{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WI5AZ25LPBUTOEPQUFRT2XQZ7Z","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":"91105bb6f11c0cc7505300310ae32c1162daed1be0d881a1d3cc7454e1f0d05d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2004-09-30T17:31:56Z","title_canon_sha256":"d015281179fff7a3161922d6f2a416fc22daa02c354a934a47deaefed633d551"},"schema_version":"1.0","source":{"id":"math/0409605","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409605","created_at":"2026-05-18T04:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409605v3","created_at":"2026-05-18T04:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409605","created_at":"2026-05-18T04:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"WI5AZ25LPBUT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"WI5AZ25LPBUTOEPQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"WI5AZ25L","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a6d8ed97178f3921a698b19a169702573add3e660ee7e54a1f3e21ccf30a431e","target":"graph","created_at":"2026-05-18T04:04:52Z","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":"Given a result of Herman, we provide a new elementary proof of the fact that the connected component of the group of compactly supported diffeomorphisms is perfect and hence simple. Moreover, we show that every diffeomorphism $g$, which is sufficiently close to the identity, can be represented as a product of four commutators, $g=[h_1,k_1]\\circ...\\circ[h_4,k_4]$, where the factors $h_i$ and $k_i$ can be chosen to depend smoothly on $g$.","authors_text":"Josef Teichmann, Stefan Haller, Tomasz Rybicki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2004-09-30T17:31:56Z","title":"Smooth perfectness for the group of diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409605","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":"sha256:1c39f709131ef3b8fadcced44d18e5c39d7d1571f85822df61634bcb0d429771","target":"record","created_at":"2026-05-18T04:04:52Z","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":"91105bb6f11c0cc7505300310ae32c1162daed1be0d881a1d3cc7454e1f0d05d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2004-09-30T17:31:56Z","title_canon_sha256":"d015281179fff7a3161922d6f2a416fc22daa02c354a934a47deaefed633d551"},"schema_version":"1.0","source":{"id":"math/0409605","kind":"arxiv","version":3}},"canonical_sha256":"b23a0cebab78693711f0a1633d5e19fe6d8cd82daa622d9c6b3e6870cff57534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b23a0cebab78693711f0a1633d5e19fe6d8cd82daa622d9c6b3e6870cff57534","first_computed_at":"2026-05-18T04:04:52.430081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:52.430081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xv6Q+ghJwdZyRW6JV1A1GQmz/csgKzyFGLvDKDjdlewLhh81Qy+PI07OUe5LUBUGJei2TtyM4wxHk9n9thXxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:52.430673Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0409605","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c39f709131ef3b8fadcced44d18e5c39d7d1571f85822df61634bcb0d429771","sha256:a6d8ed97178f3921a698b19a169702573add3e660ee7e54a1f3e21ccf30a431e"],"state_sha256":"6f66b8572a6da89be9a6cd6183e23f1e239d4f60dd91cd261bba24c96e8ea660"}