{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:XUMRINEMJYXTVMWK34V2VVRKAM","short_pith_number":"pith:XUMRINEM","canonical_record":{"source":{"id":"math/0408400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-08-29T19:24:47Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"ba9ee81101f86eae29076dc96bcd0908236ef04ba922efc100f81330bfbbc3e3","abstract_canon_sha256":"f288816b5074817e6c90d3dfcb5b3d4ca518775b3c941c994eb5515a815b0c85"},"schema_version":"1.0"},"canonical_sha256":"bd1914348c4e2f3ab2cadf2baad62a031d13bbb92533c7f3f8936bfafa159c06","source":{"kind":"arxiv","id":"math/0408400","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408400","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408400v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408400","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"XUMRINEMJYXT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XUMRINEMJYXTVMWK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XUMRINEM","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:XUMRINEMJYXTVMWK34V2VVRKAM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0408400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-08-29T19:24:47Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"ba9ee81101f86eae29076dc96bcd0908236ef04ba922efc100f81330bfbbc3e3","abstract_canon_sha256":"f288816b5074817e6c90d3dfcb5b3d4ca518775b3c941c994eb5515a815b0c85"},"schema_version":"1.0"},"canonical_sha256":"bd1914348c4e2f3ab2cadf2baad62a031d13bbb92533c7f3f8936bfafa159c06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:54.574945Z","signature_b64":"J96vxqPWJLcfTo0d4zxppLHdA/1x1Dv4pjKNwanzmd8dSQG6N8VtxTY/TJqjQX48aXcWFHdJkL2s5WsHi5TxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd1914348c4e2f3ab2cadf2baad62a031d13bbb92533c7f3f8936bfafa159c06","last_reissued_at":"2026-05-18T02:40:54.574498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:54.574498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0408400","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":"2026-05-18T02:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqlKu0+RdpjvAPm3XKAjBGC3l+w+m28gGyuuqb3DLPN0sPektciDVY9twpyBjGv7TScsF5KmcXJJZPU3X4UMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T15:13:54.449560Z"},"content_sha256":"7759a4e2a3fbfa7e9bc828d2ea1b1040566e76ed193df6ceebd238310073dbde","schema_version":"1.0","event_id":"sha256:7759a4e2a3fbfa7e9bc828d2ea1b1040566e76ed193df6ceebd238310073dbde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:XUMRINEMJYXTVMWK34V2VVRKAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperlinearity, essentially free actions and $L^2$-invariants. The sofic property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Endre Szab\\'o, G\\'abor Elek","submitted_at":"2004-08-29T19:24:47Z","abstract_excerpt":"We prove that Connes' Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds for sofic groups as well. We introduce the notion of essentially free actions and amenable actions and study their properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408400","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":"2026-05-18T02:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fPjeS6JaWQ/Q0qxemXuRWgkvlyGGzcArXFZiDNQdl1h7pwatjjkcwcgTXDwQp0VNknlnf8KWO9NOscBLIotBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T15:13:54.450271Z"},"content_sha256":"e51589999f118a0684223933be5377444bd7eb1aaea88755a6f7b4d9ddaf2f4e","schema_version":"1.0","event_id":"sha256:e51589999f118a0684223933be5377444bd7eb1aaea88755a6f7b4d9ddaf2f4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUMRINEMJYXTVMWK34V2VVRKAM/bundle.json","state_url":"https://pith.science/pith/XUMRINEMJYXTVMWK34V2VVRKAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUMRINEMJYXTVMWK34V2VVRKAM/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":"2026-05-23T15:13:54Z","links":{"resolver":"https://pith.science/pith/XUMRINEMJYXTVMWK34V2VVRKAM","bundle":"https://pith.science/pith/XUMRINEMJYXTVMWK34V2VVRKAM/bundle.json","state":"https://pith.science/pith/XUMRINEMJYXTVMWK34V2VVRKAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUMRINEMJYXTVMWK34V2VVRKAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:XUMRINEMJYXTVMWK34V2VVRKAM","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":"f288816b5074817e6c90d3dfcb5b3d4ca518775b3c941c994eb5515a815b0c85","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-08-29T19:24:47Z","title_canon_sha256":"ba9ee81101f86eae29076dc96bcd0908236ef04ba922efc100f81330bfbbc3e3"},"schema_version":"1.0","source":{"id":"math/0408400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408400","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408400v2","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408400","created_at":"2026-05-18T02:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"XUMRINEMJYXT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XUMRINEMJYXTVMWK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XUMRINEM","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:e51589999f118a0684223933be5377444bd7eb1aaea88755a6f7b4d9ddaf2f4e","target":"graph","created_at":"2026-05-18T02:40:54Z","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 that Connes' Embedding Conjecture holds for the von Neumann algebras of sofic groups, that is sofic groups are hyperlinear. Hence we provide some new examples of hyperlinearity. We also show that the Determinant Conjecture holds for sofic groups as well. We introduce the notion of essentially free actions and amenable actions and study their properties.","authors_text":"Endre Szab\\'o, G\\'abor Elek","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-08-29T19:24:47Z","title":"Hyperlinearity, essentially free actions and $L^2$-invariants. The sofic property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408400","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":"sha256:7759a4e2a3fbfa7e9bc828d2ea1b1040566e76ed193df6ceebd238310073dbde","target":"record","created_at":"2026-05-18T02:40:54Z","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":"f288816b5074817e6c90d3dfcb5b3d4ca518775b3c941c994eb5515a815b0c85","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2004-08-29T19:24:47Z","title_canon_sha256":"ba9ee81101f86eae29076dc96bcd0908236ef04ba922efc100f81330bfbbc3e3"},"schema_version":"1.0","source":{"id":"math/0408400","kind":"arxiv","version":2}},"canonical_sha256":"bd1914348c4e2f3ab2cadf2baad62a031d13bbb92533c7f3f8936bfafa159c06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd1914348c4e2f3ab2cadf2baad62a031d13bbb92533c7f3f8936bfafa159c06","first_computed_at":"2026-05-18T02:40:54.574498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:54.574498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J96vxqPWJLcfTo0d4zxppLHdA/1x1Dv4pjKNwanzmd8dSQG6N8VtxTY/TJqjQX48aXcWFHdJkL2s5WsHi5TxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:54.574945Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7759a4e2a3fbfa7e9bc828d2ea1b1040566e76ed193df6ceebd238310073dbde","sha256:e51589999f118a0684223933be5377444bd7eb1aaea88755a6f7b4d9ddaf2f4e"],"state_sha256":"afe8285c37a4fb3aad19d7924db6ba9e17e283a2389edde93b0fd1cba98e9661"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6HJX4+OSj+5SoypoCDhW76wUgImd6aXUhl5xhTYtoS5dcCtJcmgp+7QK7KAtvdBwGBEgVdtkMmviC14jaK9OAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T15:13:54.454359Z","bundle_sha256":"0988fa904a6edc6d6fea4437b53f835010a7ef335d755f2589851a1256345a62"}}