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We show that the cocycle $A$ over the action of $T$ is conjugate to a block conformal cocycle.\n  This statement is used in the recent paper by Eskin-Mirzakhani on the classifications of invariant measures for the SL(2,R) action on moduli space. The ingredients of the proof are essentially contained in the papers of Guivarch and Raugi and"},"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":"1309.0160","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-31T21:30:45Z","cross_cats_sorted":[],"title_canon_sha256":"338ecf0d88ac6bb928b48aba53354370afbb879d6b6850445699f20a5bd823cd","abstract_canon_sha256":"5f955642238c0888c697df5915ae3fd67d65faea4d473b12a2bfb7bd4cec5890"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:48.963521Z","signature_b64":"DmpsGicw2nZYU2mbBUXCY1ArW92m4WQfJ/CmuUOziT1Mx3r/iaCwDqH5YGmlVZu8fvAJvDarA5ltFft0rnvSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5664c130e14f0a9abd497ac92bc736dd54f4440ce220f7e423794cff6199a3c","last_reissued_at":"2026-05-17T23:56:48.963010Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:48.963010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semisimplicity of the Lyapunov spectrum for irreducible cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Eskin, Carlos Matheus","submitted_at":"2013-08-31T21:30:45Z","abstract_excerpt":"Let $G$ be a semisimple Lie group acting on a space $X$, let $\\mu$ be a compactly supported measure on $G$, and let $A$ be a strongly irreducible linear cocycle over the action of $G$. We then have a random walk on $X$, and let $T$ be the associated shift map. We show that the cocycle $A$ over the action of $T$ is conjugate to a block conformal cocycle.\n  This statement is used in the recent paper by Eskin-Mirzakhani on the classifications of invariant measures for the SL(2,R) action on moduli space. 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