{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:S3BBHNULWNTC6EB2UOKCUKWE6O","short_pith_number":"pith:S3BBHNUL","schema_version":"1.0","canonical_sha256":"96c213b68bb3662f103aa3942a2ac4f3aeebf6df6890397e9403d3b662320ddd","source":{"kind":"arxiv","id":"hep-th/0111263","version":2},"attestation_state":"computed","paper":{"title":"Entropy of Operator-valued Random Variables: A Variational Principle for Large N Matrix Models","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"G. S. Krishnaswami, L. Akant, S. G. Rajeev (U. Rochester)","submitted_at":"2001-11-28T20:25:37Z","abstract_excerpt":"We show that, in 't Hooft's large N limit, matrix models can be formulated as a classical theory whose equations of motion are the factorized Schwinger--Dyson equations. We discover an action principle for this classical theory. This action contains a universal term describing the entropy of the non-commutative probability distributions. We show that this entropy is a nontrivial 1-cocycle of the non-commutative analogue of the diffeomorphism group and derive an explicit formula for it. The action principle allows us to solve matrix models using novel variational approximation methods; in the s"},"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":"hep-th/0111263","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2001-11-28T20:25:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ebf975af6fef70e1bae25601b1017f39803bea2bfab95665afdefdbd3e571f9a","abstract_canon_sha256":"b78aaceb2d42db45c68022d2e7546e25c003d504aceef45bfc16d44ffdb27c9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:36:11.372810Z","signature_b64":"HY7Ha2LhPtZWgRQQvV8a8S4GaJzzElnzl7fGbQyqfQ0hdZpE6b2GQO1Dmd5yJUkWNGBB+A8cSNQwIb/8LbhgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96c213b68bb3662f103aa3942a2ac4f3aeebf6df6890397e9403d3b662320ddd","last_reissued_at":"2026-05-18T02:36:11.372262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:36:11.372262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy of Operator-valued Random Variables: A Variational Principle for Large N Matrix Models","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"G. S. Krishnaswami, L. Akant, S. G. Rajeev (U. Rochester)","submitted_at":"2001-11-28T20:25:37Z","abstract_excerpt":"We show that, in 't Hooft's large N limit, matrix models can be formulated as a classical theory whose equations of motion are the factorized Schwinger--Dyson equations. We discover an action principle for this classical theory. This action contains a universal term describing the entropy of the non-commutative probability distributions. We show that this entropy is a nontrivial 1-cocycle of the non-commutative analogue of the diffeomorphism group and derive an explicit formula for it. The action principle allows us to solve matrix models using novel variational approximation methods; in the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0111263","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":""},"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":"hep-th/0111263","created_at":"2026-05-18T02:36:11.372352+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0111263v2","created_at":"2026-05-18T02:36:11.372352+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0111263","created_at":"2026-05-18T02:36:11.372352+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3BBHNULWNTC","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3BBHNULWNTC6EB2","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3BBHNUL","created_at":"2026-05-18T12:25:50.845339+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/S3BBHNULWNTC6EB2UOKCUKWE6O","json":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O.json","graph_json":"https://pith.science/api/pith-number/S3BBHNULWNTC6EB2UOKCUKWE6O/graph.json","events_json":"https://pith.science/api/pith-number/S3BBHNULWNTC6EB2UOKCUKWE6O/events.json","paper":"https://pith.science/paper/S3BBHNUL"},"agent_actions":{"view_html":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O","download_json":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O.json","view_paper":"https://pith.science/paper/S3BBHNUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0111263&json=true","fetch_graph":"https://pith.science/api/pith-number/S3BBHNULWNTC6EB2UOKCUKWE6O/graph.json","fetch_events":"https://pith.science/api/pith-number/S3BBHNULWNTC6EB2UOKCUKWE6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O/action/storage_attestation","attest_author":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O/action/author_attestation","sign_citation":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O/action/citation_signature","submit_replication":"https://pith.science/pith/S3BBHNULWNTC6EB2UOKCUKWE6O/action/replication_record"}},"created_at":"2026-05-18T02:36:11.372352+00:00","updated_at":"2026-05-18T02:36:11.372352+00:00"}