{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5PWQDOVQ54NONGDK2QIRDMAC6T","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":"b701e998a83ee98e70d206eebfd357b7b03a31d65fd6e2b59c285d917115395f","cross_cats_sorted":["hep-th","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-29T06:15:48Z","title_canon_sha256":"62865342cdb18851f5c1be1f6c37754617bd5d85084b5ff6722320ab2b2db5ae"},"schema_version":"1.0","source":{"id":"1501.07351","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07351","created_at":"2026-05-18T01:31:45Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07351v3","created_at":"2026-05-18T01:31:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07351","created_at":"2026-05-18T01:31:45Z"},{"alias_kind":"pith_short_12","alias_value":"5PWQDOVQ54NO","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5PWQDOVQ54NONGDK","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5PWQDOVQ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:1b2d4f18eb751b4faa2ac5350cfa3c2654951c8b7345ed1dd835244504f0733d","target":"graph","created_at":"2026-05-18T01:31:45Z","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":"The quantum elliptic $R$-matrices of Baxter-Belavin type satisfy the associative Yang-Baxter equation in ${\\rm Mat}(N,\\mathbb C)^{\\otimes 3}$. The latter can be considered as noncommutative analogue of the Fay identity for the scalar Kronecker function. In this paper we extend the list of $R$-matrix valued analogues of elliptic function identities. In particular, we propose counterparts of the Fay identities in ${\\rm Mat}(N,\\mathbb C)^{\\otimes 2}$. As an application we construct $R$-matrix valued $2N^2\\times 2N^2$ Lax pairs for the Painlev\\'e VI equation (in elliptic form) with four free const","authors_text":"A. Levin, A. Zotov, M. Olshanetsky","cross_cats":["hep-th","math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-29T06:15:48Z","title":"Quantum Baxter-Belavin R-matrices and multidimensional Lax pairs for Painleve VI"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07351","kind":"arxiv","version":3},"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":"sha256:4b839da9119b318f38cdfea8308c3a6597c94b69738772ab394ac5447af96a55","target":"record","created_at":"2026-05-18T01:31:45Z","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":"b701e998a83ee98e70d206eebfd357b7b03a31d65fd6e2b59c285d917115395f","cross_cats_sorted":["hep-th","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-29T06:15:48Z","title_canon_sha256":"62865342cdb18851f5c1be1f6c37754617bd5d85084b5ff6722320ab2b2db5ae"},"schema_version":"1.0","source":{"id":"1501.07351","kind":"arxiv","version":3}},"canonical_sha256":"ebed01bab0ef1ae6986ad41111b002f4cdb3ffb6f19eb59b87d4b199c7adabca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebed01bab0ef1ae6986ad41111b002f4cdb3ffb6f19eb59b87d4b199c7adabca","first_computed_at":"2026-05-18T01:31:45.762073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:45.762073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txMYhP3HNZN/QT5DUB3EDkhKcDHMvO+vecBDj/D6QjzguReQkL/y4ugdFiDmaXZHmaXj8O+1FU1WWWutmWzsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:45.762655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07351","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b839da9119b318f38cdfea8308c3a6597c94b69738772ab394ac5447af96a55","sha256:1b2d4f18eb751b4faa2ac5350cfa3c2654951c8b7345ed1dd835244504f0733d"],"state_sha256":"cef215679d7d1a55c4ce87f1ef314a0f86316c180c1ed2a0283e87f1f593f544"}