{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BTCGCBKV5ZP5JCAUKCQRHJLWX7","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":"f3b9ec7b9bc6ac2e35d641329e02e168c90e68748deb499d8fb50042c5d06c7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-16T18:02:10Z","title_canon_sha256":"f1529dc12794d9dc6c42237c72595c240e783951587054b3d8be10a9e74c1068"},"schema_version":"1.0","source":{"id":"1705.05865","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05865","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05865v5","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05865","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"BTCGCBKV5ZP5","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BTCGCBKV5ZP5JCAU","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BTCGCBKV","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:ce802650d8b13c6a692395dafb2ccd1d4161e65f4faa0e12673ae10e027e5a16","target":"graph","created_at":"2026-05-17T23:59:18Z","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 Virasoro conformal block decomposition of the genus two partition function of a two-dimensional CFT by expanding around a Z3-invariant Riemann surface that is a three-fold cover of the Riemann sphere branched at four points, and explore constraints from genus two modular invariance and unitarity. In particular, we find 'critical surfaces' that constrain the structure constants of a CFT beyond what is accessible via the crossing equation on the sphere.","authors_text":"Minjae Cho, Scott Collier, Xi Yin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-16T18:02:10Z","title":"Genus Two Modular Bootstrap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05865","kind":"arxiv","version":5},"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:e56c392b18eaf55132aca5c76e5fef3e17e0c7d15597db6c11ddbaaf63d74ad7","target":"record","created_at":"2026-05-17T23:59:18Z","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":"f3b9ec7b9bc6ac2e35d641329e02e168c90e68748deb499d8fb50042c5d06c7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-05-16T18:02:10Z","title_canon_sha256":"f1529dc12794d9dc6c42237c72595c240e783951587054b3d8be10a9e74c1068"},"schema_version":"1.0","source":{"id":"1705.05865","kind":"arxiv","version":5}},"canonical_sha256":"0cc4610555ee5fd4881450a113a576bfd672ab6146b85cb1ed48e7320663f9ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cc4610555ee5fd4881450a113a576bfd672ab6146b85cb1ed48e7320663f9ef","first_computed_at":"2026-05-17T23:59:18.068021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:18.068021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Inl1Kpi6vWjD+Us+IL5BSxPO2QOAiV9W1lkmbRR3qjBp/21TtzEkeooDmZp6CGdlUuXN3Xl04YeDKtsnRRNBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:18.068447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05865","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e56c392b18eaf55132aca5c76e5fef3e17e0c7d15597db6c11ddbaaf63d74ad7","sha256:ce802650d8b13c6a692395dafb2ccd1d4161e65f4faa0e12673ae10e027e5a16"],"state_sha256":"a411a643a26fd0bd5b3e608947fd2d1f7bdcec4fec7ac8f5c21758989ed17645"}