{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:HTWKKHTL4PO6VQZ6FDIDNGOL23","short_pith_number":"pith:HTWKKHTL","canonical_record":{"source":{"id":"2112.10827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-20T19:43:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e9f051120b6214495cb68ee361c105bfc23dd0c4b6d24bb275bf2e136921572","abstract_canon_sha256":"bccc79d8861cb4ea4cf115754cf6a0c99e5ac9288ac3081a063574eb45d9b4af"},"schema_version":"1.0"},"canonical_sha256":"3ceca51e6be3ddeac33e28d03699cbd6ca047787af226d2711af8b76155cc0d7","source":{"kind":"arxiv","id":"2112.10827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.10827","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"2112.10827v1","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.10827","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"HTWKKHTL4PO6","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"pith_short_16","alias_value":"HTWKKHTL4PO6VQZ6","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"pith_short_8","alias_value":"HTWKKHTL","created_at":"2026-07-05T04:39:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:HTWKKHTL4PO6VQZ6FDIDNGOL23","target":"record","payload":{"canonical_record":{"source":{"id":"2112.10827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-20T19:43:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8e9f051120b6214495cb68ee361c105bfc23dd0c4b6d24bb275bf2e136921572","abstract_canon_sha256":"bccc79d8861cb4ea4cf115754cf6a0c99e5ac9288ac3081a063574eb45d9b4af"},"schema_version":"1.0"},"canonical_sha256":"3ceca51e6be3ddeac33e28d03699cbd6ca047787af226d2711af8b76155cc0d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:39:25.251812Z","signature_b64":"9ei6I+MntHrBeo9Evw+3DzKWVtNcUOt5r1TmPBAqnKeHzspE9YGRSdGrpzzqNtEl/7AvIUtzzA+XamnmQLW+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ceca51e6be3ddeac33e28d03699cbd6ca047787af226d2711af8b76155cc0d7","last_reissued_at":"2026-07-05T04:39:25.251321Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:39:25.251321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.10827","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:39:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AAwB84N0Xo75lK3t6J/BQb9DZ0a1MV0JiJ30pQ3JKt5xsbA6cvGlZni3iumn7MTKiG/LvU7KS8siUJLgYYbVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T19:06:54.042509Z"},"content_sha256":"db06460feb4ad1975ef61b118d7bc2341f7db79bf6a0bfdd39ded54c0ac373f6","schema_version":"1.0","event_id":"sha256:db06460feb4ad1975ef61b118d7bc2341f7db79bf6a0bfdd39ded54c0ac373f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:HTWKKHTL4PO6VQZ6FDIDNGOL23","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Ilija Buric, Jeremy A. Mann, Lorenzo Quintavalle, Sylvain Lacroix, Volker Schomerus","submitted_at":"2021-12-20T19:43:29Z","abstract_excerpt":"We continue the exploration of multipoint scalar comb channel blocks for conformal field theories in 3D and 4D. The central goal here is to construct novel comb channel cross ratios that are well adapted to perform projections onto all intermediate primary fields. More concretely, our new set of cross ratios includes three for each intermediate mixed symmetry tensor exchange. These variables are designed such that the associated power series expansion coincides with the sum over descendants. The leading term of this expansion is argued to factorise into a product of lower point blocks. We esta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10827","kind":"arxiv","version":1},"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/2112.10827/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":"2026-07-05T04:39:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ei78JlSYvv1rl96lc7Z7g8VKQKbwJLouDkjvbYqIbO0Zq+76xJ8LHBNa6m08ohxTCrsWpUCHpfjw6mTXCZyJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T19:06:54.043013Z"},"content_sha256":"291c4faf5bac377c7bc243c9c7a0528992c5fce068b0375eccbd7b4643cdb04d","schema_version":"1.0","event_id":"sha256:291c4faf5bac377c7bc243c9c7a0528992c5fce068b0375eccbd7b4643cdb04d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23/bundle.json","state_url":"https://pith.science/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23/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":"2026-08-07T19:06:54Z","links":{"resolver":"https://pith.science/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23","bundle":"https://pith.science/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23/bundle.json","state":"https://pith.science/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTWKKHTL4PO6VQZ6FDIDNGOL23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HTWKKHTL4PO6VQZ6FDIDNGOL23","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":"bccc79d8861cb4ea4cf115754cf6a0c99e5ac9288ac3081a063574eb45d9b4af","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-20T19:43:29Z","title_canon_sha256":"8e9f051120b6214495cb68ee361c105bfc23dd0c4b6d24bb275bf2e136921572"},"schema_version":"1.0","source":{"id":"2112.10827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.10827","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"2112.10827v1","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.10827","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"HTWKKHTL4PO6","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"pith_short_16","alias_value":"HTWKKHTL4PO6VQZ6","created_at":"2026-07-05T04:39:25Z"},{"alias_kind":"pith_short_8","alias_value":"HTWKKHTL","created_at":"2026-07-05T04:39:25Z"}],"graph_snapshots":[{"event_id":"sha256:291c4faf5bac377c7bc243c9c7a0528992c5fce068b0375eccbd7b4643cdb04d","target":"graph","created_at":"2026-07-05T04:39:25Z","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/2112.10827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We continue the exploration of multipoint scalar comb channel blocks for conformal field theories in 3D and 4D. The central goal here is to construct novel comb channel cross ratios that are well adapted to perform projections onto all intermediate primary fields. More concretely, our new set of cross ratios includes three for each intermediate mixed symmetry tensor exchange. These variables are designed such that the associated power series expansion coincides with the sum over descendants. The leading term of this expansion is argued to factorise into a product of lower point blocks. We esta","authors_text":"Ilija Buric, Jeremy A. Mann, Lorenzo Quintavalle, Sylvain Lacroix, Volker Schomerus","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-20T19:43:29Z","title":"Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.10827","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:db06460feb4ad1975ef61b118d7bc2341f7db79bf6a0bfdd39ded54c0ac373f6","target":"record","created_at":"2026-07-05T04:39:25Z","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":"bccc79d8861cb4ea4cf115754cf6a0c99e5ac9288ac3081a063574eb45d9b4af","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-12-20T19:43:29Z","title_canon_sha256":"8e9f051120b6214495cb68ee361c105bfc23dd0c4b6d24bb275bf2e136921572"},"schema_version":"1.0","source":{"id":"2112.10827","kind":"arxiv","version":1}},"canonical_sha256":"3ceca51e6be3ddeac33e28d03699cbd6ca047787af226d2711af8b76155cc0d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ceca51e6be3ddeac33e28d03699cbd6ca047787af226d2711af8b76155cc0d7","first_computed_at":"2026-07-05T04:39:25.251321Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:39:25.251321Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ei6I+MntHrBeo9Evw+3DzKWVtNcUOt5r1TmPBAqnKeHzspE9YGRSdGrpzzqNtEl/7AvIUtzzA+XamnmQLW+Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:39:25.251812Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.10827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db06460feb4ad1975ef61b118d7bc2341f7db79bf6a0bfdd39ded54c0ac373f6","sha256:291c4faf5bac377c7bc243c9c7a0528992c5fce068b0375eccbd7b4643cdb04d"],"state_sha256":"ccefaa5f66b292b486b4599516dcf647ded6b7f464b9be540cc8aa0bf50d1a37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hr3ZNenF0F7mMRxRr9C5eHT35pQydwp7SO1Su0PzEMWghVtvGCyxSh+1X+Ndj4IE3bVMxFK6Ts3Uyy7I++Q5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T19:06:54.046804Z","bundle_sha256":"bfa9a5a82cee4e30a614035597517ca427baf7f14d90a99155cd3a19b249bc5b"}}