{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:R3QK6THGFHETBTHDROG4OLN7SP","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":"6d4391522c853477b7c5aebd6112773b0085722ac61c4a77630293e4d7a111df","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-05-20T16:01:23Z","title_canon_sha256":"e10420e0df607bc60667bdd9f89086b83bbc108c4cc48ad7d21bad0c086fb425"},"schema_version":"1.0","source":{"id":"1905.08187","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.08187","created_at":"2026-07-05T00:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1905.08187v2","created_at":"2026-07-05T00:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08187","created_at":"2026-07-05T00:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"R3QK6THGFHET","created_at":"2026-07-05T00:55:27Z"},{"alias_kind":"pith_short_16","alias_value":"R3QK6THGFHETBTHD","created_at":"2026-07-05T00:55:27Z"},{"alias_kind":"pith_short_8","alias_value":"R3QK6THG","created_at":"2026-07-05T00:55:27Z"}],"graph_snapshots":[{"event_id":"sha256:6d43f716fe82874f1b93d9a28ccb875a3dc20798bbd5556ec55a763f93fa66c9","target":"graph","created_at":"2026-07-05T00:55:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1905.08187/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X_1,\\dots,X_n$ be operators in a finite von Neumann algebra and consider their division closure in the affiliated unbounded operators. We address the question when this division closure is a skew field (aka division ring) and when it is the free skew field. We show that the first property is equivalent to the strong Atiyah property and that the second property can be characterized in terms of the non-commutative distribution of $X_1,\\dots,X_n$. More precisely, $X_1,\\dots,X_n$ generate the free skew field if and only if there exist no non-zero finite rank operators $T_1,\\dots,T_n$ such tha","authors_text":"Roland Speicher, Sheng Yin, Tobias Mai","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-05-20T16:01:23Z","title":"The free field: realization via unbounded operators and Atiyah property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08187","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:accfdb83d78145964e8e175096f63e3473c8fb55a0c8f875695f9105787ff86d","target":"record","created_at":"2026-07-05T00:55:27Z","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":"6d4391522c853477b7c5aebd6112773b0085722ac61c4a77630293e4d7a111df","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-05-20T16:01:23Z","title_canon_sha256":"e10420e0df607bc60667bdd9f89086b83bbc108c4cc48ad7d21bad0c086fb425"},"schema_version":"1.0","source":{"id":"1905.08187","kind":"arxiv","version":2}},"canonical_sha256":"8ee0af4ce629c930cce38b8dc72dbf93c277f730ec06a4a689d9375f6f2c0950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ee0af4ce629c930cce38b8dc72dbf93c277f730ec06a4a689d9375f6f2c0950","first_computed_at":"2026-07-05T00:55:27.615110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:55:27.615110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XO1fzo+f9tll9kRq97skPezudYiW5zHJ+PRRxCclMgu91Mn/ToorNKzHhfHcq5HlX1/XGuOMQfAj95AVyEEmCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:55:27.615491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.08187","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:accfdb83d78145964e8e175096f63e3473c8fb55a0c8f875695f9105787ff86d","sha256:6d43f716fe82874f1b93d9a28ccb875a3dc20798bbd5556ec55a763f93fa66c9"],"state_sha256":"269e8acac95a0ad907f5aa85a83c87c27f9ad04632c0a208155f2eb105e84912"}