{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PYNLZ47BDQQ46EDURAUCKCZMBX","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":"492659d2b5d7b6b9119c348701b21971f9ff1639e636947d390733f496967eb7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-08-09T05:58:29Z","title_canon_sha256":"66d07634cbc0c2898f74a9ebfd4fcb53ab95b11a4777a8b426f082b3061d149e"},"schema_version":"1.0","source":{"id":"1308.2035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2035","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2035v1","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2035","created_at":"2026-05-18T03:16:18Z"},{"alias_kind":"pith_short_12","alias_value":"PYNLZ47BDQQ4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"PYNLZ47BDQQ46EDU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"PYNLZ47B","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:f811f9bdf631a077427736c5164eb342976b3df568d0ba21faa83860678e003f","target":"graph","created_at":"2026-05-18T03:16:18Z","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 compute the generating series for the simplest class of bi-free cumulants, beyond free cumulants, the two-bands bi-free cumulants of a pair of a left and a right variable. We also consider two-faced systems with a commutation condition implying that two-bands moments, that is expectation values of the product of a monomial of left and a monomial of right variables determine the other moments. Examples include hyponormal operators, dual systems in free entropy theory and bi-partite systems.","authors_text":"Dan-Virgil Voiculescu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-08-09T05:58:29Z","title":"Free Probability for Pairs of Faces II: 2-Variables Bi-free $R$-Transform and Systems with Rank $\\le 1$ Commutation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2035","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:cad562fb784e140a3f4f2cd4637c6e687c896aa6733db5a1bac70786bea2fc43","target":"record","created_at":"2026-05-18T03:16:18Z","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":"492659d2b5d7b6b9119c348701b21971f9ff1639e636947d390733f496967eb7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-08-09T05:58:29Z","title_canon_sha256":"66d07634cbc0c2898f74a9ebfd4fcb53ab95b11a4777a8b426f082b3061d149e"},"schema_version":"1.0","source":{"id":"1308.2035","kind":"arxiv","version":1}},"canonical_sha256":"7e1abcf3e11c21cf10748828250b2c0df8886d9d0aff7580f7a7879b169fe8b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e1abcf3e11c21cf10748828250b2c0df8886d9d0aff7580f7a7879b169fe8b3","first_computed_at":"2026-05-18T03:16:18.421173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:18.421173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WGqm2CEOAw6bVXgQH3H4io5Etk1X5g+2j9HZ+upv6w9o8+KOqt9kSo5VBfWXYxubJc3aT/ENmaC9B2hzb22jDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:18.421661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cad562fb784e140a3f4f2cd4637c6e687c896aa6733db5a1bac70786bea2fc43","sha256:f811f9bdf631a077427736c5164eb342976b3df568d0ba21faa83860678e003f"],"state_sha256":"10526fc81816480ddcaa00713f82f51579e8e9fc80990c2dae8ca4db91b18556"}