{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2XHASAMJIGV2XFCPN3P3Y3PCGO","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":"39e3ff10a73a7ab07c639d9a4481ed5f51a33c230ed4dea7be602d8aa88d9672","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-14T17:35:16Z","title_canon_sha256":"6a6ad2646656d4b77ded1d8b51e21bb46852d7e89c31f5fe2c1c73d6cf4e49a4"},"schema_version":"1.0","source":{"id":"1803.05418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05418","created_at":"2026-05-18T00:13:27Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05418v1","created_at":"2026-05-18T00:13:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05418","created_at":"2026-05-18T00:13:27Z"},{"alias_kind":"pith_short_12","alias_value":"2XHASAMJIGV2","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2XHASAMJIGV2XFCP","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2XHASAMJ","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:9ad2c996208937271f43a388191ad021e3136abb2c2f8a2800c7d1fb1daada2f","target":"graph","created_at":"2026-05-18T00:13:27Z","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 present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov formula (the DOZZ formula) for the 3 point structure constants of Liouville Conformal Field Theory (LCFT) starting from a rigorous probabilistic construction of the functional integral defining LCFT given earlier by the authors and David. A crucial ingredient in our argument is a probabilistic derivation of the reflection relation in LCFT based on a refined tail analysis of Gaussian multiplicative chaos measures.","authors_text":"Antti Kupiainen, R\\'emi Rhodes, Vincent Vargas","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-14T17:35:16Z","title":"The DOZZ Formula from the Path Integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05418","kind":"arxiv","version":1},"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":"sha256:23d6a5fc0692828b5a4051ac2ca588e8343cfd73c506c8743c2655300d459330","target":"record","created_at":"2026-05-18T00:13:27Z","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":"39e3ff10a73a7ab07c639d9a4481ed5f51a33c230ed4dea7be602d8aa88d9672","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-03-14T17:35:16Z","title_canon_sha256":"6a6ad2646656d4b77ded1d8b51e21bb46852d7e89c31f5fe2c1c73d6cf4e49a4"},"schema_version":"1.0","source":{"id":"1803.05418","kind":"arxiv","version":1}},"canonical_sha256":"d5ce09018941abab944f6edfbc6de2339253c2b88d8419a519eba8c710f9cb0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5ce09018941abab944f6edfbc6de2339253c2b88d8419a519eba8c710f9cb0a","first_computed_at":"2026-05-18T00:13:27.057620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:27.057620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gJaI6/QUAB4l2UObOnHw99cEG766FFjMU4IMjPhWwLlzTox7RHzvCWCmpotNxXI0yT5BmGmMr1qKoK/2yeg5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:27.058375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23d6a5fc0692828b5a4051ac2ca588e8343cfd73c506c8743c2655300d459330","sha256:9ad2c996208937271f43a388191ad021e3136abb2c2f8a2800c7d1fb1daada2f"],"state_sha256":"80b6dcaa98fadbb072c096dfead293157b5315ba610c83f6c7cea0417e4240ac"}