{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DCGHJKWLU6CASBX37QG6ZFZ7IZ","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":"e0f62621b2e1b8faf032a02e41032541064c4638064f1ac4830431f95c5abe4b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-09-08T09:00:49Z","title_canon_sha256":"0d5468e0810315390ed38a976d6e51ddc2c54cf7aec1b256c697421f4343537b"},"schema_version":"1.0","source":{"id":"2009.03589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.03589","created_at":"2026-07-05T01:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"2009.03589v1","created_at":"2026-07-05T01:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.03589","created_at":"2026-07-05T01:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"DCGHJKWLU6CA","created_at":"2026-07-05T01:33:48Z"},{"alias_kind":"pith_short_16","alias_value":"DCGHJKWLU6CASBX3","created_at":"2026-07-05T01:33:48Z"},{"alias_kind":"pith_short_8","alias_value":"DCGHJKWL","created_at":"2026-07-05T01:33:48Z"}],"graph_snapshots":[{"event_id":"sha256:6794475fe2296fbba8e150aa63faad1074b294bc0b7b494ad7fbc0c4bdfddcfd","target":"graph","created_at":"2026-07-05T01:33:48Z","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/2009.03589/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This in an introduction to the theory of non-commutative distributions of non-commuting operators or random matrices. Starting from the basic problem to find a good approach to the meaning of \"non-commutative distribution\" we will, in particular, cover: free analysis, which is a version of complex analysis for several non-commuting variables; the operator-valued version of free probability theory (combinatorial but also analytic aspects); the linearization trick to reduce non-linear scalar problems to linear operator-valued problems; the combination of operator-valued convolution and lineariza","authors_text":"Roland Speicher","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-09-08T09:00:49Z","title":"Lecture Notes on \"Non-Commutative Distributions\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.03589","kind":"arxiv","version":1},"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":"sha256:5059c0397f58a7272a88d78d1a263c8c7951b91b0d2ededcc68ce8437e6980c8","target":"record","created_at":"2026-07-05T01:33:48Z","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":"e0f62621b2e1b8faf032a02e41032541064c4638064f1ac4830431f95c5abe4b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2020-09-08T09:00:49Z","title_canon_sha256":"0d5468e0810315390ed38a976d6e51ddc2c54cf7aec1b256c697421f4343537b"},"schema_version":"1.0","source":{"id":"2009.03589","kind":"arxiv","version":1}},"canonical_sha256":"188c74aacba7840906fbfc0dec973f46794a35e1dc9f84bcc74127c17450c456","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"188c74aacba7840906fbfc0dec973f46794a35e1dc9f84bcc74127c17450c456","first_computed_at":"2026-07-05T01:33:48.862953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:33:48.862953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLOw6gb8xXpEBwffKQl0c2yVGkduq9427eIzb3/E/B/ggoaVRmuK5oGk4ZoF8BKGPEUXj8T75uO/LVIti8gHBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:33:48.863306Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.03589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5059c0397f58a7272a88d78d1a263c8c7951b91b0d2ededcc68ce8437e6980c8","sha256:6794475fe2296fbba8e150aa63faad1074b294bc0b7b494ad7fbc0c4bdfddcfd"],"state_sha256":"db67e2af382c28642158bbcb8063e3488bc764627eaee65fe6ba8b2999d170ea"}