{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HT27L7KUHVUT2PKC2OB5LEWZTY","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":"4a018e84c85dda457fadb5c79a89a7b85eec34be2dec33bf3d765bffbfaea618","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2014-02-05T17:46:46Z","title_canon_sha256":"e46d39affc615d5b728b05e9540100ab4b75e5395f3caab76d2cc9286cf24a39"},"schema_version":"1.0","source":{"id":"1402.1101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1101","created_at":"2026-05-18T03:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1101v1","created_at":"2026-05-18T03:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1101","created_at":"2026-05-18T03:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"HT27L7KUHVUT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HT27L7KUHVUT2PKC","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HT27L7KU","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:99839d4d98cf71eaae71facf1b8b99e3e919f28a5a2fd296ca4df4bf92272607","target":"graph","created_at":"2026-05-18T03:00:01Z","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":"Let $G$ be the group of unimodular automorphisms of $\\mathbb C^2$. In the paper we prove two interesting results about this group. The first one is about absence of non-trivial finite-dimensional representations of $G$. The second one, we show that any non-trivial group endomorphism of $G$ is a monomorphism, which implies that $G$ is hopfian.","authors_text":"Alimjon Eshmatov, Farkhod Eshmatov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2014-02-05T17:46:46Z","title":"The group of unimodular automorphisms of $\\mathbb{C}^2$ is hopfian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1101","kind":"arxiv","version":1},"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":"sha256:3a4650823a3473eb0cbe865a0d80e98d10f6c2146457b8d02aa4a10b4573546b","target":"record","created_at":"2026-05-18T03:00:01Z","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":"4a018e84c85dda457fadb5c79a89a7b85eec34be2dec33bf3d765bffbfaea618","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2014-02-05T17:46:46Z","title_canon_sha256":"e46d39affc615d5b728b05e9540100ab4b75e5395f3caab76d2cc9286cf24a39"},"schema_version":"1.0","source":{"id":"1402.1101","kind":"arxiv","version":1}},"canonical_sha256":"3cf5f5fd543d693d3d42d383d592d99e296d2e81b7eed6794ee4abcf407b827d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cf5f5fd543d693d3d42d383d592d99e296d2e81b7eed6794ee4abcf407b827d","first_computed_at":"2026-05-18T03:00:01.701632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:01.701632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+VHoCcdaNv9BuJgSINLkrrtYEkhFySxO8ZfM9w5GOgUfIb5ouvkyOT0/hjp1oynXCdKY4Dxgi3T/8Z4nqzT/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:01.702436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a4650823a3473eb0cbe865a0d80e98d10f6c2146457b8d02aa4a10b4573546b","sha256:99839d4d98cf71eaae71facf1b8b99e3e919f28a5a2fd296ca4df4bf92272607"],"state_sha256":"249e1655a390856da3be5b6d5e0121308028e865f7ec69142ad84376ee71ea31"}