{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5FTDNMLD5DN7QEEQGAAXMGMROK","short_pith_number":"pith:5FTDNMLD","canonical_record":{"source":{"id":"1604.05684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-19T18:26:32Z","cross_cats_sorted":[],"title_canon_sha256":"b59905d0eb6886eb831ef7061b63c3c918ff3acf98196eea1d5d03a9964861f0","abstract_canon_sha256":"dd10b6431111692f74b7731f460de80de01c1994da186528645a72f19114527b"},"schema_version":"1.0"},"canonical_sha256":"e96636b163e8dbf81090300176199172a72f01cb9d26d2887c86fdc73ac9719a","source":{"kind":"arxiv","id":"1604.05684","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05684","created_at":"2026-05-18T01:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05684v2","created_at":"2026-05-18T01:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05684","created_at":"2026-05-18T01:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"5FTDNMLD5DN7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5FTDNMLD5DN7QEEQ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5FTDNMLD","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5FTDNMLD5DN7QEEQGAAXMGMROK","target":"record","payload":{"canonical_record":{"source":{"id":"1604.05684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-19T18:26:32Z","cross_cats_sorted":[],"title_canon_sha256":"b59905d0eb6886eb831ef7061b63c3c918ff3acf98196eea1d5d03a9964861f0","abstract_canon_sha256":"dd10b6431111692f74b7731f460de80de01c1994da186528645a72f19114527b"},"schema_version":"1.0"},"canonical_sha256":"e96636b163e8dbf81090300176199172a72f01cb9d26d2887c86fdc73ac9719a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:11.079613Z","signature_b64":"YKvuOjmXHLctQNH+yTYGZTS2zSx0EqUgWO+j4GCkqFNN7w5GNeIr0k2+5FJSJBSv8qsh7Hh7XrwVhwFGa9XSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e96636b163e8dbf81090300176199172a72f01cb9d26d2887c86fdc73ac9719a","last_reissued_at":"2026-05-18T01:13:11.079225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:11.079225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.05684","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":"2026-05-18T01:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oZQen+ZD84kVbw3TEErCkfmqxl2rXxNVexos7QbqceXchO5da3UikdBg2wJdRn7HDUWTWj7eVxjkjfIJLCSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:56:11.989228Z"},"content_sha256":"6a5bb4dd7960a823dd6da16edb78b52ff5d38e9e2c3f26bae64316676c62b4f1","schema_version":"1.0","event_id":"sha256:6a5bb4dd7960a823dd6da16edb78b52ff5d38e9e2c3f26bae64316676c62b4f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5FTDNMLD5DN7QEEQGAAXMGMROK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structural properties of close II$_1$ factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Alan D. Wiggins, Allan M. Sinclair, Erik Christensen, Jan Cameron, Roger R. Smith, Stuart White","submitted_at":"2016-04-19T18:26:32Z","abstract_excerpt":"We show that a number of key structural properties transfer between sufficiently close II$_1$ factors, including solidity, strong solidity, uniqueness of Cartan masas and property $\\Gamma$. We also examine II$_1$ factors close to tensor product factors, showing that such factors also factorise as a tensor product in a fashion close to the original."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05684","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":"2026-05-18T01:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TtpIkBzyZEEVqoL4dwHGj7tZSKSqvqajr71jgReg/7pEb+EXGeIQByaRjmVw1aNMSbEaSW0FREUBVdKvviqvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:56:11.989598Z"},"content_sha256":"61d42d8f0271b69bbad0a4ef6b28c2b05681d21e89edcc62815aea4efcec1032","schema_version":"1.0","event_id":"sha256:61d42d8f0271b69bbad0a4ef6b28c2b05681d21e89edcc62815aea4efcec1032"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FTDNMLD5DN7QEEQGAAXMGMROK/bundle.json","state_url":"https://pith.science/pith/5FTDNMLD5DN7QEEQGAAXMGMROK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FTDNMLD5DN7QEEQGAAXMGMROK/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":"2026-05-25T18:56:11Z","links":{"resolver":"https://pith.science/pith/5FTDNMLD5DN7QEEQGAAXMGMROK","bundle":"https://pith.science/pith/5FTDNMLD5DN7QEEQGAAXMGMROK/bundle.json","state":"https://pith.science/pith/5FTDNMLD5DN7QEEQGAAXMGMROK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FTDNMLD5DN7QEEQGAAXMGMROK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5FTDNMLD5DN7QEEQGAAXMGMROK","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":"dd10b6431111692f74b7731f460de80de01c1994da186528645a72f19114527b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-19T18:26:32Z","title_canon_sha256":"b59905d0eb6886eb831ef7061b63c3c918ff3acf98196eea1d5d03a9964861f0"},"schema_version":"1.0","source":{"id":"1604.05684","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05684","created_at":"2026-05-18T01:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05684v2","created_at":"2026-05-18T01:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05684","created_at":"2026-05-18T01:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"5FTDNMLD5DN7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5FTDNMLD5DN7QEEQ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5FTDNMLD","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:61d42d8f0271b69bbad0a4ef6b28c2b05681d21e89edcc62815aea4efcec1032","target":"graph","created_at":"2026-05-18T01:13:11Z","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 show that a number of key structural properties transfer between sufficiently close II$_1$ factors, including solidity, strong solidity, uniqueness of Cartan masas and property $\\Gamma$. We also examine II$_1$ factors close to tensor product factors, showing that such factors also factorise as a tensor product in a fashion close to the original.","authors_text":"Alan D. Wiggins, Allan M. Sinclair, Erik Christensen, Jan Cameron, Roger R. Smith, Stuart White","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-19T18:26:32Z","title":"Structural properties of close II$_1$ factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05684","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":"sha256:6a5bb4dd7960a823dd6da16edb78b52ff5d38e9e2c3f26bae64316676c62b4f1","target":"record","created_at":"2026-05-18T01:13:11Z","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":"dd10b6431111692f74b7731f460de80de01c1994da186528645a72f19114527b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-19T18:26:32Z","title_canon_sha256":"b59905d0eb6886eb831ef7061b63c3c918ff3acf98196eea1d5d03a9964861f0"},"schema_version":"1.0","source":{"id":"1604.05684","kind":"arxiv","version":2}},"canonical_sha256":"e96636b163e8dbf81090300176199172a72f01cb9d26d2887c86fdc73ac9719a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e96636b163e8dbf81090300176199172a72f01cb9d26d2887c86fdc73ac9719a","first_computed_at":"2026-05-18T01:13:11.079225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:11.079225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YKvuOjmXHLctQNH+yTYGZTS2zSx0EqUgWO+j4GCkqFNN7w5GNeIr0k2+5FJSJBSv8qsh7Hh7XrwVhwFGa9XSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:11.079613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05684","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a5bb4dd7960a823dd6da16edb78b52ff5d38e9e2c3f26bae64316676c62b4f1","sha256:61d42d8f0271b69bbad0a4ef6b28c2b05681d21e89edcc62815aea4efcec1032"],"state_sha256":"ee0673fa0adc144fdf075335b033b0991b373361263f67aab36327f86775c450"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0i0QHjQ745uDRMy/bLVTeEtsNhnsQcymyGftbCZd0lZKVfhJHtGR5ltZEvqG+4+HbRUFMd0T8V9ujbeVTN5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:56:11.991960Z","bundle_sha256":"797a7fbeaabcb7a5c4f56326f8730bc4df37eaff73663f7e00a2ac85d6e3eaa7"}}