{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LH3RYTORGGEJKYY5RFA4AP6S3T","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":"23b9498e16fee852a0bd328b4bbd576aa9548db6338918940f246292bb6285f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-16T21:58:13Z","title_canon_sha256":"bf6380ef38261c3b27ffcdf2738f30b3b042db150e5e82f5fb64734918b3028b"},"schema_version":"1.0","source":{"id":"1207.3831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3831","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3831v2","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3831","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"LH3RYTORGGEJ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LH3RYTORGGEJKYY5","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LH3RYTOR","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:ee9b70ba740d0e56d507a9a2602a6beffccbe03babeca5bdb4247a0f655acfd2","target":"graph","created_at":"2026-05-18T03:38:32Z","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":"It is known that the so-called Bercovici-Pata bijection can be explained in terms of certain Hermitian random matrix ensembles $(M_{d})_{d\\geq1}$ whose asymptotic spectral distributions are free infinitely divisible. We investigate Hermitian L\\'{e}vy processes with jumps of rank one associated to these random matrix ensembles introduced in [6] and [10]. A sample path approximation by covariation processes for these matrix L\\'{e}vy processes is obtained. As a general result we prove that any $d\\times d$ complex matrix subordinator with jumps of rank one is the quadratic variation of an $\\mathbb","authors_text":"Alfonso Rocha-Arteaga, J. Armando Dom\\'inguez-Molina, V\\'ictor P\\'erez-Abreu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-16T21:58:13Z","title":"Covariation representations for Hermitian L\\'{e}vy process ensembles of free infinitely divisible distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3831","kind":"arxiv","version":2},"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":"sha256:97acd9a93cfa9e14273cd2d1cbb2f354e26e6d86159ee24b808308023b3418c9","target":"record","created_at":"2026-05-18T03:38:32Z","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":"23b9498e16fee852a0bd328b4bbd576aa9548db6338918940f246292bb6285f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-16T21:58:13Z","title_canon_sha256":"bf6380ef38261c3b27ffcdf2738f30b3b042db150e5e82f5fb64734918b3028b"},"schema_version":"1.0","source":{"id":"1207.3831","kind":"arxiv","version":2}},"canonical_sha256":"59f71c4dd1318895631d8941c03fd2dcfe40cd8c9b1a55339dd4bd6867cdf6f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59f71c4dd1318895631d8941c03fd2dcfe40cd8c9b1a55339dd4bd6867cdf6f4","first_computed_at":"2026-05-18T03:38:32.835897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:32.835897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KV0wa+CAMPqqTbjW6bWMVTEtZbxvqKfz97mUPdcyjpbd116IDgRiPzgc44CNssRv/fIdW6WYVkR7kUQUBKPkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:32.836400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97acd9a93cfa9e14273cd2d1cbb2f354e26e6d86159ee24b808308023b3418c9","sha256:ee9b70ba740d0e56d507a9a2602a6beffccbe03babeca5bdb4247a0f655acfd2"],"state_sha256":"fcf15c79b1f9009c919925ffa3db3d2b08d377ece191a5cf89933abc2392a5d6"}