{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PBV2DMZ7QR6TLOTBLSZHWOY6IZ","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":"147681f65f3ad8ca56fac41ba25652bba716ad4efa185f60639c963bc59a2996","cross_cats_sorted":["math-ph","math.MP","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T04:24:59Z","title_canon_sha256":"4f84c9370a493d567b040eb95432f39e55ad667160f43d4f3af6067d33aba53b"},"schema_version":"1.0","source":{"id":"2501.15765","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.15765","created_at":"2026-07-05T12:02:39Z"},{"alias_kind":"arxiv_version","alias_value":"2501.15765v3","created_at":"2026-07-05T12:02:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.15765","created_at":"2026-07-05T12:02:39Z"},{"alias_kind":"pith_short_12","alias_value":"PBV2DMZ7QR6T","created_at":"2026-07-05T12:02:39Z"},{"alias_kind":"pith_short_16","alias_value":"PBV2DMZ7QR6TLOTB","created_at":"2026-07-05T12:02:39Z"},{"alias_kind":"pith_short_8","alias_value":"PBV2DMZ7","created_at":"2026-07-05T12:02:39Z"}],"graph_snapshots":[{"event_id":"sha256:ee22b9ba21ba9e4b7421dfe40cae04cbc15c19f9053b7d00cb06930c5a88a612","target":"graph","created_at":"2026-07-05T12:02:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.15765/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Any square complex matrix of size $n\\times n$ can be partially characterized by its $n$ eigenvalues and/or $n$ singular values. While no one-to-one correspondence exists between those two kinds of values on a deterministic level, for random complex matrices drawn from a bi-unitarily invariant ensemble, a bijection exists between the underlying singular value ensemble and the corresponding eigenvalue ensemble. This enabled the recent finding of an explicit formula for the joint probability density between $1$ eigenvalue and $k$ singular values, coined $1,k$-point function. We derive here the la","authors_text":"Matthias Allard","cross_cats":["math-ph","math.MP","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T04:24:59Z","title":"Hard edge asymptotics of correlation functions between singular values and eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15765","kind":"arxiv","version":3},"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":"sha256:16d8570b5b18e1761d0467f73db4c49db6eedcc8b20a1691e6fc0fc819e539c7","target":"record","created_at":"2026-07-05T12:02:39Z","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":"147681f65f3ad8ca56fac41ba25652bba716ad4efa185f60639c963bc59a2996","cross_cats_sorted":["math-ph","math.MP","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-27T04:24:59Z","title_canon_sha256":"4f84c9370a493d567b040eb95432f39e55ad667160f43d4f3af6067d33aba53b"},"schema_version":"1.0","source":{"id":"2501.15765","kind":"arxiv","version":3}},"canonical_sha256":"786ba1b33f847d35ba615cb27b3b1e4643c1dcb849e0bbef264ac4d7d5f44a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"786ba1b33f847d35ba615cb27b3b1e4643c1dcb849e0bbef264ac4d7d5f44a7b","first_computed_at":"2026-07-05T12:02:39.952651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:02:39.952651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VS1JCGCO8wdqTBWZhPIOgXuplUEq06fMcUGsu6LoSR/kTavWwhvEgVSzLGf11S2Uc0Oz0cgZEA+P/rZos/cnBg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:02:39.953134Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.15765","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16d8570b5b18e1761d0467f73db4c49db6eedcc8b20a1691e6fc0fc819e539c7","sha256:ee22b9ba21ba9e4b7421dfe40cae04cbc15c19f9053b7d00cb06930c5a88a612"],"state_sha256":"a06020165eef0099cfc5098e6b7491f3cf5153ceac5c41ffa2e215f766485f11"}