{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KAS3OU5IQAWLOEKCX7TB3WNDI3","short_pith_number":"pith:KAS3OU5I","canonical_record":{"source":{"id":"1812.02254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-05T22:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"0290845d7cb118f87d3392bb7d3b0e6b4962ff519e40c052c6efdeabe9998358","abstract_canon_sha256":"a7d2ca95c855a8efad3ba281962641c1de26feab8750d5ac909e4e9414b9f57c"},"schema_version":"1.0"},"canonical_sha256":"5025b753a8802cb71142bfe61dd9a346eedb24390f0b897ff3399bfdf4b9a856","source":{"kind":"arxiv","id":"1812.02254","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02254","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02254v2","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02254","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"KAS3OU5IQAWL","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KAS3OU5IQAWLOEKC","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KAS3OU5I","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KAS3OU5IQAWLOEKCX7TB3WNDI3","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02254","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-05T22:27:22Z","cross_cats_sorted":[],"title_canon_sha256":"0290845d7cb118f87d3392bb7d3b0e6b4962ff519e40c052c6efdeabe9998358","abstract_canon_sha256":"a7d2ca95c855a8efad3ba281962641c1de26feab8750d5ac909e4e9414b9f57c"},"schema_version":"1.0"},"canonical_sha256":"5025b753a8802cb71142bfe61dd9a346eedb24390f0b897ff3399bfdf4b9a856","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:47.779741Z","signature_b64":"TSdT58IknoJNf/L7TtAcBCV/7TW6j4i9uMuzDxP0S4u+TC95naQy+doeDW+IvHv+IGmAjfuchIkMyiLJI2oWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5025b753a8802cb71142bfe61dd9a346eedb24390f0b897ff3399bfdf4b9a856","last_reissued_at":"2026-05-17T23:39:47.779202Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:47.779202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02254","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":"2026-05-17T23:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BaFeJ8AIEQqLJp8yUiYc3ss8+SgSCVGsBehs8tHbJ/Hlafcn+ZgblAEYjvPu8Kmxh2Rkwma92jU6PNCypIwyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:38:24.851847Z"},"content_sha256":"aee583fd8f0423c1e3d86c00d44145ba87d1d84022b11ecb9edf8f8465a5ddd0","schema_version":"1.0","event_id":"sha256:aee583fd8f0423c1e3d86c00d44145ba87d1d84022b11ecb9edf8f8465a5ddd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KAS3OU5IQAWLOEKCX7TB3WNDI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Crossing-Symmetric OPE Inversion Formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dalimil Mazac","submitted_at":"2018-12-05T22:27:22Z","abstract_excerpt":"We derive a Lorentzian OPE inversion formula for the principal series of $sl(2,\\mathbb{R})$. Unlike the standard Lorentzian inversion formula in higher dimensions, the formula described here only applies to fully crossing-symmetric four-point functions and makes crossing symmetry manifest. In particular, inverting a single conformal block in the crossed channel returns the coefficient function of the crossing-symmetric sum of Witten exchange diagrams in AdS, including the direct-channel exchange. The inversion kernel exhibits poles at the double-trace scaling dimensions, whose contributions mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02254","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":""},"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":"2026-05-17T23:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PO7QEmkOR1GbrqVGYN1SYGdled5M+wVyapD9n7RI+tMrbq7Wca+Lgc3J1k2bXGSn9E9PvymvvfyyIwOdl+0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:38:24.852187Z"},"content_sha256":"aa187bca86a487f5e902cfc95a6816b53eb5e8a74a494e8afac2490599e027bf","schema_version":"1.0","event_id":"sha256:aa187bca86a487f5e902cfc95a6816b53eb5e8a74a494e8afac2490599e027bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3/bundle.json","state_url":"https://pith.science/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3/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":"2026-06-01T19:38:24Z","links":{"resolver":"https://pith.science/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3","bundle":"https://pith.science/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3/bundle.json","state":"https://pith.science/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAS3OU5IQAWLOEKCX7TB3WNDI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KAS3OU5IQAWLOEKCX7TB3WNDI3","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":"a7d2ca95c855a8efad3ba281962641c1de26feab8750d5ac909e4e9414b9f57c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-05T22:27:22Z","title_canon_sha256":"0290845d7cb118f87d3392bb7d3b0e6b4962ff519e40c052c6efdeabe9998358"},"schema_version":"1.0","source":{"id":"1812.02254","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02254","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02254v2","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02254","created_at":"2026-05-17T23:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"KAS3OU5IQAWL","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KAS3OU5IQAWLOEKC","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KAS3OU5I","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:aa187bca86a487f5e902cfc95a6816b53eb5e8a74a494e8afac2490599e027bf","target":"graph","created_at":"2026-05-17T23:39:47Z","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 derive a Lorentzian OPE inversion formula for the principal series of $sl(2,\\mathbb{R})$. Unlike the standard Lorentzian inversion formula in higher dimensions, the formula described here only applies to fully crossing-symmetric four-point functions and makes crossing symmetry manifest. In particular, inverting a single conformal block in the crossed channel returns the coefficient function of the crossing-symmetric sum of Witten exchange diagrams in AdS, including the direct-channel exchange. The inversion kernel exhibits poles at the double-trace scaling dimensions, whose contributions mu","authors_text":"Dalimil Mazac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-05T22:27:22Z","title":"A Crossing-Symmetric OPE Inversion Formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02254","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:aee583fd8f0423c1e3d86c00d44145ba87d1d84022b11ecb9edf8f8465a5ddd0","target":"record","created_at":"2026-05-17T23:39:47Z","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":"a7d2ca95c855a8efad3ba281962641c1de26feab8750d5ac909e4e9414b9f57c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-05T22:27:22Z","title_canon_sha256":"0290845d7cb118f87d3392bb7d3b0e6b4962ff519e40c052c6efdeabe9998358"},"schema_version":"1.0","source":{"id":"1812.02254","kind":"arxiv","version":2}},"canonical_sha256":"5025b753a8802cb71142bfe61dd9a346eedb24390f0b897ff3399bfdf4b9a856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5025b753a8802cb71142bfe61dd9a346eedb24390f0b897ff3399bfdf4b9a856","first_computed_at":"2026-05-17T23:39:47.779202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:47.779202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TSdT58IknoJNf/L7TtAcBCV/7TW6j4i9uMuzDxP0S4u+TC95naQy+doeDW+IvHv+IGmAjfuchIkMyiLJI2oWBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:47.779741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02254","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aee583fd8f0423c1e3d86c00d44145ba87d1d84022b11ecb9edf8f8465a5ddd0","sha256:aa187bca86a487f5e902cfc95a6816b53eb5e8a74a494e8afac2490599e027bf"],"state_sha256":"70ee210bec22f3e8aceedc78ba179146d14ecbe6489c2bca190802b63dc60772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ob1O9XGkw4+FsGNrVhQzMuVrndGqd4Lt1yD7dTys8VYCyfCBZ+lzHf8hwP2flbv1Q/ugqcpkJLHV86EZKchCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:38:24.854214Z","bundle_sha256":"2b7b5fc041507c29da1c30e38b08639bd431e15f54273b12384abc0c9a5a68c9"}}