{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:N2FZ44AQUNPRTC4WHETYD6BBKA","short_pith_number":"pith:N2FZ44AQ","canonical_record":{"source":{"id":"1206.0882","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-05T11:33:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"922ff19f83b1624cfc366d09ec52a769afe08b3c8b5259792b606c479392ad78","abstract_canon_sha256":"e78a0e3b87acf30d2e79cd61d69a5aae98b45580ce06647315cd0330ffb3245b"},"schema_version":"1.0"},"canonical_sha256":"6e8b9e7010a35f198b96392781f82150244d592f4b4e39c84481da5d758e414d","source":{"kind":"arxiv","id":"1206.0882","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0882","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0882v5","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0882","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"N2FZ44AQUNPR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N2FZ44AQUNPRTC4W","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N2FZ44AQ","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:N2FZ44AQUNPRTC4WHETYD6BBKA","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0882","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-05T11:33:08Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"922ff19f83b1624cfc366d09ec52a769afe08b3c8b5259792b606c479392ad78","abstract_canon_sha256":"e78a0e3b87acf30d2e79cd61d69a5aae98b45580ce06647315cd0330ffb3245b"},"schema_version":"1.0"},"canonical_sha256":"6e8b9e7010a35f198b96392781f82150244d592f4b4e39c84481da5d758e414d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:09.864845Z","signature_b64":"HqZT0Gf/nh3MRE6t09gkoIQDOlcG924wVeWRpe2MPU3DL5FkrcS2+t+tYLklxieJln03PpjTJLZb4Xv5B5TZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e8b9e7010a35f198b96392781f82150244d592f4b4e39c84481da5d758e414d","last_reissued_at":"2026-05-18T03:20:09.864380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:09.864380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0882","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RFxDrqx56l9/NodY8LVBbo8QdyxH/mF3Cl963PH+IB3FiTqIWS3gPoXoIjyOISi7MrPUoHYdBEuJcoIRA/08AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:23:02.129502Z"},"content_sha256":"dc2a08f264b0f069f09d76dc3b120aa4bddeb51223a99a902007e1fd1e757ce2","schema_version":"1.0","event_id":"sha256:dc2a08f264b0f069f09d76dc3b120aa4bddeb51223a99a902007e1fd1e757ce2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:N2FZ44AQUNPRTC4WHETYD6BBKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Endoscopic classification of representations of quasi-split unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Chung Pang Mok","submitted_at":"2012-06-05T11:33:08Z","abstract_excerpt":"In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0882","kind":"arxiv","version":5},"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":"2026-05-18T03:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWdKPXCpMDFbiJNMn7+KxjxG1XSeCl+RzjviWGEvceCXXMZEO7qu9+wcuQwwY3HUMZklJ+F5DfkKR/ToazF0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:23:02.130222Z"},"content_sha256":"442e27987d64f1d467b50140ebf861b1ae963864ac2a1e7568cf4f5b543ff9ef","schema_version":"1.0","event_id":"sha256:442e27987d64f1d467b50140ebf861b1ae963864ac2a1e7568cf4f5b543ff9ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2FZ44AQUNPRTC4WHETYD6BBKA/bundle.json","state_url":"https://pith.science/pith/N2FZ44AQUNPRTC4WHETYD6BBKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2FZ44AQUNPRTC4WHETYD6BBKA/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":"2026-06-09T19:23:02Z","links":{"resolver":"https://pith.science/pith/N2FZ44AQUNPRTC4WHETYD6BBKA","bundle":"https://pith.science/pith/N2FZ44AQUNPRTC4WHETYD6BBKA/bundle.json","state":"https://pith.science/pith/N2FZ44AQUNPRTC4WHETYD6BBKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2FZ44AQUNPRTC4WHETYD6BBKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N2FZ44AQUNPRTC4WHETYD6BBKA","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":"e78a0e3b87acf30d2e79cd61d69a5aae98b45580ce06647315cd0330ffb3245b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-05T11:33:08Z","title_canon_sha256":"922ff19f83b1624cfc366d09ec52a769afe08b3c8b5259792b606c479392ad78"},"schema_version":"1.0","source":{"id":"1206.0882","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0882","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0882v5","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0882","created_at":"2026-05-18T03:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"N2FZ44AQUNPR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N2FZ44AQUNPRTC4W","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N2FZ44AQ","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:442e27987d64f1d467b50140ebf861b1ae963864ac2a1e7568cf4f5b543ff9ef","target":"graph","created_at":"2026-05-18T03:20:09Z","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"},"paper":{"abstract_excerpt":"In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.","authors_text":"Chung Pang Mok","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-05T11:33:08Z","title":"Endoscopic classification of representations of quasi-split unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0882","kind":"arxiv","version":5},"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:dc2a08f264b0f069f09d76dc3b120aa4bddeb51223a99a902007e1fd1e757ce2","target":"record","created_at":"2026-05-18T03:20:09Z","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":"e78a0e3b87acf30d2e79cd61d69a5aae98b45580ce06647315cd0330ffb3245b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-05T11:33:08Z","title_canon_sha256":"922ff19f83b1624cfc366d09ec52a769afe08b3c8b5259792b606c479392ad78"},"schema_version":"1.0","source":{"id":"1206.0882","kind":"arxiv","version":5}},"canonical_sha256":"6e8b9e7010a35f198b96392781f82150244d592f4b4e39c84481da5d758e414d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e8b9e7010a35f198b96392781f82150244d592f4b4e39c84481da5d758e414d","first_computed_at":"2026-05-18T03:20:09.864380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:09.864380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HqZT0Gf/nh3MRE6t09gkoIQDOlcG924wVeWRpe2MPU3DL5FkrcS2+t+tYLklxieJln03PpjTJLZb4Xv5B5TZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:09.864845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0882","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc2a08f264b0f069f09d76dc3b120aa4bddeb51223a99a902007e1fd1e757ce2","sha256:442e27987d64f1d467b50140ebf861b1ae963864ac2a1e7568cf4f5b543ff9ef"],"state_sha256":"6b71b31a6083f1ce2835320e6a9ef49b24e7be980038729ea358d6175cb698b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVI2GfcTB+aJkyUTGiEjfVgJgoSS4Dt6Zwiuxm4g7KASbdvDXBhLI7jwd96glcX56JcA3tc9NLDpHRbMCsq5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:23:02.134889Z","bundle_sha256":"c4eb15f9653dcbdbd0c1737e568a741299f8a2b390db948d2de3b52706568d65"}}