{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y3TBTVYMTMTA22QMJ54ALDESGP","short_pith_number":"pith:Y3TBTVYM","canonical_record":{"source":{"id":"1812.03782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-10T13:36:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d44fd385f01b0458f8af600f14a5a2db82fdc369cac4f2e97c94f1d4459a4a8b","abstract_canon_sha256":"37174efbdf9fe46649f5415347985352332b7033c6fc092bdc9031bf9f416507"},"schema_version":"1.0"},"canonical_sha256":"c6e619d70c9b260d6a0c4f78058c9233e6905504e50e3956c2baa1f472bb4e4f","source":{"kind":"arxiv","id":"1812.03782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03782","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03782v1","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03782","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"pith_short_12","alias_value":"Y3TBTVYMTMTA","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"Y3TBTVYMTMTA22QM","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"Y3TBTVYM","created_at":"2026-07-05T00:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y3TBTVYMTMTA22QMJ54ALDESGP","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-10T13:36:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d44fd385f01b0458f8af600f14a5a2db82fdc369cac4f2e97c94f1d4459a4a8b","abstract_canon_sha256":"37174efbdf9fe46649f5415347985352332b7033c6fc092bdc9031bf9f416507"},"schema_version":"1.0"},"canonical_sha256":"c6e619d70c9b260d6a0c4f78058c9233e6905504e50e3956c2baa1f472bb4e4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:33:10.200756Z","signature_b64":"zq5Kz37fjW/Ba7g2oUEs1IHe3+Fs53ayggIpLMQmHzmNY+EaGWrIPFPdly1YgMGCIedXQ6lkjNbeuhZjbBwnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e619d70c9b260d6a0c4f78058c9233e6905504e50e3956c2baa1f472bb4e4f","last_reissued_at":"2026-07-05T00:33:10.200280Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:33:10.200280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03782","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":"2026-07-05T00:33:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZO225fLfzf4qt0XaUbSQtodPRcFqYfWAAX6kOA7CfmU3vtgTZJbNaXXWB0vjtpAcufjQqqw2ef7oXZYF01g0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:38:11.219426Z"},"content_sha256":"0fc8aa07138659b1795e93139e6e2b58bfc1a72b4e7c75419e4c78ec3004bf4f","schema_version":"1.0","event_id":"sha256:0fc8aa07138659b1795e93139e6e2b58bfc1a72b4e7c75419e4c78ec3004bf4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y3TBTVYMTMTA22QMJ54ALDESGP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolic spaces, principal series and ${\\rm O}(2,\\infty)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Arturo S\\'anchez, Pierre Py","submitted_at":"2018-12-10T13:36:25Z","abstract_excerpt":"We prove that there exists no irreducible representation of the identity component of the isometry group ${\\rm PO}(1,n)$ of the real hyperbolic space of dimension $n$ into the group ${\\rm O}(2,\\infty)$, if $n\\geq 3$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of ${\\rm PO}(1,n)^{\\circ}$ into the groups ${\\rm O}(p,\\infty)$ for other values of $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03782","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/1812.03782/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":"2026-07-05T00:33:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuqQEOA+f51MHYuR8E65vlcCJW0TiIWnziY4ixxfIcTgxowNfLHFJIgOJKYmccS0FvHrbaEGBJRZk61+fhAbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:38:11.220084Z"},"content_sha256":"b12a86c7b60a1d8a11b7d046b163648cb61aaac25fae3d117544272978bd7124","schema_version":"1.0","event_id":"sha256:b12a86c7b60a1d8a11b7d046b163648cb61aaac25fae3d117544272978bd7124"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3TBTVYMTMTA22QMJ54ALDESGP/bundle.json","state_url":"https://pith.science/pith/Y3TBTVYMTMTA22QMJ54ALDESGP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3TBTVYMTMTA22QMJ54ALDESGP/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":"2026-07-08T07:38:11Z","links":{"resolver":"https://pith.science/pith/Y3TBTVYMTMTA22QMJ54ALDESGP","bundle":"https://pith.science/pith/Y3TBTVYMTMTA22QMJ54ALDESGP/bundle.json","state":"https://pith.science/pith/Y3TBTVYMTMTA22QMJ54ALDESGP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3TBTVYMTMTA22QMJ54ALDESGP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y3TBTVYMTMTA22QMJ54ALDESGP","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":"37174efbdf9fe46649f5415347985352332b7033c6fc092bdc9031bf9f416507","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-10T13:36:25Z","title_canon_sha256":"d44fd385f01b0458f8af600f14a5a2db82fdc369cac4f2e97c94f1d4459a4a8b"},"schema_version":"1.0","source":{"id":"1812.03782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03782","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03782v1","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03782","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"pith_short_12","alias_value":"Y3TBTVYMTMTA","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"Y3TBTVYMTMTA22QM","created_at":"2026-07-05T00:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"Y3TBTVYM","created_at":"2026-07-05T00:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:b12a86c7b60a1d8a11b7d046b163648cb61aaac25fae3d117544272978bd7124","target":"graph","created_at":"2026-07-05T00:33:10Z","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/1812.03782/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that there exists no irreducible representation of the identity component of the isometry group ${\\rm PO}(1,n)$ of the real hyperbolic space of dimension $n$ into the group ${\\rm O}(2,\\infty)$, if $n\\geq 3$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of ${\\rm PO}(1,n)^{\\circ}$ into the groups ${\\rm O}(p,\\infty)$ for other values of $p$.","authors_text":"Arturo S\\'anchez, Pierre Py","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-10T13:36:25Z","title":"Hyperbolic spaces, principal series and ${\\rm O}(2,\\infty)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03782","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":"sha256:0fc8aa07138659b1795e93139e6e2b58bfc1a72b4e7c75419e4c78ec3004bf4f","target":"record","created_at":"2026-07-05T00:33:10Z","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":"37174efbdf9fe46649f5415347985352332b7033c6fc092bdc9031bf9f416507","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-12-10T13:36:25Z","title_canon_sha256":"d44fd385f01b0458f8af600f14a5a2db82fdc369cac4f2e97c94f1d4459a4a8b"},"schema_version":"1.0","source":{"id":"1812.03782","kind":"arxiv","version":1}},"canonical_sha256":"c6e619d70c9b260d6a0c4f78058c9233e6905504e50e3956c2baa1f472bb4e4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6e619d70c9b260d6a0c4f78058c9233e6905504e50e3956c2baa1f472bb4e4f","first_computed_at":"2026-07-05T00:33:10.200280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:33:10.200280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zq5Kz37fjW/Ba7g2oUEs1IHe3+Fs53ayggIpLMQmHzmNY+EaGWrIPFPdly1YgMGCIedXQ6lkjNbeuhZjbBwnCw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:33:10.200756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fc8aa07138659b1795e93139e6e2b58bfc1a72b4e7c75419e4c78ec3004bf4f","sha256:b12a86c7b60a1d8a11b7d046b163648cb61aaac25fae3d117544272978bd7124"],"state_sha256":"113b7ed1816ca074185b19801c34c1fc06b72c093a0906c164591664376dfd81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVca2BIZvt/Bv6qoOId4eyzPx0Yl9d/6JMvQ5BN+W+zzsKfUbU8AWPwv+ljxLcEE8A2nAQoqI/2ZS21Sp4ouBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T07:38:11.223553Z","bundle_sha256":"13ea9ebb363cd44dfc50be4b55c6bca6de4760cfc5c054ba3123436edfa98019"}}