{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5WO3PWJRZMG2P3U3DM6ZNUSYIC","short_pith_number":"pith:5WO3PWJR","canonical_record":{"source":{"id":"2408.02747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-05T18:06:17Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"8125fcec082e396042480f158ebbd86e8416e31bc8db9990cd8edade13258c0c","abstract_canon_sha256":"ebd72fa87b34da1886bed5da73ed873b703380b53f632faebfbfbe02139355f2"},"schema_version":"1.0"},"canonical_sha256":"ed9db7d931cb0da7ee9b1b3d96d258409fcb59b7ad614dabe61635c79d72c3c1","source":{"kind":"arxiv","id":"2408.02747","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.02747","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"2408.02747v1","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.02747","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"5WO3PWJRZMG2","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"pith_short_16","alias_value":"5WO3PWJRZMG2P3U3","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"pith_short_8","alias_value":"5WO3PWJR","created_at":"2026-07-05T08:52:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5WO3PWJRZMG2P3U3DM6ZNUSYIC","target":"record","payload":{"canonical_record":{"source":{"id":"2408.02747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-05T18:06:17Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"8125fcec082e396042480f158ebbd86e8416e31bc8db9990cd8edade13258c0c","abstract_canon_sha256":"ebd72fa87b34da1886bed5da73ed873b703380b53f632faebfbfbe02139355f2"},"schema_version":"1.0"},"canonical_sha256":"ed9db7d931cb0da7ee9b1b3d96d258409fcb59b7ad614dabe61635c79d72c3c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:52:39.459969Z","signature_b64":"V1PC0h8H+yS7hr1SC+iQi5j68yZHP1a5u81+9eKifN4oEIqEWeFi3nyBayH3IcAKooFhr65/R8SmOGUWdt6pCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed9db7d931cb0da7ee9b1b3d96d258409fcb59b7ad614dabe61635c79d72c3c1","last_reissued_at":"2026-07-05T08:52:39.459511Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:52:39.459511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.02747","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":"2026-07-05T08:52:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v/yBBZJNud3DNwxV8w5GaXszUwDTWP2ewchvnFSWiYvz2i5s7/AFiPTurWe1vQ8WCX84MsaJv9+mXCYSNCp/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:21:47.716537Z"},"content_sha256":"e0f2a60b09fc26eddf180f7e03fe2e8c7ac4541f849ff27354434596893eb5a2","schema_version":"1.0","event_id":"sha256:e0f2a60b09fc26eddf180f7e03fe2e8c7ac4541f849ff27354434596893eb5a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5WO3PWJRZMG2P3U3DM6ZNUSYIC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermal One-point Functions and Their Partial Wave Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Alessandro Vichi, Francesco Russo, Ilija Buric, Volker Schomerus","submitted_at":"2024-08-05T18:06:17Z","abstract_excerpt":"In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on $S^1 \\times S^{d-1}$. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant conformal blocks for an external field of arbitrary spin and with any spin exchange along the thermal circle, at least in three dimensions. This is achieved by identifying solutions to the Casimir equations with a special class of spherical functions in the harmonic analysis of the conformal group. The resulting blocks are then applied to study the decomposi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02747","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/2408.02747/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":"2026-07-05T08:52:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECD8TtqDRQtpLgw4/9NN9k6KCpY7K4yMmsoxdLFgdZGRfybsTyDEPTFhqeMhxlT7i15wkAzTf9UZ8orRlkq+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:21:47.717474Z"},"content_sha256":"768c3f75e040ba7d5cb2086ec849f3ee325a0ecbc81ff360cf3e7e69ce906ef2","schema_version":"1.0","event_id":"sha256:768c3f75e040ba7d5cb2086ec849f3ee325a0ecbc81ff360cf3e7e69ce906ef2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC/bundle.json","state_url":"https://pith.science/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC/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":"2026-08-08T09:21:47Z","links":{"resolver":"https://pith.science/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC","bundle":"https://pith.science/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC/bundle.json","state":"https://pith.science/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5WO3PWJRZMG2P3U3DM6ZNUSYIC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5WO3PWJRZMG2P3U3DM6ZNUSYIC","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":"ebd72fa87b34da1886bed5da73ed873b703380b53f632faebfbfbe02139355f2","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-05T18:06:17Z","title_canon_sha256":"8125fcec082e396042480f158ebbd86e8416e31bc8db9990cd8edade13258c0c"},"schema_version":"1.0","source":{"id":"2408.02747","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.02747","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"2408.02747v1","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.02747","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"5WO3PWJRZMG2","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"pith_short_16","alias_value":"5WO3PWJRZMG2P3U3","created_at":"2026-07-05T08:52:39Z"},{"alias_kind":"pith_short_8","alias_value":"5WO3PWJR","created_at":"2026-07-05T08:52:39Z"}],"graph_snapshots":[{"event_id":"sha256:768c3f75e040ba7d5cb2086ec849f3ee325a0ecbc81ff360cf3e7e69ce906ef2","target":"graph","created_at":"2026-07-05T08:52:39Z","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/2408.02747/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on $S^1 \\times S^{d-1}$. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant conformal blocks for an external field of arbitrary spin and with any spin exchange along the thermal circle, at least in three dimensions. This is achieved by identifying solutions to the Casimir equations with a special class of spherical functions in the harmonic analysis of the conformal group. The resulting blocks are then applied to study the decomposi","authors_text":"Alessandro Vichi, Francesco Russo, Ilija Buric, Volker Schomerus","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-05T18:06:17Z","title":"Thermal One-point Functions and Their Partial Wave Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02747","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:e0f2a60b09fc26eddf180f7e03fe2e8c7ac4541f849ff27354434596893eb5a2","target":"record","created_at":"2026-07-05T08:52:39Z","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":"ebd72fa87b34da1886bed5da73ed873b703380b53f632faebfbfbe02139355f2","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-05T18:06:17Z","title_canon_sha256":"8125fcec082e396042480f158ebbd86e8416e31bc8db9990cd8edade13258c0c"},"schema_version":"1.0","source":{"id":"2408.02747","kind":"arxiv","version":1}},"canonical_sha256":"ed9db7d931cb0da7ee9b1b3d96d258409fcb59b7ad614dabe61635c79d72c3c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed9db7d931cb0da7ee9b1b3d96d258409fcb59b7ad614dabe61635c79d72c3c1","first_computed_at":"2026-07-05T08:52:39.459511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:52:39.459511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V1PC0h8H+yS7hr1SC+iQi5j68yZHP1a5u81+9eKifN4oEIqEWeFi3nyBayH3IcAKooFhr65/R8SmOGUWdt6pCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:52:39.459969Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.02747","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0f2a60b09fc26eddf180f7e03fe2e8c7ac4541f849ff27354434596893eb5a2","sha256:768c3f75e040ba7d5cb2086ec849f3ee325a0ecbc81ff360cf3e7e69ce906ef2"],"state_sha256":"c0a7033c03464a48342179fd898ad4ae2951d9bee1fd2b1eb752a34a5bba933a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bzwqRKqY7HL8IlA1KAjMcT96IJph6ujLTKzb2B8n0GSL42M4wqQoWpWvx3dQY4EGm145/HE9vlaB31KWUqYEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:21:47.724303Z","bundle_sha256":"7ecbb14ba325ae0f208f94d3a58b034f4213e15e0fa91c53ac99e20c25f829d1"}}