{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4KH67BIOYMFVRKA7BAZPSJOZKJ","short_pith_number":"pith:4KH67BIO","canonical_record":{"source":{"id":"1310.6548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-24T10:18:21Z","cross_cats_sorted":["math.AG","math.AT","math.GT"],"title_canon_sha256":"acc3a0870807ebc6dd7024058302d219943add54a07c41c91aadf7ce5a9d041b","abstract_canon_sha256":"a8522dc48ddc6f7d97bc04fb8816e3ee56be744e7ccc8ed05fd60ebf01f1ac2a"},"schema_version":"1.0"},"canonical_sha256":"e28fef850ec30b58a81f0832f925d9526a2722a20e5c8f296a638bde5d27b9ce","source":{"kind":"arxiv","id":"1310.6548","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6548","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6548v2","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6548","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"4KH67BIOYMFV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4KH67BIOYMFVRKA7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4KH67BIO","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4KH67BIOYMFVRKA7BAZPSJOZKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-24T10:18:21Z","cross_cats_sorted":["math.AG","math.AT","math.GT"],"title_canon_sha256":"acc3a0870807ebc6dd7024058302d219943add54a07c41c91aadf7ce5a9d041b","abstract_canon_sha256":"a8522dc48ddc6f7d97bc04fb8816e3ee56be744e7ccc8ed05fd60ebf01f1ac2a"},"schema_version":"1.0"},"canonical_sha256":"e28fef850ec30b58a81f0832f925d9526a2722a20e5c8f296a638bde5d27b9ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:20.460382Z","signature_b64":"8DsjcJpwZkY9ILf7qfG39fbBRCTPMITu3KJpBsNBbIngDkLh/Ev3vx8hRsN2wuhuDWLulhGlmQkyiuItJ9siBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e28fef850ec30b58a81f0832f925d9526a2722a20e5c8f296a638bde5d27b9ce","last_reissued_at":"2026-05-18T03:03:20.459860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:20.459860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6548","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6XA0GK+ECpUqe8nBQJP3BzgJmcGQX/e7hMAIorFvQEubfR4dKfElojZVa7cs5zJJ69PMOKCx6wEJ3+DMfb4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:24:40.321016Z"},"content_sha256":"b58524a86d3c92858745a1a61e1fabbc31d6e861dd0f77f65676ecd2fe99fee2","schema_version":"1.0","event_id":"sha256:b58524a86d3c92858745a1a61e1fabbc31d6e861dd0f77f65676ecd2fe99fee2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4KH67BIOYMFVRKA7BAZPSJOZKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite subgroups of diffeomorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT","math.GT"],"primary_cat":"math.GR","authors_text":"Vladimir L. Popov","submitted_at":"2013-10-24T10:18:21Z","abstract_excerpt":"We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite simple subgroups of diffeomorphism groups of compact smooth topological manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6548","kind":"arxiv","version":2},"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":"2026-05-18T03:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g/oXVTec19VWrrYrnaJFDuEaTKtQhARPmi61lmS1HVkUT/I8SS8EgVpZMS5Gs/MJg3xh7JiN3TPtyQqfSAbSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:24:40.321367Z"},"content_sha256":"351de211f65cb850646d440b3f9f83daf748a928d8777ede175f16315f7d9fd4","schema_version":"1.0","event_id":"sha256:351de211f65cb850646d440b3f9f83daf748a928d8777ede175f16315f7d9fd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ/bundle.json","state_url":"https://pith.science/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ/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":"2026-06-01T11:24:40Z","links":{"resolver":"https://pith.science/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ","bundle":"https://pith.science/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ/bundle.json","state":"https://pith.science/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4KH67BIOYMFVRKA7BAZPSJOZKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4KH67BIOYMFVRKA7BAZPSJOZKJ","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":"a8522dc48ddc6f7d97bc04fb8816e3ee56be744e7ccc8ed05fd60ebf01f1ac2a","cross_cats_sorted":["math.AG","math.AT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-24T10:18:21Z","title_canon_sha256":"acc3a0870807ebc6dd7024058302d219943add54a07c41c91aadf7ce5a9d041b"},"schema_version":"1.0","source":{"id":"1310.6548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6548","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6548v2","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6548","created_at":"2026-05-18T03:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"4KH67BIOYMFV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4KH67BIOYMFVRKA7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4KH67BIO","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:351de211f65cb850646d440b3f9f83daf748a928d8777ede175f16315f7d9fd4","target":"graph","created_at":"2026-05-18T03:03:20Z","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 prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite simple subgroups of diffeomorphism groups of compact smooth topological manifolds.","authors_text":"Vladimir L. Popov","cross_cats":["math.AG","math.AT","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-24T10:18:21Z","title":"Finite subgroups of diffeomorphism groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6548","kind":"arxiv","version":2},"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:b58524a86d3c92858745a1a61e1fabbc31d6e861dd0f77f65676ecd2fe99fee2","target":"record","created_at":"2026-05-18T03:03:20Z","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":"a8522dc48ddc6f7d97bc04fb8816e3ee56be744e7ccc8ed05fd60ebf01f1ac2a","cross_cats_sorted":["math.AG","math.AT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-10-24T10:18:21Z","title_canon_sha256":"acc3a0870807ebc6dd7024058302d219943add54a07c41c91aadf7ce5a9d041b"},"schema_version":"1.0","source":{"id":"1310.6548","kind":"arxiv","version":2}},"canonical_sha256":"e28fef850ec30b58a81f0832f925d9526a2722a20e5c8f296a638bde5d27b9ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e28fef850ec30b58a81f0832f925d9526a2722a20e5c8f296a638bde5d27b9ce","first_computed_at":"2026-05-18T03:03:20.459860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:20.459860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8DsjcJpwZkY9ILf7qfG39fbBRCTPMITu3KJpBsNBbIngDkLh/Ev3vx8hRsN2wuhuDWLulhGlmQkyiuItJ9siBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:20.460382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b58524a86d3c92858745a1a61e1fabbc31d6e861dd0f77f65676ecd2fe99fee2","sha256:351de211f65cb850646d440b3f9f83daf748a928d8777ede175f16315f7d9fd4"],"state_sha256":"9fbe60c526e3acb4595ffa6f6310c653564d5c5683192c4015b385eacf39f0a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGSIRGaz5LJHBBOLCVsp9jrVVtddjQyR6IJsq5D/8qlLMUe2jzzurksHaLJDKYSW7rWDeYNW0WenPmMYHr1aBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:24:40.323271Z","bundle_sha256":"73459786ca61fbd0018b89e6dbe1151d61802ae1e6734a2b5e532ceeaf95d283"}}