{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UTT6LAGNRDP273XFKNQX6K4ARR","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":"5be00deb27830d6db6bb0f0e33a80b46c71c0000ff8973f3efef9cf7ab801c89","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-21T19:19:41Z","title_canon_sha256":"4e570018168906077d4707c8c490caaa66324a3434b0d981268850bf49767aea"},"schema_version":"1.0","source":{"id":"1605.06689","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06689","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06689v4","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06689","created_at":"2026-05-18T00:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"UTT6LAGNRDP2","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UTT6LAGNRDP273XF","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UTT6LAGN","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:350bdf11e0415398c11af67314c4d6fda4d11784e4c891e44c40cfa66e895820","target":"graph","created_at":"2026-05-18T00:23:57Z","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":"In [5], O. Bauer interpreted the chordal Loewner equation in terms of non-commutative probability theory. We follow this perspective and identify the chordal Loewner equations as the non-autonomous versions of evolution equations for semigroups in monotone and anti-monotone probability theory. We also look at the corresponding equation for free probability theory.","authors_text":"Sebastian Schlei{\\ss}inger","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-21T19:19:41Z","title":"The Chordal Loewner Equation and Monotone Probability Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06689","kind":"arxiv","version":4},"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":"sha256:44fe2369dece96532e1f199952bcd0b9d83d7de74291bc426862b9b205b0fbb7","target":"record","created_at":"2026-05-18T00:23:57Z","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":"5be00deb27830d6db6bb0f0e33a80b46c71c0000ff8973f3efef9cf7ab801c89","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-05-21T19:19:41Z","title_canon_sha256":"4e570018168906077d4707c8c490caaa66324a3434b0d981268850bf49767aea"},"schema_version":"1.0","source":{"id":"1605.06689","kind":"arxiv","version":4}},"canonical_sha256":"a4e7e580cd88dfafeee553617f2b808c4b5993872be05bedc30eefc563fac2aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4e7e580cd88dfafeee553617f2b808c4b5993872be05bedc30eefc563fac2aa","first_computed_at":"2026-05-18T00:23:57.191949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:57.191949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dzR8OJxw+s5Pz12CC0jliWzggUtm4ensabL9TLMPveR+WmD/9hYiOLd76KpuFMbuSJVKYHTxKqhQB5GeH0m9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:57.192629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06689","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44fe2369dece96532e1f199952bcd0b9d83d7de74291bc426862b9b205b0fbb7","sha256:350bdf11e0415398c11af67314c4d6fda4d11784e4c891e44c40cfa66e895820"],"state_sha256":"d39920723e001a43d8cac8853d1cb37a10d69666030adde43088f5dc0945d9ff"}