{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R5QMHYXM7DF4NEFWZTOR7G65LQ","short_pith_number":"pith:R5QMHYXM","canonical_record":{"source":{"id":"1405.3554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-14T15:59:24Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cd381c1eda076ee791047bcc05191133cc694dee732f3629734d57d3f5e58b91","abstract_canon_sha256":"26f3dd6f25f86059b885f48408d8782fff57e018fb75ce113babb572618f7560"},"schema_version":"1.0"},"canonical_sha256":"8f60c3e2ecf8cbc690b6ccdd1f9bdd5c175aa15ec635157060983e677b7db470","source":{"kind":"arxiv","id":"1405.3554","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3554","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3554v1","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3554","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"R5QMHYXM7DF4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R5QMHYXM7DF4NEFW","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R5QMHYXM","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R5QMHYXM7DF4NEFWZTOR7G65LQ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.3554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-14T15:59:24Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cd381c1eda076ee791047bcc05191133cc694dee732f3629734d57d3f5e58b91","abstract_canon_sha256":"26f3dd6f25f86059b885f48408d8782fff57e018fb75ce113babb572618f7560"},"schema_version":"1.0"},"canonical_sha256":"8f60c3e2ecf8cbc690b6ccdd1f9bdd5c175aa15ec635157060983e677b7db470","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:50.569556Z","signature_b64":"jQX7AtxTw1DEKwJvPJjInN7jtKhHsV8ZXxNC+E3oDLJ4gJIJcgM3aFB4O+dXPc3LS1/9h54tqnTiCr6SjhpBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f60c3e2ecf8cbc690b6ccdd1f9bdd5c175aa15ec635157060983e677b7db470","last_reissued_at":"2026-05-18T02:51:50.569105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:50.569105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.3554","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q/uRrcV6MG/Zkp6eXAQJ9uNvrrLHhlffjNjQB10Ab29D+7DP5Lf3afhN9h0T7g+McTx3OsPv9O03d5yIWdp0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:46:30.590635Z"},"content_sha256":"05a793db60c0339c684e84077a340a2697ada47f5622d597b9726ab54a603d3e","schema_version":"1.0","event_id":"sha256:05a793db60c0339c684e84077a340a2697ada47f5622d597b9726ab54a603d3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R5QMHYXM7DF4NEFWZTOR7G65LQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some applications of H\\\"older's theorem in groups of analytic diffeomorphisms of 1-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Azer Akhmedov, Michael P. Cohen","submitted_at":"2014-05-14T15:59:24Z","abstract_excerpt":"We obtain a simple obstruction to embedding groups into the analytic diffeomorphism groups of 1-manifolds. Using this, we classify all RAAGs which embed into $\\mathrm{Diff}_{+}^{\\omega }(\\mathbb{S}^1)$. We also prove that a branch group does not embed into $\\mathrm{Diff}_{+}^{\\omega }(\\mathbb{S}^1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3554","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1n8bcExZJ2bABjDO2MkwNMspRRAt9Y1kGasZPE4QC46s+ALILnCMjPjq53JjjfXTZFUTbGyduzlJGObQDtQtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:46:30.590977Z"},"content_sha256":"c5dd352f09ac237e4692f37809c862d98f27abde8577ca5ee1f11468ce4d253e","schema_version":"1.0","event_id":"sha256:c5dd352f09ac237e4692f37809c862d98f27abde8577ca5ee1f11468ce4d253e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ/bundle.json","state_url":"https://pith.science/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T10:46:30Z","links":{"resolver":"https://pith.science/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ","bundle":"https://pith.science/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ/bundle.json","state":"https://pith.science/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5QMHYXM7DF4NEFWZTOR7G65LQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R5QMHYXM7DF4NEFWZTOR7G65LQ","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":"26f3dd6f25f86059b885f48408d8782fff57e018fb75ce113babb572618f7560","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-14T15:59:24Z","title_canon_sha256":"cd381c1eda076ee791047bcc05191133cc694dee732f3629734d57d3f5e58b91"},"schema_version":"1.0","source":{"id":"1405.3554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3554","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3554v1","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3554","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"R5QMHYXM7DF4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R5QMHYXM7DF4NEFW","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R5QMHYXM","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:c5dd352f09ac237e4692f37809c862d98f27abde8577ca5ee1f11468ce4d253e","target":"graph","created_at":"2026-05-18T02:51:50Z","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":"We obtain a simple obstruction to embedding groups into the analytic diffeomorphism groups of 1-manifolds. Using this, we classify all RAAGs which embed into $\\mathrm{Diff}_{+}^{\\omega }(\\mathbb{S}^1)$. We also prove that a branch group does not embed into $\\mathrm{Diff}_{+}^{\\omega }(\\mathbb{S}^1)$.","authors_text":"Azer Akhmedov, Michael P. Cohen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-14T15:59:24Z","title":"Some applications of H\\\"older's theorem in groups of analytic diffeomorphisms of 1-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3554","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":"sha256:05a793db60c0339c684e84077a340a2697ada47f5622d597b9726ab54a603d3e","target":"record","created_at":"2026-05-18T02:51:50Z","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":"26f3dd6f25f86059b885f48408d8782fff57e018fb75ce113babb572618f7560","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-14T15:59:24Z","title_canon_sha256":"cd381c1eda076ee791047bcc05191133cc694dee732f3629734d57d3f5e58b91"},"schema_version":"1.0","source":{"id":"1405.3554","kind":"arxiv","version":1}},"canonical_sha256":"8f60c3e2ecf8cbc690b6ccdd1f9bdd5c175aa15ec635157060983e677b7db470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f60c3e2ecf8cbc690b6ccdd1f9bdd5c175aa15ec635157060983e677b7db470","first_computed_at":"2026-05-18T02:51:50.569105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:50.569105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jQX7AtxTw1DEKwJvPJjInN7jtKhHsV8ZXxNC+E3oDLJ4gJIJcgM3aFB4O+dXPc3LS1/9h54tqnTiCr6SjhpBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:50.569556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05a793db60c0339c684e84077a340a2697ada47f5622d597b9726ab54a603d3e","sha256:c5dd352f09ac237e4692f37809c862d98f27abde8577ca5ee1f11468ce4d253e"],"state_sha256":"4d4d0f4c270fcecbd0d19d1079092cb67c0d363ace83cdef7bb84062f240e8be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hUkNdYumA+KQX7ymVdNE1tZG1ignH2QDo2dq4EhMUw575zP8pP381NrHpugWlGDoguNXcJlwsRE1nkW8D9aSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:46:30.593545Z","bundle_sha256":"56dcdbb7d790f20d298e8375b78b60c3ca8752b32dbd6606b5f1b161c5e8e586"}}