{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SD5M3I3XST3ZXBKEVGUWA7SCE5","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":"d59567d71bfb959b8e02797380fee29950f49fbd8913b6969ab5d4c0e1c9ebb3","cross_cats_sorted":["math.AT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-13T12:55:49Z","title_canon_sha256":"67aee4a734d7ca5b308dad33bb079534e25d1f411bf25dbc1a87586ac8979b39"},"schema_version":"1.0","source":{"id":"1112.2881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2881","created_at":"2026-05-18T04:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2881v1","created_at":"2026-05-18T04:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2881","created_at":"2026-05-18T04:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"SD5M3I3XST3Z","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SD5M3I3XST3ZXBKE","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SD5M3I3X","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:40ebc63910018e60aade6446888cb8380a0f6889fefd56e2735ee9f34091ffd6","target":"graph","created_at":"2026-05-18T04:06:32Z","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 work one shows that given a connected $C^\\infty$-manifold $M$ of dimension $\\geq 2$ and a finite subgroup $G\\subset \\Diff(M)$, there exists a complete vector field $X$ on $M$ such that its automorphism group equals $G\\times \\mathbb{R}$ where the factor $\\mathbb{R}$ comes from the flow of $X$.","authors_text":"A. Viruel, F. J. Turiel","cross_cats":["math.AT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-13T12:55:49Z","title":"Finite $C^\\infty$-actions are described by one vector field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2881","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:a9ce4737eee2d2cc6b9d54e72d6c4419a0a41afe96d2658a232ae98d6be319a5","target":"record","created_at":"2026-05-18T04:06:32Z","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":"d59567d71bfb959b8e02797380fee29950f49fbd8913b6969ab5d4c0e1c9ebb3","cross_cats_sorted":["math.AT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-13T12:55:49Z","title_canon_sha256":"67aee4a734d7ca5b308dad33bb079534e25d1f411bf25dbc1a87586ac8979b39"},"schema_version":"1.0","source":{"id":"1112.2881","kind":"arxiv","version":1}},"canonical_sha256":"90facda37794f79b8544a9a9607e422752290a087f13c58a0ad2968fa29326fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90facda37794f79b8544a9a9607e422752290a087f13c58a0ad2968fa29326fe","first_computed_at":"2026-05-18T04:06:32.161849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:32.161849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U57ugEgcqgki5tc+BR2koRk05IGjcAsjukG+urfFPq13pSq/M14hIxCighi+hBAHtCaUoxn0iry6sXohYa1yBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:32.162559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9ce4737eee2d2cc6b9d54e72d6c4419a0a41afe96d2658a232ae98d6be319a5","sha256:40ebc63910018e60aade6446888cb8380a0f6889fefd56e2735ee9f34091ffd6"],"state_sha256":"2a48adabd8f9258a6cb55fa4c05e471efcb2f14b0ff528035f7bca795086e854"}