{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:QZ2Y2CWM2X6DU4BCDAU42YUPAU","short_pith_number":"pith:QZ2Y2CWM","canonical_record":{"source":{"id":"2210.01299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-04T01:03:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"cc49d0585e20d637c0b9a120520338d00b3890089066a2da1231626334c697e6","abstract_canon_sha256":"009c872b3318ee3d16a0543ae5ac79e1d5890bf0003e11ca43d7c85c256c1e19"},"schema_version":"1.0"},"canonical_sha256":"86758d0accd5fc3a70221829cd628f053a8962b3897130cc443b10afae1d3df9","source":{"kind":"arxiv","id":"2210.01299","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.01299","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"2210.01299v1","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.01299","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"QZ2Y2CWM2X6D","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"pith_short_16","alias_value":"QZ2Y2CWM2X6DU4BC","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"pith_short_8","alias_value":"QZ2Y2CWM","created_at":"2026-07-05T05:03:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:QZ2Y2CWM2X6DU4BCDAU42YUPAU","target":"record","payload":{"canonical_record":{"source":{"id":"2210.01299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-04T01:03:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"cc49d0585e20d637c0b9a120520338d00b3890089066a2da1231626334c697e6","abstract_canon_sha256":"009c872b3318ee3d16a0543ae5ac79e1d5890bf0003e11ca43d7c85c256c1e19"},"schema_version":"1.0"},"canonical_sha256":"86758d0accd5fc3a70221829cd628f053a8962b3897130cc443b10afae1d3df9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:03:09.177173Z","signature_b64":"nyAdEJczURcWTSLpJMd7nT6SVtJgjdJ0nZyQpYfbQCvBOkFqj6bTCifObgyIHCXE7/E0Y4sOTB5PvzSQBj+9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86758d0accd5fc3a70221829cd628f053a8962b3897130cc443b10afae1d3df9","last_reissued_at":"2026-07-05T05:03:09.176765Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:03:09.176765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.01299","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":"2026-07-05T05:03:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aN+J0Ow4mpemHLd3KWT61XYAu4/XDlaZZ9EsGtg9/Cfi4Xxeqpezo8ftersfiJNA1Iao4CCKok4yKmf/nNOuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:43:18.638913Z"},"content_sha256":"47d2d0a8642ae7c2d368e950fe6754fd233832102d510682f406dc1572a7ba73","schema_version":"1.0","event_id":"sha256:47d2d0a8642ae7c2d368e950fe6754fd233832102d510682f406dc1572a7ba73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:QZ2Y2CWM2X6DU4BCDAU42YUPAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Quantum Field Theory and Causal Symmetric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gestur Olafsson, Karl-Hermann Neeb","submitted_at":"2022-10-04T01:03:12Z","abstract_excerpt":"In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann algebras,we focus on Euler elements of the Lie algebra, i.e., elements whose adjoint action defines a 3-grading. We study the wedge regions they determine in corresponding causal symmetric spaces and describe some methods to construct nets of von Neumann algebras on causal symmetric spaces that satisfy abstract versions of the Reeh--Schlieder and the Bisognano-Wic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.01299","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/2210.01299/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":"2026-07-05T05:03:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODQNoa/X/WRVL/xlPq2bUrJX5g1tJzpWY99T8bSNVY7C7TYaKqSb/ip6XPZ5DwA+6evE+TCbD6AG0OfK9qLqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:43:18.639678Z"},"content_sha256":"b3898c6b026efe7c06377da062b235eeca40911c0268d5388abe077001ba5d96","schema_version":"1.0","event_id":"sha256:b3898c6b026efe7c06377da062b235eeca40911c0268d5388abe077001ba5d96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU/bundle.json","state_url":"https://pith.science/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU/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":"2026-08-08T19:43:18Z","links":{"resolver":"https://pith.science/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU","bundle":"https://pith.science/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU/bundle.json","state":"https://pith.science/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZ2Y2CWM2X6DU4BCDAU42YUPAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QZ2Y2CWM2X6DU4BCDAU42YUPAU","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":"009c872b3318ee3d16a0543ae5ac79e1d5890bf0003e11ca43d7c85c256c1e19","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-04T01:03:12Z","title_canon_sha256":"cc49d0585e20d637c0b9a120520338d00b3890089066a2da1231626334c697e6"},"schema_version":"1.0","source":{"id":"2210.01299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.01299","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"2210.01299v1","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.01299","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"QZ2Y2CWM2X6D","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"pith_short_16","alias_value":"QZ2Y2CWM2X6DU4BC","created_at":"2026-07-05T05:03:09Z"},{"alias_kind":"pith_short_8","alias_value":"QZ2Y2CWM","created_at":"2026-07-05T05:03:09Z"}],"graph_snapshots":[{"event_id":"sha256:b3898c6b026efe7c06377da062b235eeca40911c0268d5388abe077001ba5d96","target":"graph","created_at":"2026-07-05T05:03:09Z","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/2210.01299/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann algebras,we focus on Euler elements of the Lie algebra, i.e., elements whose adjoint action defines a 3-grading. We study the wedge regions they determine in corresponding causal symmetric spaces and describe some methods to construct nets of von Neumann algebras on causal symmetric spaces that satisfy abstract versions of the Reeh--Schlieder and the Bisognano-Wic","authors_text":"Gestur Olafsson, Karl-Hermann Neeb","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-04T01:03:12Z","title":"Algebraic Quantum Field Theory and Causal Symmetric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.01299","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":"sha256:47d2d0a8642ae7c2d368e950fe6754fd233832102d510682f406dc1572a7ba73","target":"record","created_at":"2026-07-05T05:03:09Z","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":"009c872b3318ee3d16a0543ae5ac79e1d5890bf0003e11ca43d7c85c256c1e19","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-10-04T01:03:12Z","title_canon_sha256":"cc49d0585e20d637c0b9a120520338d00b3890089066a2da1231626334c697e6"},"schema_version":"1.0","source":{"id":"2210.01299","kind":"arxiv","version":1}},"canonical_sha256":"86758d0accd5fc3a70221829cd628f053a8962b3897130cc443b10afae1d3df9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86758d0accd5fc3a70221829cd628f053a8962b3897130cc443b10afae1d3df9","first_computed_at":"2026-07-05T05:03:09.176765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:03:09.176765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nyAdEJczURcWTSLpJMd7nT6SVtJgjdJ0nZyQpYfbQCvBOkFqj6bTCifObgyIHCXE7/E0Y4sOTB5PvzSQBj+9BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:03:09.177173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.01299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47d2d0a8642ae7c2d368e950fe6754fd233832102d510682f406dc1572a7ba73","sha256:b3898c6b026efe7c06377da062b235eeca40911c0268d5388abe077001ba5d96"],"state_sha256":"b80e4628bec27e9a1dfcf68ca782cc4cf54fe9cf39b8b0e5c0927ac867b2e005"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGIRF95I3gJRyG1Issovrm2TCkC6xEV/W+xR97HI3WLbjBcfxD7rzfZWeJlw2h6A9G+rE8vYMD2hFbaNspJuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:43:18.645232Z","bundle_sha256":"2ff6bccb4ffe4c167302a78e0a1f1c7ae86218dd612a0ea2a641d7ce2f89fedd"}}