{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4AQZLK73QFEVX2U42LLS24ACWX","short_pith_number":"pith:4AQZLK73","canonical_record":{"source":{"id":"2012.03972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-07T19:00:05Z","cross_cats_sorted":[],"title_canon_sha256":"5b3ef500fe919028f6e2fcdf358d1eb47a88bb4493bd8f047e2db365f7d12bef","abstract_canon_sha256":"328a66f55570381eb3577761889b967d66c6a410382c213e6bb164222c215adb"},"schema_version":"1.0"},"canonical_sha256":"e02195abfb81495bea9cd2d72d7002b5fd4d41385f6e7b87dc70450c79fc35ba","source":{"kind":"arxiv","id":"2012.03972","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03972","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03972v2","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03972","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"4AQZLK73QFEV","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"pith_short_16","alias_value":"4AQZLK73QFEVX2U4","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"pith_short_8","alias_value":"4AQZLK73","created_at":"2026-07-05T07:45:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4AQZLK73QFEVX2U42LLS24ACWX","target":"record","payload":{"canonical_record":{"source":{"id":"2012.03972","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-07T19:00:05Z","cross_cats_sorted":[],"title_canon_sha256":"5b3ef500fe919028f6e2fcdf358d1eb47a88bb4493bd8f047e2db365f7d12bef","abstract_canon_sha256":"328a66f55570381eb3577761889b967d66c6a410382c213e6bb164222c215adb"},"schema_version":"1.0"},"canonical_sha256":"e02195abfb81495bea9cd2d72d7002b5fd4d41385f6e7b87dc70450c79fc35ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:45:24.463000Z","signature_b64":"+rXo/S5OfalNJ+y32HLR0jmqzC79Pamdgu6qHi5sXrc3mteObjODfp4ANiWnjIpRHID66WmY5RxXyStk8UTdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e02195abfb81495bea9cd2d72d7002b5fd4d41385f6e7b87dc70450c79fc35ba","last_reissued_at":"2026-07-05T07:45:24.462535Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:45:24.462535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.03972","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:45:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"is+6E6KeIIV55Z9e/uuQkwyhyxPz7o1UwjBCQ+olOCe0VE65BYg0TDfmNB8ksuL8yZNb5IfBmrlj62W5Gwi3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T06:58:39.483932Z"},"content_sha256":"986ad3e88a4a2ca3bc1f73079510110ac4fda910fc685427f646aad4145e59b2","schema_version":"1.0","event_id":"sha256:986ad3e88a4a2ca3bc1f73079510110ac4fda910fc685427f646aad4145e59b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4AQZLK73QFEVX2U42LLS24ACWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$T\\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Masaki Shigemori, Shinji Hirano, Tatsuki Nakajima","submitted_at":"2020-12-07T19:00:05Z","abstract_excerpt":"We study stress-tensor correlators in the $T\\bar{T}$-deformed conformal field theories in two dimensions. Using the random geometry approach to the $T\\bar{T}$ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $T\\bar{T}$ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $T\\bar{T}$ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03972","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.03972/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:45:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQjzsR5EaJkqgnkaCeJOkhMreooGIsFCujYdzVuonOJeoUBDewkZh6YxNrWQSWccD2jQ7DrpVSWaV8/MvThjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T06:58:39.484291Z"},"content_sha256":"03e4341a33234907554a7adc5751320d10864c38f8048aac40ac4dd4744c1216","schema_version":"1.0","event_id":"sha256:03e4341a33234907554a7adc5751320d10864c38f8048aac40ac4dd4744c1216"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4AQZLK73QFEVX2U42LLS24ACWX/bundle.json","state_url":"https://pith.science/pith/4AQZLK73QFEVX2U42LLS24ACWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4AQZLK73QFEVX2U42LLS24ACWX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-24T06:58:39Z","links":{"resolver":"https://pith.science/pith/4AQZLK73QFEVX2U42LLS24ACWX","bundle":"https://pith.science/pith/4AQZLK73QFEVX2U42LLS24ACWX/bundle.json","state":"https://pith.science/pith/4AQZLK73QFEVX2U42LLS24ACWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4AQZLK73QFEVX2U42LLS24ACWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4AQZLK73QFEVX2U42LLS24ACWX","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":"328a66f55570381eb3577761889b967d66c6a410382c213e6bb164222c215adb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-07T19:00:05Z","title_canon_sha256":"5b3ef500fe919028f6e2fcdf358d1eb47a88bb4493bd8f047e2db365f7d12bef"},"schema_version":"1.0","source":{"id":"2012.03972","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.03972","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"arxiv_version","alias_value":"2012.03972v2","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03972","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"pith_short_12","alias_value":"4AQZLK73QFEV","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"pith_short_16","alias_value":"4AQZLK73QFEVX2U4","created_at":"2026-07-05T07:45:24Z"},{"alias_kind":"pith_short_8","alias_value":"4AQZLK73","created_at":"2026-07-05T07:45:24Z"}],"graph_snapshots":[{"event_id":"sha256:03e4341a33234907554a7adc5751320d10864c38f8048aac40ac4dd4744c1216","target":"graph","created_at":"2026-07-05T07:45:24Z","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/2012.03972/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study stress-tensor correlators in the $T\\bar{T}$-deformed conformal field theories in two dimensions. Using the random geometry approach to the $T\\bar{T}$ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $T\\bar{T}$ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $T\\bar{T}$ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check co","authors_text":"Masaki Shigemori, Shinji Hirano, Tatsuki Nakajima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-07T19:00:05Z","title":"$T\\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03972","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":"sha256:986ad3e88a4a2ca3bc1f73079510110ac4fda910fc685427f646aad4145e59b2","target":"record","created_at":"2026-07-05T07:45:24Z","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":"328a66f55570381eb3577761889b967d66c6a410382c213e6bb164222c215adb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2020-12-07T19:00:05Z","title_canon_sha256":"5b3ef500fe919028f6e2fcdf358d1eb47a88bb4493bd8f047e2db365f7d12bef"},"schema_version":"1.0","source":{"id":"2012.03972","kind":"arxiv","version":2}},"canonical_sha256":"e02195abfb81495bea9cd2d72d7002b5fd4d41385f6e7b87dc70450c79fc35ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e02195abfb81495bea9cd2d72d7002b5fd4d41385f6e7b87dc70450c79fc35ba","first_computed_at":"2026-07-05T07:45:24.462535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:45:24.462535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+rXo/S5OfalNJ+y32HLR0jmqzC79Pamdgu6qHi5sXrc3mteObjODfp4ANiWnjIpRHID66WmY5RxXyStk8UTdBg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:45:24.463000Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.03972","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:986ad3e88a4a2ca3bc1f73079510110ac4fda910fc685427f646aad4145e59b2","sha256:03e4341a33234907554a7adc5751320d10864c38f8048aac40ac4dd4744c1216"],"state_sha256":"523b81b5454ea2af7879e95e825136e278d06070a72c0af8a36622afa01b372b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cs065Pfk4FlOcclqxAIyLHil9M534K+cXvGzQMpf/SxdxgDJzyavc8fIG/Hl92p0WNDjatNBH/GSAw0gL+3iCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-24T06:58:39.486397Z","bundle_sha256":"9e45f70fb9b986295a7f1fbb9874a197c431e2c723bc42b56a0692906d2c7260"}}