{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6N63MPCVFRH6KRJI7Q6BUA4WKP","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":"73ba20c743e3ade37048edd46b19615de5400e0a5863640b5e609fe1383816a0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-16T08:32:18Z","title_canon_sha256":"10fbe52e842e489857f5350ccb182f4c927935372cc1cca40df1bef6126d912e"},"schema_version":"1.0","source":{"id":"1501.03910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03910","created_at":"2026-05-18T00:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03910v1","created_at":"2026-05-18T00:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03910","created_at":"2026-05-18T00:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"6N63MPCVFRH6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6N63MPCVFRH6KRJI","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6N63MPCV","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:8eaa02227a9dad3c5cca9d5d51a5287afb7f19076e70836eb3254a57abbaf0d2","target":"graph","created_at":"2026-05-18T00:09:36Z","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 prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a multiplication of a truncated unitary matrix with a random matrix. We show that the structure of polynomial ensembles and of certain Pfaffian ensembles is preserved. Furthermore we derive the joint singular value density of a product of truncated unitary matrices and its corresponding correlation kernel which can be written as a double contour integral. This leads to hard edge scaling limits that also","authors_text":"Arno B.J. Kuijlaars, Dries Stivigny, Mario Kieburg","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-16T08:32:18Z","title":"Singular value statistics of matrix products with truncated unitary matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03910","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:d99342aa0a0bd857dd9f5124ddd0add79ea6ccee6e906f0a8ed25841deff3e8d","target":"record","created_at":"2026-05-18T00:09:36Z","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":"73ba20c743e3ade37048edd46b19615de5400e0a5863640b5e609fe1383816a0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-16T08:32:18Z","title_canon_sha256":"10fbe52e842e489857f5350ccb182f4c927935372cc1cca40df1bef6126d912e"},"schema_version":"1.0","source":{"id":"1501.03910","kind":"arxiv","version":1}},"canonical_sha256":"f37db63c552c4fe54528fc3c1a039653f2e2bdc61a3a95cc07d3290ea4cd6143","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f37db63c552c4fe54528fc3c1a039653f2e2bdc61a3a95cc07d3290ea4cd6143","first_computed_at":"2026-05-18T00:09:36.973887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:36.973887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gqseEdkypHi1ZohE9IRARZwAX7eAYiKeA6QY1hded8ikrmCKgni9MVVe0Mi0iGOe2PG/15RQqxwztHqOovPMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:36.974405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d99342aa0a0bd857dd9f5124ddd0add79ea6ccee6e906f0a8ed25841deff3e8d","sha256:8eaa02227a9dad3c5cca9d5d51a5287afb7f19076e70836eb3254a57abbaf0d2"],"state_sha256":"5e09f2bd657e60f0c380bbda039b68425587a3debcc35bbb21c93c1e9a506574"}