{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LKW5SHVBO4JTWZ4FEYME5IT7JP","short_pith_number":"pith:LKW5SHVB","schema_version":"1.0","canonical_sha256":"5aadd91ea177133b678526184ea27f4bd34d5c3c39229d9e3b0281b56850b818","source":{"kind":"arxiv","id":"1308.2952","version":1},"attestation_state":"computed","paper":{"title":"Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Joel A. Tropp, Richard Y. Chen","submitted_at":"2013-08-13T19:28:16Z","abstract_excerpt":"Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities."},"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":"1308.2952","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-13T19:28:16Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"ee23c5dffcdc5b5392af671094dab85335a65a56e0287623f006a1e8a0452dbe","abstract_canon_sha256":"fac9a859394a8da5e40afa5aaedd98be02ab0b1507cff4fe399ec166a0cd5657"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:08.174308Z","signature_b64":"KdhalVXGdenfzdy1rMy3TaDJ7sFHhn0WyOo7q7nXa+ilG9YYx7MfM5IB4E+oDoDIiEs6rn6SsWXb3t4Siwr8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5aadd91ea177133b678526184ea27f4bd34d5c3c39229d9e3b0281b56850b818","last_reissued_at":"2026-05-18T02:53:08.173625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:08.173625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subadditivity of Matrix phi-Entropy and Concentration of Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Joel A. Tropp, Richard Y. Chen","submitted_at":"2013-08-13T19:28:16Z","abstract_excerpt":"Matrix concentration inequalities provide a direct way to bound the typical spectral norm of a random matrix. The methods for establishing these results often parallel classical arguments, such as the Laplace transform method. This work develops a matrix extension of the entropy method, and it applies these ideas to obtain some matrix concentration inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2952","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1308.2952","created_at":"2026-05-18T02:53:08.173740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.2952v1","created_at":"2026-05-18T02:53:08.173740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2952","created_at":"2026-05-18T02:53:08.173740+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKW5SHVBO4JT","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKW5SHVBO4JTWZ4F","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKW5SHVB","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP","json":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP.json","graph_json":"https://pith.science/api/pith-number/LKW5SHVBO4JTWZ4FEYME5IT7JP/graph.json","events_json":"https://pith.science/api/pith-number/LKW5SHVBO4JTWZ4FEYME5IT7JP/events.json","paper":"https://pith.science/paper/LKW5SHVB"},"agent_actions":{"view_html":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP","download_json":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP.json","view_paper":"https://pith.science/paper/LKW5SHVB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.2952&json=true","fetch_graph":"https://pith.science/api/pith-number/LKW5SHVBO4JTWZ4FEYME5IT7JP/graph.json","fetch_events":"https://pith.science/api/pith-number/LKW5SHVBO4JTWZ4FEYME5IT7JP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP/action/storage_attestation","attest_author":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP/action/author_attestation","sign_citation":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP/action/citation_signature","submit_replication":"https://pith.science/pith/LKW5SHVBO4JTWZ4FEYME5IT7JP/action/replication_record"}},"created_at":"2026-05-18T02:53:08.173740+00:00","updated_at":"2026-05-18T02:53:08.173740+00:00"}