{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HXDDGLFU5KC7VOMRWMBTYKF4WM","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":"483acec5a1cdd3357d687ac391a899cc3ab523cd1dba04b8d8eb7b43c945c519","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-07T12:08:21Z","title_canon_sha256":"e72f88454892d9b6df516d9a64a5bd585da5501809733e70890f4ed7c85fe9b4"},"schema_version":"1.0","source":{"id":"1402.1612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1612","created_at":"2026-05-18T02:59:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1612v1","created_at":"2026-05-18T02:59:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1612","created_at":"2026-05-18T02:59:46Z"},{"alias_kind":"pith_short_12","alias_value":"HXDDGLFU5KC7","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HXDDGLFU5KC7VOMR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HXDDGLFU","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:030d44882b79f8a8eff16fd6e7e64b4faff5447aee1f5768e5f3202d79af8913","target":"graph","created_at":"2026-05-18T02:59:46Z","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":"By a classical result of Jordan, each finite subgroup G of a complex linear group GL_n(C) has an abelian subgroup whose index in G is bounded by a constant depending only on n. We consider the problem if this remains true for finite subgroups G of the diffeomorphism group of a smooth manifold, and show that it is true for all compact 3-manifolds as well as for Euclidean spaces of dimension n < 7. The question remains open at present e.g. for odd-dimensional spheres of dimension greater or equal to five, and for Euclidean spaces of dimension greater or equal to seven.","authors_text":"Bruno P. Zimmermann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-07T12:08:21Z","title":"On Jordan type bounds for finite groups of diffeomorphisms of 3-manifolds and Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1612","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":"sha256:198ffb6c13b5d7d488503c8965f9e017ad338adfdb4e1a8eab6570945bdfc3e2","target":"record","created_at":"2026-05-18T02:59:46Z","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":"483acec5a1cdd3357d687ac391a899cc3ab523cd1dba04b8d8eb7b43c945c519","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-02-07T12:08:21Z","title_canon_sha256":"e72f88454892d9b6df516d9a64a5bd585da5501809733e70890f4ed7c85fe9b4"},"schema_version":"1.0","source":{"id":"1402.1612","kind":"arxiv","version":1}},"canonical_sha256":"3dc6332cb4ea85fab991b3033c28bcb3234424c403744dd346c82455b70a132d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dc6332cb4ea85fab991b3033c28bcb3234424c403744dd346c82455b70a132d","first_computed_at":"2026-05-18T02:59:46.671671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:46.671671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+r/ZemppjBh2Eq3qtwG02U5HO0pscg3H03+cTVLKBLeVkBoHYoLmXnifIt9wN2FeQp5damkbL+SkF9NYIMfRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:46.672727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:198ffb6c13b5d7d488503c8965f9e017ad338adfdb4e1a8eab6570945bdfc3e2","sha256:030d44882b79f8a8eff16fd6e7e64b4faff5447aee1f5768e5f3202d79af8913"],"state_sha256":"866021d900e56445674c4a3049bed42a5ea7f0784a0d720476d3c96c7d89d79b"}