeter Kraft, Immanuel van Santen n\\'e Stampfli","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-21T13:12:58Z","title":"Is the affine space determined by its automorphism group?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06883","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:743b96f6cff729f37427a7904aa6395acf29cca0ccc2f968bdd8b756c1c41949","target":"record","created_at":"2026-05-18T00:20:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d1af5c83dc8a8ac8f2eff44fe6dd9203e4ddf4b50e07e0120134c6d81a499ff9","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-21T13:12:58Z","title_canon_sha256":"f3845d1369da5ef10b566247361a085a0836a71dc60baf27dc40648a00584ef1"},"schema_version":"1.0","source":{"id":"1707.06883","kind":"arxiv","version":3}},"canonical_sha256":"5a9c6e32c7f0b99c7eb4f793fbe6d633735f0dcd23d0a24317165a81ddfefc9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a9c6e32c7f0b99c7eb4f793fbe6d633735f0dcd23d0a24317165a81ddfefc9d","first_computed_at":"2026-05-18T00:20:22.127752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:22.127752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dgg7PKkcwMnA4DajWRTHj9FQkJm4Lf27m+piCYjSidTOjwWfEr0QwxghlQvWo3T1o6Xc18eGEK984cuLZfBRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:22.128464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06883","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:743b96f6cff729f37427a7904aa6395acf29cca0ccc2f968bdd8b756c1c41949","sha256:1590ecb62bfbe7d9125f2f0b71955b39e9c5dd5035597764952d2a3554c6b735"],"state_sha256":"5fee8959f255bc5009565fa94c8624d044a1d3481f13d2e17f9882540ab1e332"}