{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4YORH7N56TDO2UGU5K3PPF3RTL","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":"117037057fad46162c9d16fb3351b3211567c8b88ecfae0f93ab7bfc1e753e24","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T06:59:52Z","title_canon_sha256":"bcfef35e70436a4345bd34be249f983d20b1447e6e00986322e963f02251657b"},"schema_version":"1.0","source":{"id":"2606.27774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27774","created_at":"2026-06-29T01:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27774v1","created_at":"2026-06-29T01:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27774","created_at":"2026-06-29T01:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"4YORH7N56TDO","created_at":"2026-06-29T01:14:48Z"},{"alias_kind":"pith_short_16","alias_value":"4YORH7N56TDO2UGU","created_at":"2026-06-29T01:14:48Z"},{"alias_kind":"pith_short_8","alias_value":"4YORH7N5","created_at":"2026-06-29T01:14:48Z"}],"graph_snapshots":[{"event_id":"sha256:d2914346b24bf0d1e963cc87e0a1484f1976b4663eb13a2371bda4efd98a9680","target":"graph","created_at":"2026-06-29T01:14:48Z","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/2606.27774/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the asymptotics of a block-Wishart random matrix ensemble of the type ${\\boldsymbol W}_k = ({\\boldsymbol X}^* \\otimes {\\boldsymbol I}_k){\\boldsymbol T}({\\boldsymbol X}\\otimes{\\boldsymbol I}_k)$ for ${\\boldsymbol X} \\in\\mathbb{C}^{n\\times p}$ with i.i.d. rows satisfying a suitable concentration-of-measure property, and ${\\boldsymbol T} := \\textrm{\\bf Diag}({\\boldsymbol T}_i)_{i\\in[n]}$ a block diagonal matrix with self-adjoint blocks ${\\boldsymbol T}_i\\in \\mathbb{C}^{k\\times k}$, under the proportional asymptotics $n/p\\to\\alpha$ with $k$ fixed. These matrices play a prominent role in","authors_text":"Andrea Montanari, Basil Saeed","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T06:59:52Z","title":"Variational Formulas for the Spectrum of Block Wishart Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27774","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":"sha256:5ba5fc30b4b01b6055ba3d1fa07897656cfcdcdb633b1c8d3b4b7c1bd8ba7bac","target":"record","created_at":"2026-06-29T01:14:48Z","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":"117037057fad46162c9d16fb3351b3211567c8b88ecfae0f93ab7bfc1e753e24","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-26T06:59:52Z","title_canon_sha256":"bcfef35e70436a4345bd34be249f983d20b1447e6e00986322e963f02251657b"},"schema_version":"1.0","source":{"id":"2606.27774","kind":"arxiv","version":1}},"canonical_sha256":"e61d13fdbdf4c6ed50d4eab6f797719ac05d6cb3ac22650e51372a54ad8801ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e61d13fdbdf4c6ed50d4eab6f797719ac05d6cb3ac22650e51372a54ad8801ea","first_computed_at":"2026-06-29T01:14:48.008077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T01:14:48.008077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r75ACpYKMKmkq8UqYczuumOW/2FT5OlEf/T1HtvVEUZikOwcJhSZkeCIVlbGh+Y6PfLpBI16N6nT1mts8nSSAQ==","signature_status":"signed_v1","signed_at":"2026-06-29T01:14:48.008449Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ba5fc30b4b01b6055ba3d1fa07897656cfcdcdb633b1c8d3b4b7c1bd8ba7bac","sha256:d2914346b24bf0d1e963cc87e0a1484f1976b4663eb13a2371bda4efd98a9680"],"state_sha256":"9f8f22f8bcfe046122b8a2f8027c84c3c7c95f796deca69e0224950e29866b93"}