{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JBGG3N2ARL3LZ32OC54RYKZRLT","short_pith_number":"pith:JBGG3N2A","schema_version":"1.0","canonical_sha256":"484c6db7408af6bcef4e17791c2b315ce5178b23a51ca5a5ad15bab732bedc68","source":{"kind":"arxiv","id":"1201.5241","version":1},"attestation_state":"computed","paper":{"title":"Entropy functions and determinant inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongning Guo, Raymond Yeung, Terence Chan","submitted_at":"2012-01-25T11:51:34Z","abstract_excerpt":"In this paper, we show that the characterisation of all determinant inequalities for $n \\times n$ positive definite matrices is equivalent to determining the smallest closed and convex cone containing all entropy functions induced by $n$ scalar Gaussian random variables. We have obtained inner and outer bounds on the cone by using representable functions and entropic functions. In particular, these bounds are tight and explicit for $n \\le 3$, implying that determinant inequalities for $3 \\times 3$ positive definite matrices are completely characterized by Shannon-type information 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":"1201.5241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-25T11:51:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"993814440240bbe728252564c1c4a38e6ed9f2af3a8ac0fb9dffaca7b4f3de3d","abstract_canon_sha256":"a4d97ef94cfd243ee61daa68d8539c995a8d706b84a3c6c2e2f7dfe3c35435ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:55.245404Z","signature_b64":"ws152yAj6YHUykYe/mb2vrk129cYUCPgX099PV+WP8g9L9o+JnlRkbJysyw6JX1c2nWqPX3vJIzDEcVnHnUNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"484c6db7408af6bcef4e17791c2b315ce5178b23a51ca5a5ad15bab732bedc68","last_reissued_at":"2026-05-18T04:03:55.244740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:55.244740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy functions and determinant inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongning Guo, Raymond Yeung, Terence Chan","submitted_at":"2012-01-25T11:51:34Z","abstract_excerpt":"In this paper, we show that the characterisation of all determinant inequalities for $n \\times n$ positive definite matrices is equivalent to determining the smallest closed and convex cone containing all entropy functions induced by $n$ scalar Gaussian random variables. We have obtained inner and outer bounds on the cone by using representable functions and entropic functions. In particular, these bounds are tight and explicit for $n \\le 3$, implying that determinant inequalities for $3 \\times 3$ positive definite matrices are completely characterized by Shannon-type information inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5241","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":"1201.5241","created_at":"2026-05-18T04:03:55.244841+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5241v1","created_at":"2026-05-18T04:03:55.244841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5241","created_at":"2026-05-18T04:03:55.244841+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBGG3N2ARL3L","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBGG3N2ARL3LZ32O","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBGG3N2A","created_at":"2026-05-18T12:27:11.947152+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/JBGG3N2ARL3LZ32OC54RYKZRLT","json":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT.json","graph_json":"https://pith.science/api/pith-number/JBGG3N2ARL3LZ32OC54RYKZRLT/graph.json","events_json":"https://pith.science/api/pith-number/JBGG3N2ARL3LZ32OC54RYKZRLT/events.json","paper":"https://pith.science/paper/JBGG3N2A"},"agent_actions":{"view_html":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT","download_json":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT.json","view_paper":"https://pith.science/paper/JBGG3N2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5241&json=true","fetch_graph":"https://pith.science/api/pith-number/JBGG3N2ARL3LZ32OC54RYKZRLT/graph.json","fetch_events":"https://pith.science/api/pith-number/JBGG3N2ARL3LZ32OC54RYKZRLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT/action/storage_attestation","attest_author":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT/action/author_attestation","sign_citation":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT/action/citation_signature","submit_replication":"https://pith.science/pith/JBGG3N2ARL3LZ32OC54RYKZRLT/action/replication_record"}},"created_at":"2026-05-18T04:03:55.244841+00:00","updated_at":"2026-05-18T04:03:55.244841+00:00"}