{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:65MOSTCVVAHOFVPFIET6OT72FA","short_pith_number":"pith:65MOSTCV","canonical_record":{"source":{"id":"1208.0416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-02T06:59:32Z","cross_cats_sorted":[],"title_canon_sha256":"13cccad11a0963759f7ecbfaa5636c590adfb1c2cd222dfaee0e95401675621d","abstract_canon_sha256":"b6910c01570d22b39fa257003558a3d723993f2e70f38b5a6ef72cbb06e75acb"},"schema_version":"1.0"},"canonical_sha256":"f758e94c55a80ee2d5e54127e74ffa281b914b3c63e001c9b5e5f9f5c36c878b","source":{"kind":"arxiv","id":"1208.0416","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0416","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0416v2","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0416","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"pith_short_12","alias_value":"65MOSTCVVAHO","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"65MOSTCVVAHOFVPF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"65MOSTCV","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:65MOSTCVVAHOFVPFIET6OT72FA","target":"record","payload":{"canonical_record":{"source":{"id":"1208.0416","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-02T06:59:32Z","cross_cats_sorted":[],"title_canon_sha256":"13cccad11a0963759f7ecbfaa5636c590adfb1c2cd222dfaee0e95401675621d","abstract_canon_sha256":"b6910c01570d22b39fa257003558a3d723993f2e70f38b5a6ef72cbb06e75acb"},"schema_version":"1.0"},"canonical_sha256":"f758e94c55a80ee2d5e54127e74ffa281b914b3c63e001c9b5e5f9f5c36c878b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:06.658172Z","signature_b64":"zRmEw7jOp2kWclxnOP7S3cnVRs+MRBLbE70G5yKk2h0KYB2M0ZYWgcK7Uqi6raUX+NigsxtPYaKa8IPjgBr0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f758e94c55a80ee2d5e54127e74ffa281b914b3c63e001c9b5e5f9f5c36c878b","last_reissued_at":"2026-05-18T03:46:06.657567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:06.657567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.0416","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3f6RvgbdVzSisZhMbacTnS+S0OWzADu8sohe5DlYAU9ZLXpRg73TkpMey4B2YS3Ai2K8SGKruPJW9AWOfuphBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:28:42.599430Z"},"content_sha256":"bab3ef953efa662305d604479dcdfd598e0b4e29d8de7854e4afd291b1cb0d89","schema_version":"1.0","event_id":"sha256:bab3ef953efa662305d604479dcdfd598e0b4e29d8de7854e4afd291b1cb0d89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:65MOSTCVVAHOFVPFIET6OT72FA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representations of complex semi-simple Lie groups and Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Apoorva Khare","submitted_at":"2012-08-02T06:59:32Z","abstract_excerpt":"This article is an exposition of the 1967 Annals paper by Parthasarathy, Ranga Rao, and Varadarajan, on irreducible admissible Harish-Chandra modules over complex semisimple Lie groups and Lie algebras. It was written in Winter 2012 to be part of a special collection organized to mark 10 years and 25 volumes of the series \"Texts and Readings in Mathematics (TRIM)\". Each article in this collection is intended to give nonspecialists in its field, an appreciation for the impact and contributions of the paper being surveyed. Thus, the author has kept the prerequisites for this article down to a ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0416","kind":"arxiv","version":2},"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":"2026-05-18T03:46:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ngphztwBAALAlvyIu9dZVl/EY7gjedk38KbUQ6Gg2zmG0ZvDUXXIeC4Z5nZmVeigbIzTR06f2IBl2DxVfTANBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:28:42.599774Z"},"content_sha256":"dd92abbe65c9c3579b4c15415f252d77076b560fc94c1a41100661bc7c885a6b","schema_version":"1.0","event_id":"sha256:dd92abbe65c9c3579b4c15415f252d77076b560fc94c1a41100661bc7c885a6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/65MOSTCVVAHOFVPFIET6OT72FA/bundle.json","state_url":"https://pith.science/pith/65MOSTCVVAHOFVPFIET6OT72FA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/65MOSTCVVAHOFVPFIET6OT72FA/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":"2026-06-01T14:28:42Z","links":{"resolver":"https://pith.science/pith/65MOSTCVVAHOFVPFIET6OT72FA","bundle":"https://pith.science/pith/65MOSTCVVAHOFVPFIET6OT72FA/bundle.json","state":"https://pith.science/pith/65MOSTCVVAHOFVPFIET6OT72FA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/65MOSTCVVAHOFVPFIET6OT72FA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:65MOSTCVVAHOFVPFIET6OT72FA","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":"b6910c01570d22b39fa257003558a3d723993f2e70f38b5a6ef72cbb06e75acb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-02T06:59:32Z","title_canon_sha256":"13cccad11a0963759f7ecbfaa5636c590adfb1c2cd222dfaee0e95401675621d"},"schema_version":"1.0","source":{"id":"1208.0416","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0416","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0416v2","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0416","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"pith_short_12","alias_value":"65MOSTCVVAHO","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"65MOSTCVVAHOFVPF","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"65MOSTCV","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:dd92abbe65c9c3579b4c15415f252d77076b560fc94c1a41100661bc7c885a6b","target":"graph","created_at":"2026-05-18T03:46:06Z","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":"This article is an exposition of the 1967 Annals paper by Parthasarathy, Ranga Rao, and Varadarajan, on irreducible admissible Harish-Chandra modules over complex semisimple Lie groups and Lie algebras. It was written in Winter 2012 to be part of a special collection organized to mark 10 years and 25 volumes of the series \"Texts and Readings in Mathematics (TRIM)\". Each article in this collection is intended to give nonspecialists in its field, an appreciation for the impact and contributions of the paper being surveyed. Thus, the author has kept the prerequisites for this article down to a ba","authors_text":"Apoorva Khare","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-02T06:59:32Z","title":"Representations of complex semi-simple Lie groups and Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0416","kind":"arxiv","version":2},"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:bab3ef953efa662305d604479dcdfd598e0b4e29d8de7854e4afd291b1cb0d89","target":"record","created_at":"2026-05-18T03:46:06Z","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":"b6910c01570d22b39fa257003558a3d723993f2e70f38b5a6ef72cbb06e75acb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-02T06:59:32Z","title_canon_sha256":"13cccad11a0963759f7ecbfaa5636c590adfb1c2cd222dfaee0e95401675621d"},"schema_version":"1.0","source":{"id":"1208.0416","kind":"arxiv","version":2}},"canonical_sha256":"f758e94c55a80ee2d5e54127e74ffa281b914b3c63e001c9b5e5f9f5c36c878b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f758e94c55a80ee2d5e54127e74ffa281b914b3c63e001c9b5e5f9f5c36c878b","first_computed_at":"2026-05-18T03:46:06.657567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:06.657567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zRmEw7jOp2kWclxnOP7S3cnVRs+MRBLbE70G5yKk2h0KYB2M0ZYWgcK7Uqi6raUX+NigsxtPYaKa8IPjgBr0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:06.658172Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0416","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bab3ef953efa662305d604479dcdfd598e0b4e29d8de7854e4afd291b1cb0d89","sha256:dd92abbe65c9c3579b4c15415f252d77076b560fc94c1a41100661bc7c885a6b"],"state_sha256":"7bbf9ca0ada362e94cf4ff0f7ccb760f42bc2ca1f03d5b723f3da5574756170d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+idFKsh4BRbQB2jr4AoyU0THV3FgdFbAPOYG44wOtYFYCkVTsc+WPN0DE2XwFp/RZX9zOob5wLF2ZiGIkcHxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:28:42.601736Z","bundle_sha256":"74bebcff778a568211fa998376426f83e4fd8f845a4bb1ef59aca736638db70b"}}