{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YN5NKGVP2VBMJCHW2Z7FTRYRQI","short_pith_number":"pith:YN5NKGVP","canonical_record":{"source":{"id":"1603.08797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-29T14:55:24Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"aa2567d52e75be0d00d4c9ec1ddef4e9104ad005cc2a82b71b1efb8c0d6bfc52","abstract_canon_sha256":"7f11c9b312e4fc52daae5b1b842a5fb6bd14118219ba452b894545a3aac0c62b"},"schema_version":"1.0"},"canonical_sha256":"c37ad51aafd542c488f6d67e59c7118207587c66b8b72bffe34e6754564bc675","source":{"kind":"arxiv","id":"1603.08797","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08797","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08797v1","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08797","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"YN5NKGVP2VBM","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YN5NKGVP2VBMJCHW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YN5NKGVP","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YN5NKGVP2VBMJCHW2Z7FTRYRQI","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08797","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-29T14:55:24Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"aa2567d52e75be0d00d4c9ec1ddef4e9104ad005cc2a82b71b1efb8c0d6bfc52","abstract_canon_sha256":"7f11c9b312e4fc52daae5b1b842a5fb6bd14118219ba452b894545a3aac0c62b"},"schema_version":"1.0"},"canonical_sha256":"c37ad51aafd542c488f6d67e59c7118207587c66b8b72bffe34e6754564bc675","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:05.300069Z","signature_b64":"tzNCUNmeOrF8Yl/P7RIbH0CEMWL1uoKquAZHH2BCZ+lNyJz4EDu8HJYjGK1c4oXd0Dwb2+1bnFirLFOjJ7wWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c37ad51aafd542c488f6d67e59c7118207587c66b8b72bffe34e6754564bc675","last_reissued_at":"2026-05-18T01:18:05.299365Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:05.299365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08797","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":"2026-05-18T01:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxSn/tG8HcYaFPa7AQ8hZ+6dUW8m37Q36EDc0ebILfZN9blc8JmqM+BR/kh+AyKLHicCULNGnWFIvFTaPvFmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:32:28.769033Z"},"content_sha256":"adb9d806bf8a406fd1564e47c2a60e66036b857de7a47b942ea3a22553e14f43","schema_version":"1.0","event_id":"sha256:adb9d806bf8a406fd1564e47c2a60e66036b857de7a47b942ea3a22553e14f43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YN5NKGVP2VBMJCHW2Z7FTRYRQI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Second Adjoint Theorem for SL(2,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RT","authors_text":"Nigel Higson, Tyrone Crisp","submitted_at":"2016-03-29T14:55:24Z","abstract_excerpt":"We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08797","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":""},"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":"2026-05-18T01:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l6hGRdl2b/pr4A/7ZvOKnHaiL9puf6o7Fg0v2tFW6DxV7NHnPUT2POroR90URAeUMCO/hlIxzDDIiXTTJr/uBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:32:28.769500Z"},"content_sha256":"b9a61ed41fad11d22dddbb46f9ab6cb64f2104fb10a550e7dbc581702e142f0f","schema_version":"1.0","event_id":"sha256:b9a61ed41fad11d22dddbb46f9ab6cb64f2104fb10a550e7dbc581702e142f0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI/bundle.json","state_url":"https://pith.science/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI/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":"2026-05-30T09:32:28Z","links":{"resolver":"https://pith.science/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI","bundle":"https://pith.science/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI/bundle.json","state":"https://pith.science/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YN5NKGVP2VBMJCHW2Z7FTRYRQI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YN5NKGVP2VBMJCHW2Z7FTRYRQI","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":"7f11c9b312e4fc52daae5b1b842a5fb6bd14118219ba452b894545a3aac0c62b","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-29T14:55:24Z","title_canon_sha256":"aa2567d52e75be0d00d4c9ec1ddef4e9104ad005cc2a82b71b1efb8c0d6bfc52"},"schema_version":"1.0","source":{"id":"1603.08797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08797","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08797v1","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08797","created_at":"2026-05-18T01:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"YN5NKGVP2VBM","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YN5NKGVP2VBMJCHW","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YN5NKGVP","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:b9a61ed41fad11d22dddbb46f9ab6cb64f2104fb10a550e7dbc581702e142f0f","target":"graph","created_at":"2026-05-18T01:18:05Z","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"},"paper":{"abstract_excerpt":"We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).","authors_text":"Nigel Higson, Tyrone Crisp","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-29T14:55:24Z","title":"A Second Adjoint Theorem for SL(2,R)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08797","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:adb9d806bf8a406fd1564e47c2a60e66036b857de7a47b942ea3a22553e14f43","target":"record","created_at":"2026-05-18T01:18:05Z","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":"7f11c9b312e4fc52daae5b1b842a5fb6bd14118219ba452b894545a3aac0c62b","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-29T14:55:24Z","title_canon_sha256":"aa2567d52e75be0d00d4c9ec1ddef4e9104ad005cc2a82b71b1efb8c0d6bfc52"},"schema_version":"1.0","source":{"id":"1603.08797","kind":"arxiv","version":1}},"canonical_sha256":"c37ad51aafd542c488f6d67e59c7118207587c66b8b72bffe34e6754564bc675","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c37ad51aafd542c488f6d67e59c7118207587c66b8b72bffe34e6754564bc675","first_computed_at":"2026-05-18T01:18:05.299365Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:05.299365Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tzNCUNmeOrF8Yl/P7RIbH0CEMWL1uoKquAZHH2BCZ+lNyJz4EDu8HJYjGK1c4oXd0Dwb2+1bnFirLFOjJ7wWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:05.300069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adb9d806bf8a406fd1564e47c2a60e66036b857de7a47b942ea3a22553e14f43","sha256:b9a61ed41fad11d22dddbb46f9ab6cb64f2104fb10a550e7dbc581702e142f0f"],"state_sha256":"c69e40f39c24eb88792c4898978b779b26444f34f5f2c1121f2111788047dff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D39Sua3f65M379laQnXp/ArdZtX6qgu4YNr6+WkelHwVAqrzDeScjhiQD8A90DSvnke7L8jYVNT7EX3JkESGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:32:28.773455Z","bundle_sha256":"1ed89a008c11b0f730097b2e7729fb66e213030041db17959f77c4f86061352b"}}