{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:O6B7BGDWWMJ7J45UT5EFX6F43O","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":"5183c21503545da2d5cfb644b6179c3e08780104d4b21b982a2bacf5965e7b78","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-06-04T20:07:30Z","title_canon_sha256":"abcd6a4e6cf8fd56ffd78902f228f7dd0dbac30759716b28695e851ddf8bf14d"},"schema_version":"1.0","source":{"id":"1506.01725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01725","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01725v1","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01725","created_at":"2026-05-17T23:54:37Z"},{"alias_kind":"pith_short_12","alias_value":"O6B7BGDWWMJ7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"O6B7BGDWWMJ7J45U","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"O6B7BGDW","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:f2b1182e0c4cbf79723eebf0b28da7bdc20d1b8af553403a2aa9fa5030f02b13","target":"graph","created_at":"2026-05-17T23:54:37Z","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 this paper, an analogue of matrix models from free probability is developed in the bi-free setting. A bi-matrix model is not simply a pair of matrix models, but a pair of matrix models where one element in the pair acts by left-multiplication on matrices and the other element acts via a `twisted'-right action. The asymptotic distributions of bi-matrix models of Gaussian random variables tend to bi-free central limit distributions with certain covariance matrices. Furthermore, many classical random matrix results immediately generalize to the bi-free setting. For example, bi-matrix models of","authors_text":"Paul Skoufranis","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-06-04T20:07:30Z","title":"Some Bi-Matrix Models for Bi-Free Limit Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01725","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":"sha256:0f2f613bc10104173bb1977810b70bf58779250dea824dc5e697f082ee0c1d8d","target":"record","created_at":"2026-05-17T23:54:37Z","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":"5183c21503545da2d5cfb644b6179c3e08780104d4b21b982a2bacf5965e7b78","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-06-04T20:07:30Z","title_canon_sha256":"abcd6a4e6cf8fd56ffd78902f228f7dd0dbac30759716b28695e851ddf8bf14d"},"schema_version":"1.0","source":{"id":"1506.01725","kind":"arxiv","version":1}},"canonical_sha256":"7783f09876b313f4f3b49f485bf8bcdb9c85d9cf633e424ab210b9c8e2e12651","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7783f09876b313f4f3b49f485bf8bcdb9c85d9cf633e424ab210b9c8e2e12651","first_computed_at":"2026-05-17T23:54:37.159488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:37.159488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fLrSO8wCuFTgc3HUoMSaszmDDfc2MiHhKC4jQRalaNzlNxZ9UcZ/Gmi0aGxVEK2Ab+bbiV9K2PdUNhTcvhLMCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:37.160095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f2f613bc10104173bb1977810b70bf58779250dea824dc5e697f082ee0c1d8d","sha256:f2b1182e0c4cbf79723eebf0b28da7bdc20d1b8af553403a2aa9fa5030f02b13"],"state_sha256":"02381b138e741a54453e1b820816b2f87f9629b53f400bc74fa431fdb0eab37e"}