{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7T7ADLQGNVLAAUXG5FWW2FTIR6","short_pith_number":"pith:7T7ADLQG","canonical_record":{"source":{"id":"1111.4554","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-19T13:16:03Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"a85e11a630cce92f9b499a6d8acd31baa40c01847ebb038030ad09678fc898c5","abstract_canon_sha256":"31258dbc43c4e1250429ef04362637eb4f477119457999a4be6eac03bbac1af9"},"schema_version":"1.0"},"canonical_sha256":"fcfe01ae066d560052e6e96d6d16688fbacb43630b0dbae0e288df3dd4e67dd3","source":{"kind":"arxiv","id":"1111.4554","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4554","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4554v3","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4554","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"7T7ADLQGNVLA","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"pith_short_16","alias_value":"7T7ADLQGNVLAAUXG","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"pith_short_8","alias_value":"7T7ADLQG","created_at":"2026-07-05T06:19:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7T7ADLQGNVLAAUXG5FWW2FTIR6","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4554","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-19T13:16:03Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"a85e11a630cce92f9b499a6d8acd31baa40c01847ebb038030ad09678fc898c5","abstract_canon_sha256":"31258dbc43c4e1250429ef04362637eb4f477119457999a4be6eac03bbac1af9"},"schema_version":"1.0"},"canonical_sha256":"fcfe01ae066d560052e6e96d6d16688fbacb43630b0dbae0e288df3dd4e67dd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:19:13.755806Z","signature_b64":"HjtTStBwhnMx5KOXBSg44ttiSM9GKmFPn7XuSUzWF+0QKynsSjDseO7ulbVYZSJla2xw8R3RImyyt9RrCTMSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcfe01ae066d560052e6e96d6d16688fbacb43630b0dbae0e288df3dd4e67dd3","last_reissued_at":"2026-07-05T06:19:13.755377Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:19:13.755377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4554","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+AY4O55AaygdheQB4jacKwjf4zpV9GYO1WRmAtWFsQvesTEtENJJi8VAvoyP8HN8RuEcvugvzSfOWq3UNIoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:12:00.375361Z"},"content_sha256":"1e87ae903316fae878017ff19c665552bcf12579d9f22e9ebc74b786bdcb187b","schema_version":"1.0","event_id":"sha256:1e87ae903316fae878017ff19c665552bcf12579d9f22e9ebc74b786bdcb187b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7T7ADLQGNVLAAUXG5FWW2FTIR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singletons and their maximal symmetry algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Xavier Bekaert","submitted_at":"2011-11-19T13:16:03Z","abstract_excerpt":"Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping algebra of the conformal algebra on these modules. These objects appear in a wide variety of areas of theoretical physics: AdS/CFT correspondence, electric-magnetic duality, higher-spin multiplets, infinite-component Majorana equations, higher-derivative symmetries, etc. Singletons and higher-spin algebras are reviewed through a list of their many equivalent de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4554","kind":"arxiv","version":3},"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/1111.4554/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":"2026-07-05T06:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ooLLAjCxDqobIidcQFvMWYaJK6I5z3nrJaimaNU83+ANA+JUst2dBae5q46LnHE3X+Bpt1rhFa853eZJz50jAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:12:00.375749Z"},"content_sha256":"a605fa66ad04f27e9e2f4608a0a099143813018dc1f6cb4ef755a247b00f8ac8","schema_version":"1.0","event_id":"sha256:a605fa66ad04f27e9e2f4608a0a099143813018dc1f6cb4ef755a247b00f8ac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6/bundle.json","state_url":"https://pith.science/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6/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":"2026-08-13T19:12:00Z","links":{"resolver":"https://pith.science/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6","bundle":"https://pith.science/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6/bundle.json","state":"https://pith.science/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7T7ADLQGNVLAAUXG5FWW2FTIR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7T7ADLQGNVLAAUXG5FWW2FTIR6","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":"31258dbc43c4e1250429ef04362637eb4f477119457999a4be6eac03bbac1af9","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-19T13:16:03Z","title_canon_sha256":"a85e11a630cce92f9b499a6d8acd31baa40c01847ebb038030ad09678fc898c5"},"schema_version":"1.0","source":{"id":"1111.4554","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4554","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4554v3","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4554","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"7T7ADLQGNVLA","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"pith_short_16","alias_value":"7T7ADLQGNVLAAUXG","created_at":"2026-07-05T06:19:13Z"},{"alias_kind":"pith_short_8","alias_value":"7T7ADLQG","created_at":"2026-07-05T06:19:13Z"}],"graph_snapshots":[{"event_id":"sha256:a605fa66ad04f27e9e2f4608a0a099143813018dc1f6cb4ef755a247b00f8ac8","target":"graph","created_at":"2026-07-05T06:19:13Z","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/1111.4554/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping algebra of the conformal algebra on these modules. These objects appear in a wide variety of areas of theoretical physics: AdS/CFT correspondence, electric-magnetic duality, higher-spin multiplets, infinite-component Majorana equations, higher-derivative symmetries, etc. Singletons and higher-spin algebras are reviewed through a list of their many equivalent de","authors_text":"Xavier Bekaert","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-19T13:16:03Z","title":"Singletons and their maximal symmetry algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4554","kind":"arxiv","version":3},"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":"sha256:1e87ae903316fae878017ff19c665552bcf12579d9f22e9ebc74b786bdcb187b","target":"record","created_at":"2026-07-05T06:19:13Z","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":"31258dbc43c4e1250429ef04362637eb4f477119457999a4be6eac03bbac1af9","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-19T13:16:03Z","title_canon_sha256":"a85e11a630cce92f9b499a6d8acd31baa40c01847ebb038030ad09678fc898c5"},"schema_version":"1.0","source":{"id":"1111.4554","kind":"arxiv","version":3}},"canonical_sha256":"fcfe01ae066d560052e6e96d6d16688fbacb43630b0dbae0e288df3dd4e67dd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcfe01ae066d560052e6e96d6d16688fbacb43630b0dbae0e288df3dd4e67dd3","first_computed_at":"2026-07-05T06:19:13.755377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:19:13.755377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HjtTStBwhnMx5KOXBSg44ttiSM9GKmFPn7XuSUzWF+0QKynsSjDseO7ulbVYZSJla2xw8R3RImyyt9RrCTMSAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:19:13.755806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4554","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e87ae903316fae878017ff19c665552bcf12579d9f22e9ebc74b786bdcb187b","sha256:a605fa66ad04f27e9e2f4608a0a099143813018dc1f6cb4ef755a247b00f8ac8"],"state_sha256":"56d217f42ce5bab6619c200825294097deda69b9b48f110c0d954de5a4242ee0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohCMPWLmOhW0KPMdJ/BOU3LXdQ10URhjS9Ec1c1f5kZBW8RWeXi7Ntx6WMkzUFOwAKPTVEGd76kYohrkDDwhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T19:12:00.378970Z","bundle_sha256":"0ed9ea4577be9d75387d2e35ff618334e890b7ce1f42eacd08a4be2af013cd7d"}}