{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4B7PMBON2B4P6NXWUW2F5RSU7I","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":"e396fbff774ec7bede0bf3adb4d06a1361a44dcf528a7dd22708aabade1464b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-24T09:23:52Z","title_canon_sha256":"b21f4d8246f5c6fd2b168cb8cd9c04d6e3689402fff8f25552dfab50f2874654"},"schema_version":"1.0","source":{"id":"1511.07618","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07618","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07618v1","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07618","created_at":"2026-05-18T01:26:04Z"},{"alias_kind":"pith_short_12","alias_value":"4B7PMBON2B4P","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4B7PMBON2B4P6NXW","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4B7PMBON","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:52fcf12adf671ccc8ec6a96f2eaf3007c70b0ecf1b43025005326fb636bac0d8","target":"graph","created_at":"2026-05-18T01:26:04Z","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":"The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.","authors_text":"Jing-Song Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-24T09:23:52Z","title":"Dirac cohomology, elliptic representations and endoscopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07618","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":"sha256:830c280bd75228a678b0c62348eb514ba69fdbfabfad4e9aad30aad606f2ebab","target":"record","created_at":"2026-05-18T01:26:04Z","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":"e396fbff774ec7bede0bf3adb4d06a1361a44dcf528a7dd22708aabade1464b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-24T09:23:52Z","title_canon_sha256":"b21f4d8246f5c6fd2b168cb8cd9c04d6e3689402fff8f25552dfab50f2874654"},"schema_version":"1.0","source":{"id":"1511.07618","kind":"arxiv","version":1}},"canonical_sha256":"e07ef605cdd078ff36f6a5b45ec654fa2f4a252a0c9157c531a098fee8fa736c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e07ef605cdd078ff36f6a5b45ec654fa2f4a252a0c9157c531a098fee8fa736c","first_computed_at":"2026-05-18T01:26:04.177917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:04.177917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hQTTRikUObZsApBpDku/XgQXl7q5P3t/UATBGnlqXZgzosFTNSeTa+EJl5GPe+ijtYoeUmlC+FGRWORCoyMLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:04.178627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07618","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:830c280bd75228a678b0c62348eb514ba69fdbfabfad4e9aad30aad606f2ebab","sha256:52fcf12adf671ccc8ec6a96f2eaf3007c70b0ecf1b43025005326fb636bac0d8"],"state_sha256":"bca2e9c71686ba215a768ed4248a5eda3fefddaf7f0509583a137f325f7a1ac4"}