{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ICTTDFQLP5Z5GU7UT5M4QTAIXH","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":"66b8a1c634a89bc0b053b5f7998e8a74c5f6420151ba0ae01524fa12f225daea","cross_cats_sorted":["hep-th","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-22T08:30:17Z","title_canon_sha256":"4db70a95d086d06e474d0a8f011a9e24b2f9b10295d6e276949e452d9a77818b"},"schema_version":"1.0","source":{"id":"1301.5105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5105","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5105v2","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5105","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"ICTTDFQLP5Z5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ICTTDFQLP5Z5GU7U","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ICTTDFQL","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:e6bf6fa686c0404def287047ae78c4701434e5a66ba772dc913f9059f4750074","target":"graph","created_at":"2026-05-18T03:31:06Z","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":"In this article we present the hexagon equations for dilogarithms which come from the analytic continuation of the dilogarithm $\\mathrm{Li}_2(z)$ to ${\\mathbf P}^1 \\setminus {0,1,\\infty}$. The hexagon equations are equivalent to the coboundary relations for a certain 1-cocycle of holomorphic functions on ${\\mathbf P}^1$, and are solved by the Riemann-Hilbert problem of additive type. They uniquely characterize the dilogarithm under the normalization condition.","authors_text":"Kimio Ueno, Shu Oi","cross_cats":["hep-th","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-22T08:30:17Z","title":"The hexagon equations for dilogarithms and the Riemann-Hilbert problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5105","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:c802ba44548c16d3009b16a197a8785b26ab5bfc7364ad77b5edb88d93f5837b","target":"record","created_at":"2026-05-18T03:31:06Z","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":"66b8a1c634a89bc0b053b5f7998e8a74c5f6420151ba0ae01524fa12f225daea","cross_cats_sorted":["hep-th","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-01-22T08:30:17Z","title_canon_sha256":"4db70a95d086d06e474d0a8f011a9e24b2f9b10295d6e276949e452d9a77818b"},"schema_version":"1.0","source":{"id":"1301.5105","kind":"arxiv","version":2}},"canonical_sha256":"40a731960b7f73d353f49f59c84c08b9f1d12bc8acf4b8e026cef97158a7ae78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40a731960b7f73d353f49f59c84c08b9f1d12bc8acf4b8e026cef97158a7ae78","first_computed_at":"2026-05-18T03:31:06.252873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:06.252873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y1Wukku2Fht2E/q9bz/amyNZuFhh1xfqFLVvv8KUB/rQu26s2EdSkuK53aeudIn8YIg3WAsw+4rLniude42nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:06.253540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c802ba44548c16d3009b16a197a8785b26ab5bfc7364ad77b5edb88d93f5837b","sha256:e6bf6fa686c0404def287047ae78c4701434e5a66ba772dc913f9059f4750074"],"state_sha256":"3de28e924674cf3a39613df1ca0ba5b43a7a983c567ffa77a5ce7add11033668"}