{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:YCYTUNBJO7BZK7RUZHAPGALTLF","short_pith_number":"pith:YCYTUNBJ","schema_version":"1.0","canonical_sha256":"c0b13a342977c3957e34c9c0f3017359432eee4fc967355f9e1651e6e51a47ae","source":{"kind":"arxiv","id":"2306.01412","version":2},"attestation_state":"computed","paper":{"title":"Matrix Inference in Growing Rank Regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Farzad Pourkamali, Jean Barbier, Nicolas Macris","submitted_at":"2023-06-02T10:04:15Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2306.01412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-02T10:04:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e5a647deef0cba75d6880c8cd9b1aa3f42b31ec3967434b31b8dc9e1b35dd959","abstract_canon_sha256":"737fc14dd5f6ee9ad31438e29cc8f31b41e19017e01cd149170fd033cc75ab27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:43:49.725300Z","signature_b64":"HboNe2vBQ/5AVC1vMl6ZP7k3XGRz/y5TMgq14e+M07la19gwf+kXVPd/53J6hAVkMiI5gWh/a6DZk+Y0ucuSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0b13a342977c3957e34c9c0f3017359432eee4fc967355f9e1651e6e51a47ae","last_reissued_at":"2026-07-05T08:43:49.724798Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:43:49.724798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix Inference in Growing Rank Regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Farzad Pourkamali, Jean Barbier, Nicolas Macris","submitted_at":"2023-06-02T10:04:15Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.01412","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.01412/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2306.01412","created_at":"2026-07-05T08:43:49.724856+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.01412v2","created_at":"2026-07-05T08:43:49.724856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.01412","created_at":"2026-07-05T08:43:49.724856+00:00"},{"alias_kind":"pith_short_12","alias_value":"YCYTUNBJO7BZ","created_at":"2026-07-05T08:43:49.724856+00:00"},{"alias_kind":"pith_short_16","alias_value":"YCYTUNBJO7BZK7RU","created_at":"2026-07-05T08:43:49.724856+00:00"},{"alias_kind":"pith_short_8","alias_value":"YCYTUNBJ","created_at":"2026-07-05T08:43:49.724856+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.07975","citing_title":"Some observations on the ambivalent role of symmetries in Bayesian inference problems","ref_index":32,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF","json":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF.json","graph_json":"https://pith.science/api/pith-number/YCYTUNBJO7BZK7RUZHAPGALTLF/graph.json","events_json":"https://pith.science/api/pith-number/YCYTUNBJO7BZK7RUZHAPGALTLF/events.json","paper":"https://pith.science/paper/YCYTUNBJ"},"agent_actions":{"view_html":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF","download_json":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF.json","view_paper":"https://pith.science/paper/YCYTUNBJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.01412&json=true","fetch_graph":"https://pith.science/api/pith-number/YCYTUNBJO7BZK7RUZHAPGALTLF/graph.json","fetch_events":"https://pith.science/api/pith-number/YCYTUNBJO7BZK7RUZHAPGALTLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF/action/storage_attestation","attest_author":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF/action/author_attestation","sign_citation":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF/action/citation_signature","submit_replication":"https://pith.science/pith/YCYTUNBJO7BZK7RUZHAPGALTLF/action/replication_record"}},"created_at":"2026-07-05T08:43:49.724856+00:00","updated_at":"2026-07-05T08:43:49.724856+00:00"}