{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:ICSMRBKZAQ7DL637II7MYJE64E","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":"43f9c27b9b4c91436ff080f0fee557bd24abfb8eb37a6f1dc10a8cc159559b2e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-12-10T19:00:49Z","title_canon_sha256":"c81cc4392bc4254b0f048a4651fb17a6a6bbd4c8f689577fb1455afdfd4c2c19"},"schema_version":"1.0","source":{"id":"hep-th/9212070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9212070","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9212070v2","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9212070","created_at":"2026-05-18T01:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"ICSMRBKZAQ7D","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"ICSMRBKZAQ7DL637","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"ICSMRBKZ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:9c1880e65c1890760c158ead83c4eb61197937232c0c3615b9d3c69a286eac3b","target":"graph","created_at":"2026-05-18T01:38:43Z","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"},"paper":{"abstract_excerpt":"We derive the discrete linear systems associated to multi--matrix models, the corresponding discrete hierarchies and the appropriate coupling conditions. We also obtain the $W_{1+\\infty}$ constraints on the partition function. We then apply to multi--matrix models the technique, developed in previous papers, of extracting hierarchies of differential equations from lattice ones without passing through a continuum limit. In a q--matrix model we find 2q coupled differential systems. The corresponding differential hierarchies are particular versions of the KP hierarchy. We show that the multi--mat","authors_text":"C.S.Xiong, L.Bonora","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1992-12-10T19:00:49Z","title":"Multi-matrix models without continuum limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9212070","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:b6c1614a06f8cf8a56986e2611ac526f82659c738e6d3fb8943512413007af36","target":"record","created_at":"2026-05-18T01:38:43Z","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":"43f9c27b9b4c91436ff080f0fee557bd24abfb8eb37a6f1dc10a8cc159559b2e","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-12-10T19:00:49Z","title_canon_sha256":"c81cc4392bc4254b0f048a4651fb17a6a6bbd4c8f689577fb1455afdfd4c2c19"},"schema_version":"1.0","source":{"id":"hep-th/9212070","kind":"arxiv","version":2}},"canonical_sha256":"40a4c88559043e35fb7f423ecc249ee11026d5eb95157f16585a9cf73971ba18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40a4c88559043e35fb7f423ecc249ee11026d5eb95157f16585a9cf73971ba18","first_computed_at":"2026-05-18T01:38:43.091184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:43.091184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IXZiSRrk7oPm01PzwfoXmzKpzHQKztN/LJ6aksJv5BuokVsq5pu+VhF01ZuqW5i/RKVYwS35acodRtj8AWqNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:43.091589Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9212070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6c1614a06f8cf8a56986e2611ac526f82659c738e6d3fb8943512413007af36","sha256:9c1880e65c1890760c158ead83c4eb61197937232c0c3615b9d3c69a286eac3b"],"state_sha256":"2216a57e99cb1da0c15122116062c94fdb63fdee39e1e8cefb063b58756073fe"}