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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.04672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-12T20:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"578c57ef3323665ff878663d3ea324bb18057ffd3ffa398edf10193770eae9c8","abstract_canon_sha256":"6e2972345d1745725ba475fba2c65514360bdd13720cec7621445a7c0d34223e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:50.048630Z","signature_b64":"6XBDQkt9cQmu/KyBdB4RL4pc1JzLNVWNQwHaxSRWVN7Vn8IJrStWsAqF2yHXqpQAPqk8D7n0/JXwo51L9wZ9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"514de1fa5f60a21d4279c5886ed5a858bae34fead8781a0c96a2d9ffa2d5a792","last_reissued_at":"2026-05-18T00:05:50.048078Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:50.048078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The twisted cohomological equation over the partially hyperbolic flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Zhenqi Jenny Wang","submitted_at":"2018-09-12T20:57:46Z","abstract_excerpt":"Let $\\mathbb{G}$ be a higher-rank connected semisimple Lie group with finite center and without compact factors. 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