{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PTJZQ3P7UI6GD5R7RNHYUBN36M","short_pith_number":"pith:PTJZQ3P7","canonical_record":{"source":{"id":"1711.02062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-06T18:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"551d16fb5bb9bcefdb91beac956722604bd61416d4f5e293aa4ead64bb85b95c","abstract_canon_sha256":"174451d268dfd5a4c1f8a7175ced3d1db593fa1cbd2e710ec943679c79c2f531"},"schema_version":"1.0"},"canonical_sha256":"7cd3986dffa23c61f63f8b4f8a05bbf335b47c005569a27cff88a1abef712eaf","source":{"kind":"arxiv","id":"1711.02062","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02062","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02062v2","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02062","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"PTJZQ3P7UI6G","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PTJZQ3P7UI6GD5R7","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PTJZQ3P7","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PTJZQ3P7UI6GD5R7RNHYUBN36M","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-06T18:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"551d16fb5bb9bcefdb91beac956722604bd61416d4f5e293aa4ead64bb85b95c","abstract_canon_sha256":"174451d268dfd5a4c1f8a7175ced3d1db593fa1cbd2e710ec943679c79c2f531"},"schema_version":"1.0"},"canonical_sha256":"7cd3986dffa23c61f63f8b4f8a05bbf335b47c005569a27cff88a1abef712eaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:36.494771Z","signature_b64":"aKL7DYj5vEeQ9oudy7ACFnD7GBZUccX3wvQtesECpjIKbiRfTBs1SgiMZlGunSFitjKsTWXzIxzT1UtjRTULCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cd3986dffa23c61f63f8b4f8a05bbf335b47c005569a27cff88a1abef712eaf","last_reissued_at":"2026-05-18T00:29:36.494215Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:36.494215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02062","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":"2026-05-18T00:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hk7Y7uaqJVTH/d+k08ds9h3rV2T+48HfA6eyXYX5CDeu9cXNi6zmYox2EG1fsOhAeTqEU2HPknqqTi5IyY7DAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:54:08.701068Z"},"content_sha256":"94561c26f0eca53f12063156e0ead280199bfe98fc0b1b2f93b5b6a7f6213809","schema_version":"1.0","event_id":"sha256:94561c26f0eca53f12063156e0ead280199bfe98fc0b1b2f93b5b6a7f6213809"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PTJZQ3P7UI6GD5R7RNHYUBN36M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A brief introduction to sofic entropy theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lewis Bowen","submitted_at":"2017-11-06T18:14:17Z","abstract_excerpt":"Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02062","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":"2026-05-18T00:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pc8tWtbnsEUJ4Z4NOxDsldHQANmWvHXvi6e2KwuoP00mK+gEcUIW836wgGInGMHrEYRT6h4zNdlewxKjAGfmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:54:08.701654Z"},"content_sha256":"35ffa1b9514175b65a94031ee0ecbe8c3c39cdcb503c6b65522df14180c1a2bd","schema_version":"1.0","event_id":"sha256:35ffa1b9514175b65a94031ee0ecbe8c3c39cdcb503c6b65522df14180c1a2bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M/bundle.json","state_url":"https://pith.science/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M/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":"2026-05-31T23:54:08Z","links":{"resolver":"https://pith.science/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M","bundle":"https://pith.science/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M/bundle.json","state":"https://pith.science/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PTJZQ3P7UI6GD5R7RNHYUBN36M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PTJZQ3P7UI6GD5R7RNHYUBN36M","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":"174451d268dfd5a4c1f8a7175ced3d1db593fa1cbd2e710ec943679c79c2f531","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-06T18:14:17Z","title_canon_sha256":"551d16fb5bb9bcefdb91beac956722604bd61416d4f5e293aa4ead64bb85b95c"},"schema_version":"1.0","source":{"id":"1711.02062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02062","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02062v2","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02062","created_at":"2026-05-18T00:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"PTJZQ3P7UI6G","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PTJZQ3P7UI6GD5R7","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PTJZQ3P7","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:35ffa1b9514175b65a94031ee0ecbe8c3c39cdcb503c6b65522df14180c1a2bd","target":"graph","created_at":"2026-05-18T00:29:36Z","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":"Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.","authors_text":"Lewis Bowen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-06T18:14:17Z","title":"A brief introduction to sofic entropy theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02062","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":"sha256:94561c26f0eca53f12063156e0ead280199bfe98fc0b1b2f93b5b6a7f6213809","target":"record","created_at":"2026-05-18T00:29:36Z","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":"174451d268dfd5a4c1f8a7175ced3d1db593fa1cbd2e710ec943679c79c2f531","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-06T18:14:17Z","title_canon_sha256":"551d16fb5bb9bcefdb91beac956722604bd61416d4f5e293aa4ead64bb85b95c"},"schema_version":"1.0","source":{"id":"1711.02062","kind":"arxiv","version":2}},"canonical_sha256":"7cd3986dffa23c61f63f8b4f8a05bbf335b47c005569a27cff88a1abef712eaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cd3986dffa23c61f63f8b4f8a05bbf335b47c005569a27cff88a1abef712eaf","first_computed_at":"2026-05-18T00:29:36.494215Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:36.494215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aKL7DYj5vEeQ9oudy7ACFnD7GBZUccX3wvQtesECpjIKbiRfTBs1SgiMZlGunSFitjKsTWXzIxzT1UtjRTULCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:36.494771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94561c26f0eca53f12063156e0ead280199bfe98fc0b1b2f93b5b6a7f6213809","sha256:35ffa1b9514175b65a94031ee0ecbe8c3c39cdcb503c6b65522df14180c1a2bd"],"state_sha256":"8d11a3e8ffd3b5f2fedbb3a50c77b0b16f71ee90329de08a375c0544d1723b77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9vHqAAZPi7HtzXMOK4rzKQIFAJoykXZW52pEJA6VK4z0QeT8BcRXzgFaia2iKPjNjpOR7iDqCis+sFaWEbgeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:54:08.704924Z","bundle_sha256":"2bc76a782d7d4b3d10d5c9f9b89c72b232a8255079b2e156cb494c1b09acf290"}}