{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MLBHDMDUXNY5NZIVVA3AY3WTPY","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":"cc2c9a395895fe02a4f8bcf867c0c3cefcd8b04be6ec01d93d45e3ad8c8ef5e4","cross_cats_sorted":["hep-th","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2010-05-23T13:00:39Z","title_canon_sha256":"2ab4de3fe691a86f1db39145db23d9348d17aef4c93ed8da1e629419feab6ce6"},"schema_version":"1.0","source":{"id":"1005.4199","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4199","created_at":"2026-05-18T02:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4199v3","created_at":"2026-05-18T02:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4199","created_at":"2026-05-18T02:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"MLBHDMDUXNY5","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MLBHDMDUXNY5NZIV","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MLBHDMDU","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:e4d3e20174147f0b9c12ed0104e740d5e80b89bf4c6b118566670a1457fdd532","target":"graph","created_at":"2026-05-18T02:33:25Z","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 the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been conjectured earlier. In particular, this provides new examples of periodicities of seeds.","authors_text":"Roberto Tateo, Tomoki Nakanishi","cross_cats":["hep-th","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2010-05-23T13:00:39Z","title":"Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4199","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":"sha256:6fe48d8215e5f1dc3b174cea63b72d2babe48d02b5f321b064adf457b4e45356","target":"record","created_at":"2026-05-18T02:33:25Z","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":"cc2c9a395895fe02a4f8bcf867c0c3cefcd8b04be6ec01d93d45e3ad8c8ef5e4","cross_cats_sorted":["hep-th","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2010-05-23T13:00:39Z","title_canon_sha256":"2ab4de3fe691a86f1db39145db23d9348d17aef4c93ed8da1e629419feab6ce6"},"schema_version":"1.0","source":{"id":"1005.4199","kind":"arxiv","version":3}},"canonical_sha256":"62c271b074bb71d6e515a8360c6ed37e34dc7e7a960a8ed32dc0040c9033458e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62c271b074bb71d6e515a8360c6ed37e34dc7e7a960a8ed32dc0040c9033458e","first_computed_at":"2026-05-18T02:33:25.788710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:25.788710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yh75H2bUnC+Y1LZtDvbYFpz9HpOBhjPs0a/eHlaMUWyl5IKHdV8xJsldjczm3C929jGNvCV8f0OM2zHLbd4iBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:25.789046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4199","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe48d8215e5f1dc3b174cea63b72d2babe48d02b5f321b064adf457b4e45356","sha256:e4d3e20174147f0b9c12ed0104e740d5e80b89bf4c6b118566670a1457fdd532"],"state_sha256":"8aa774d4945905d3aa48d092fd383c6b2a1bdabd2154c386b155592589a2b177"}