{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TYECTXMTXY4NPUXYJCN4QLRPIN","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":"9e231fb486945c502cdab389fb0252f17ff9de36f5c1ce79f4feb3ab9379dd95","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-05T07:10:20Z","title_canon_sha256":"c536ad42cc6dc4e48bdf7ce70ceaefb5a4288bac35b324d4417cc694cec06686"},"schema_version":"1.0","source":{"id":"1211.0777","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0777","created_at":"2026-05-18T03:41:19Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0777v3","created_at":"2026-05-18T03:41:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0777","created_at":"2026-05-18T03:41:19Z"},{"alias_kind":"pith_short_12","alias_value":"TYECTXMTXY4N","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TYECTXMTXY4NPUXY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TYECTXMT","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:bcd9666579a7f7c33a189f975e822d6df186cbf4cf184926e6d527a2ad31a60e","target":"graph","created_at":"2026-05-18T03:41:19Z","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":"For any unitary representation $(\\pi,\\mathcal{H})$ of $G=SL(n,\\RR)$, $n\\geq 3$ without non-trivial $G$-invariant vectors, we study smooth solutions of the cohomological equation $\\mathfrak{u}f=g$ where $\\mathfrak{u}$ is a vector in the root space of $\\mathfrak{sl}(n,\\RR)$ and $g$ is a given vector in $\\mathcal{H}$. We characterize the obstructions to solving the cohomological equation, construct smooth solutions of the cohomological equation and obtain tame Sobolev estimates for $f$.\n  We also study common solutions to (the infinitesimal version of) the cocycle equation $\\mathfrak{u}h=\\mathfra","authors_text":"Zhenqi Jenny Wang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-05T07:10:20Z","title":"Cohomological equation and cocycle rigidity of parabolic actions in $SL(n,\\RR)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0777","kind":"arxiv","version":3},"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":"sha256:9caec436749a2603bdc054af2ce003b8d97ebdc5528e5dc7e5071db3afe80ad9","target":"record","created_at":"2026-05-18T03:41:19Z","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":"9e231fb486945c502cdab389fb0252f17ff9de36f5c1ce79f4feb3ab9379dd95","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-05T07:10:20Z","title_canon_sha256":"c536ad42cc6dc4e48bdf7ce70ceaefb5a4288bac35b324d4417cc694cec06686"},"schema_version":"1.0","source":{"id":"1211.0777","kind":"arxiv","version":3}},"canonical_sha256":"9e0829dd93be38d7d2f8489bc82e2f4349cd7896a4e99b7f1dc942ff8fbfbdb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e0829dd93be38d7d2f8489bc82e2f4349cd7896a4e99b7f1dc942ff8fbfbdb2","first_computed_at":"2026-05-18T03:41:19.816442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:19.816442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pCrLxL9moxQuyFO7oMUYoKhXKKTOtJEpbH1djLpMVPIooJ2qk3ZlvhYTLI/zaf8dB3QHIDtkp2YrerW43JlIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:19.816865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0777","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9caec436749a2603bdc054af2ce003b8d97ebdc5528e5dc7e5071db3afe80ad9","sha256:bcd9666579a7f7c33a189f975e822d6df186cbf4cf184926e6d527a2ad31a60e"],"state_sha256":"78a6eb4208d7576f508bc0876935550cb7c75837edcff917c15870598dac8448"}