{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:J3HYFVXFFKC46UDQA6B2MESEIZ","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":"7039f70c3767b9a0f4da7e7c16b0c69b0e0b03fbd7d34ca23c7514ab92554f8e","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2005-04-21T14:01:12Z","title_canon_sha256":"ba8555b605b32599eab755838fd4b347c05ce261fa456a613fe5592e1228d6ee"},"schema_version":"1.0","source":{"id":"math/0504433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504433","created_at":"2026-07-04T16:56:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504433v2","created_at":"2026-07-04T16:56:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504433","created_at":"2026-07-04T16:56:38Z"},{"alias_kind":"pith_short_12","alias_value":"J3HYFVXFFKC4","created_at":"2026-07-04T16:56:38Z"},{"alias_kind":"pith_short_16","alias_value":"J3HYFVXFFKC46UDQ","created_at":"2026-07-04T16:56:38Z"},{"alias_kind":"pith_short_8","alias_value":"J3HYFVXF","created_at":"2026-07-04T16:56:38Z"}],"graph_snapshots":[{"event_id":"sha256:ff6a5a3f3ac77e70fb7ed9a5cdfa51b143a6e66dee97d327295ba3fe766848a8","target":"graph","created_at":"2026-07-04T16:56:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0504433/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the $k\\times k$ fusion eight-vertex model in terms of the corresponding fusion SOS model. Here $k\\in Z_{>0}$. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner transfer matrices, the half transfer matrices (vertex operators) and the tail operator. We give a realization of these lattice operators as well as the space of states as objects in the level $k$ representation theory of the elliptic algebra $U_{q,","authors_text":"Hitoshi Konno, Robert Weston, Takeo Kojima","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2005-04-21T14:01:12Z","title":"The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504433","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:ea40d7684161e8412f282f8dcc4b1c7becbf66c3dce7713e1ba4230e880557cb","target":"record","created_at":"2026-07-04T16:56:38Z","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":"7039f70c3767b9a0f4da7e7c16b0c69b0e0b03fbd7d34ca23c7514ab92554f8e","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2005-04-21T14:01:12Z","title_canon_sha256":"ba8555b605b32599eab755838fd4b347c05ce261fa456a613fe5592e1228d6ee"},"schema_version":"1.0","source":{"id":"math/0504433","kind":"arxiv","version":2}},"canonical_sha256":"4ecf82d6e52a85cf50700783a61244467a5443d7dc90d8fac55d57f46c43a7d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ecf82d6e52a85cf50700783a61244467a5443d7dc90d8fac55d57f46c43a7d0","first_computed_at":"2026-07-04T16:56:38.366241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:56:38.366241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e68PY2GfMiD4oRzV+ZQAE36WkOjTDuvWidzIEtTfvmRiepPpBX7vL/wUGm6/XyCWwLD19mPusJxuIW4nm9nbCg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:56:38.366659Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea40d7684161e8412f282f8dcc4b1c7becbf66c3dce7713e1ba4230e880557cb","sha256:ff6a5a3f3ac77e70fb7ed9a5cdfa51b143a6e66dee97d327295ba3fe766848a8"],"state_sha256":"39030dd9d5d94e0a467a0c2579c1a0b2faa30d102ffd3d04c02f9e4a08e356d6"}