{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4HY6YI7LOLXCFXSU7A4W7OSREP","short_pith_number":"pith:4HY6YI7L","canonical_record":{"source":{"id":"1701.02296","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-09T18:43:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f9ad1c4dae003da0b29c36a1559eea05eb0125c40ea2a66f1d31a93c98443a2a","abstract_canon_sha256":"d6aad5454d45b2447fd89376af88da64be7aec5551f627a5c5a2907185bbb2b6"},"schema_version":"1.0"},"canonical_sha256":"e1f1ec23eb72ee22de54f8396fba5123f406d3fef097f06b3245a8583c636ede","source":{"kind":"arxiv","id":"1701.02296","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02296","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02296v4","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02296","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"4HY6YI7LOLXC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HY6YI7LOLXCFXSU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HY6YI7L","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4HY6YI7LOLXCFXSU7A4W7OSREP","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02296","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-09T18:43:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"f9ad1c4dae003da0b29c36a1559eea05eb0125c40ea2a66f1d31a93c98443a2a","abstract_canon_sha256":"d6aad5454d45b2447fd89376af88da64be7aec5551f627a5c5a2907185bbb2b6"},"schema_version":"1.0"},"canonical_sha256":"e1f1ec23eb72ee22de54f8396fba5123f406d3fef097f06b3245a8583c636ede","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:20.927548Z","signature_b64":"dCv0UozKerYQTQJhDTeFhKWJa4gAxbRQFs5j8bZsWaGLXqGYfosoOHycxc/BK6V1Bs6mD43pRlMXsJHY/2qDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1f1ec23eb72ee22de54f8396fba5123f406d3fef097f06b3245a8583c636ede","last_reissued_at":"2026-05-18T00:32:20.926914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:20.926914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02296","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6o17sPcoe3uAU3gDUv8RnpRabJrtmiAnAla5VXKUjxMu9EiUpMl8+1zKCQbBeH8pdHNgkKCE0Tp3oP4lKCUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:58:40.247021Z"},"content_sha256":"e47bc3c6fed03cb70d5a044e06b9c1bf74153eacff62e8b462ea96294411b75e","schema_version":"1.0","event_id":"sha256:e47bc3c6fed03cb70d5a044e06b9c1bf74153eacff62e8b462ea96294411b75e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4HY6YI7LOLXCFXSU7A4W7OSREP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix integrals and Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.Yu. Orlov","submitted_at":"2017-01-09T18:43:19Z","abstract_excerpt":"We study multi-matrix models which may be viewed as integrals of products of tau functions which depend on the eigenvalues of products of random matrices. In the present paper we consider tau functions of the hierarchy the two-component KP (semiinfinite relativistic Toda lattice) and of hierarchy of the BKP introduced by Kac and van de Leur. Sometimes such integrals are tau functions themselves. We consider models which generate Hurwitz numbers $H^{e},f$, where $e$ is the Euler characteristic of the base surface and $f$ is the number of branch points. We show that in case the integrands contai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02296","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gH7zCRVoXKnULnkpNNJSif7SZWlc+iFMSaADq4a0FtpaqocO7mCTVatrnhmYALf9gVsIct02Yspa/gpCwq4KCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:58:40.247391Z"},"content_sha256":"32c1ca37a9cab44fa215078415c83fd95f8345dbe98df5dae08b867d1e4db85d","schema_version":"1.0","event_id":"sha256:32c1ca37a9cab44fa215078415c83fd95f8345dbe98df5dae08b867d1e4db85d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4HY6YI7LOLXCFXSU7A4W7OSREP/bundle.json","state_url":"https://pith.science/pith/4HY6YI7LOLXCFXSU7A4W7OSREP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4HY6YI7LOLXCFXSU7A4W7OSREP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T16:58:40Z","links":{"resolver":"https://pith.science/pith/4HY6YI7LOLXCFXSU7A4W7OSREP","bundle":"https://pith.science/pith/4HY6YI7LOLXCFXSU7A4W7OSREP/bundle.json","state":"https://pith.science/pith/4HY6YI7LOLXCFXSU7A4W7OSREP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4HY6YI7LOLXCFXSU7A4W7OSREP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4HY6YI7LOLXCFXSU7A4W7OSREP","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":"d6aad5454d45b2447fd89376af88da64be7aec5551f627a5c5a2907185bbb2b6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-09T18:43:19Z","title_canon_sha256":"f9ad1c4dae003da0b29c36a1559eea05eb0125c40ea2a66f1d31a93c98443a2a"},"schema_version":"1.0","source":{"id":"1701.02296","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02296","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02296v4","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02296","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"4HY6YI7LOLXC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4HY6YI7LOLXCFXSU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4HY6YI7L","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:32c1ca37a9cab44fa215078415c83fd95f8345dbe98df5dae08b867d1e4db85d","target":"graph","created_at":"2026-05-18T00:32:20Z","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 study multi-matrix models which may be viewed as integrals of products of tau functions which depend on the eigenvalues of products of random matrices. In the present paper we consider tau functions of the hierarchy the two-component KP (semiinfinite relativistic Toda lattice) and of hierarchy of the BKP introduced by Kac and van de Leur. Sometimes such integrals are tau functions themselves. We consider models which generate Hurwitz numbers $H^{e},f$, where $e$ is the Euler characteristic of the base surface and $f$ is the number of branch points. We show that in case the integrands contai","authors_text":"A.Yu. Orlov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-09T18:43:19Z","title":"Matrix integrals and Hurwitz numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02296","kind":"arxiv","version":4},"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:e47bc3c6fed03cb70d5a044e06b9c1bf74153eacff62e8b462ea96294411b75e","target":"record","created_at":"2026-05-18T00:32:20Z","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":"d6aad5454d45b2447fd89376af88da64be7aec5551f627a5c5a2907185bbb2b6","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-01-09T18:43:19Z","title_canon_sha256":"f9ad1c4dae003da0b29c36a1559eea05eb0125c40ea2a66f1d31a93c98443a2a"},"schema_version":"1.0","source":{"id":"1701.02296","kind":"arxiv","version":4}},"canonical_sha256":"e1f1ec23eb72ee22de54f8396fba5123f406d3fef097f06b3245a8583c636ede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1f1ec23eb72ee22de54f8396fba5123f406d3fef097f06b3245a8583c636ede","first_computed_at":"2026-05-18T00:32:20.926914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:20.926914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dCv0UozKerYQTQJhDTeFhKWJa4gAxbRQFs5j8bZsWaGLXqGYfosoOHycxc/BK6V1Bs6mD43pRlMXsJHY/2qDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:20.927548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02296","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e47bc3c6fed03cb70d5a044e06b9c1bf74153eacff62e8b462ea96294411b75e","sha256:32c1ca37a9cab44fa215078415c83fd95f8345dbe98df5dae08b867d1e4db85d"],"state_sha256":"ff58a740a22dacb369178c8e97f7b395da7c8463af8e14d969d96fc1dc6025e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptCbzn+bo921LYuit2AXpGnFbnFHFy/JsyDCx+78G2hdvMW/kbIdpM9MugGT6eDhUyl9z88IePRiP/Z9fgRwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T16:58:40.249238Z","bundle_sha256":"24ee89b6b3036cf80ed2986fab0241da9d30d0dc11c94ee81c4c4b19f717fa11"}}