{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YCYTUNBJO7BZK7RUZHAPGALTLF","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":"737fc14dd5f6ee9ad31438e29cc8f31b41e19017e01cd149170fd033cc75ab27","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-02T10:04:15Z","title_canon_sha256":"e5a647deef0cba75d6880c8cd9b1aa3f42b31ec3967434b31b8dc9e1b35dd959"},"schema_version":"1.0","source":{"id":"2306.01412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.01412","created_at":"2026-07-05T08:43:49Z"},{"alias_kind":"arxiv_version","alias_value":"2306.01412v2","created_at":"2026-07-05T08:43:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.01412","created_at":"2026-07-05T08:43:49Z"},{"alias_kind":"pith_short_12","alias_value":"YCYTUNBJO7BZ","created_at":"2026-07-05T08:43:49Z"},{"alias_kind":"pith_short_16","alias_value":"YCYTUNBJO7BZK7RU","created_at":"2026-07-05T08:43:49Z"},{"alias_kind":"pith_short_8","alias_value":"YCYTUNBJ","created_at":"2026-07-05T08:43:49Z"}],"graph_snapshots":[{"event_id":"sha256:edad673deb903c33418807f6993b2ad887af5c1c94f96b51adf1457531c113e8","target":"graph","created_at":"2026-07-05T08:43:49Z","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/2306.01412/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The inference of a large symmetric signal-matrix $\\mathbf{S} \\in \\mathbb{R}^{N\\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks $M=\\Theta(N^\\alpha)$ with $\\alpha\\in(0,1)$ the mutual information and minimum mean-square error (MMSE) are derived for two classes of signal-matrices: (a) $\\mathbf{S}=\\mathbf{X}\\mathbf{X}^\\intercal$ with entries of $\\mathbf{X}\\in\\mathbb{R}^{N\\times M}$ independent identically distributed; (b) $\\mathbf{S}$ sampled from a rotationally invariant distribution. Surprisingly, t","authors_text":"Farzad Pourkamali, Jean Barbier, Nicolas Macris","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-02T10:04:15Z","title":"Matrix Inference in Growing Rank Regimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.01412","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:ab40b53ba8fec7492baf8102e1478af24a67d2261096e56e66297b63640f31e7","target":"record","created_at":"2026-07-05T08:43:49Z","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":"737fc14dd5f6ee9ad31438e29cc8f31b41e19017e01cd149170fd033cc75ab27","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-02T10:04:15Z","title_canon_sha256":"e5a647deef0cba75d6880c8cd9b1aa3f42b31ec3967434b31b8dc9e1b35dd959"},"schema_version":"1.0","source":{"id":"2306.01412","kind":"arxiv","version":2}},"canonical_sha256":"c0b13a342977c3957e34c9c0f3017359432eee4fc967355f9e1651e6e51a47ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0b13a342977c3957e34c9c0f3017359432eee4fc967355f9e1651e6e51a47ae","first_computed_at":"2026-07-05T08:43:49.724798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:43:49.724798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HboNe2vBQ/5AVC1vMl6ZP7k3XGRz/y5TMgq14e+M07la19gwf+kXVPd/53J6hAVkMiI5gWh/a6DZk+Y0ucuSBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:43:49.725300Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.01412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab40b53ba8fec7492baf8102e1478af24a67d2261096e56e66297b63640f31e7","sha256:edad673deb903c33418807f6993b2ad887af5c1c94f96b51adf1457531c113e8"],"state_sha256":"8013a022a7126f15782885715858e3cd74d32d9271632dee0aca92f6e3837a19"}