{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KFG6D6S7MCRB2QTZYWEG5VNILC","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":"6e2972345d1745725ba475fba2c65514360bdd13720cec7621445a7c0d34223e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-12T20:57:46Z","title_canon_sha256":"578c57ef3323665ff878663d3ea324bb18057ffd3ffa398edf10193770eae9c8"},"schema_version":"1.0","source":{"id":"1809.04672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04672","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04672v1","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04672","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"KFG6D6S7MCRB","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KFG6D6S7MCRB2QTZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KFG6D6S7","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:e6db691674b765ab312a42e9c848ded3893d3b7fb9f251c7403896e1ee4559c9","target":"graph","created_at":"2026-05-18T00:05:50Z","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":"Let $\\mathbb{G}$ be a higher-rank connected semisimple Lie group with finite center and without compact factors. In any unitary representation $(\\pi, \\mathcal{H})$ of $\\mathbb{G}$ without non-trivial $\\mathbb{G}$-fixed vectors, we study the twisted cohomological equation $(X+m)f=g$, where $m\\in\\mathbb{R}$ and $X$ is in a $\\mathbb{R}$-split Cartan subalgebra of $\\text{Lie}(\\mathbb{G})$. 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 solution to (the","authors_text":"Zhenqi Jenny Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-12T20:57:46Z","title":"The twisted cohomological equation over the partially hyperbolic flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04672","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":"sha256:890a234045b88121f3e77580ae6a3636977d76d7d3be0aa8bcfc394d789c6389","target":"record","created_at":"2026-05-18T00:05:50Z","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":"6e2972345d1745725ba475fba2c65514360bdd13720cec7621445a7c0d34223e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-12T20:57:46Z","title_canon_sha256":"578c57ef3323665ff878663d3ea324bb18057ffd3ffa398edf10193770eae9c8"},"schema_version":"1.0","source":{"id":"1809.04672","kind":"arxiv","version":1}},"canonical_sha256":"514de1fa5f60a21d4279c5886ed5a858bae34fead8781a0c96a2d9ffa2d5a792","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"514de1fa5f60a21d4279c5886ed5a858bae34fead8781a0c96a2d9ffa2d5a792","first_computed_at":"2026-05-18T00:05:50.048078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:50.048078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6XBDQkt9cQmu/KyBdB4RL4pc1JzLNVWNQwHaxSRWVN7Vn8IJrStWsAqF2yHXqpQAPqk8D7n0/JXwo51L9wZ9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:50.048630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:890a234045b88121f3e77580ae6a3636977d76d7d3be0aa8bcfc394d789c6389","sha256:e6db691674b765ab312a42e9c848ded3893d3b7fb9f251c7403896e1ee4559c9"],"state_sha256":"c90e7ce5dad91850b1539a8026d09bb90e2e7a58efe7243eb9bfc862a8116134"}