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Under the assumption that $S$ contains an element with only one eigenvalue less than one (counted with multiplicity) and others bigger than one we prove that all the $SF$ invariant and ergodic probability measures on $\\mathrm{SL}_n(\\mathbb R)/\\mathrm{SL}_n(\\mathbb Z)$ are h"},"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":"1702.03084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-10T07:30:23Z","cross_cats_sorted":[],"title_canon_sha256":"c3581f5acfb3fa9abe183672efdc27a6d52ad1985096fd2b299bef3e5357d1a9","abstract_canon_sha256":"f736cc4a77cb4cd7cc5484c5c346107aec6d76e018abb89773f247839165b50c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:11.364282Z","signature_b64":"0ID1jDIuBn2M5NYhAVMXw25os4sjHkxcl7BJNOprhjkFMZ9urA7HZE83uZ3R1qlbxEQ2j5zQej6LCI67iXG6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69fcb143e77aabdb538a314a635b2130fa9e52436326f249e282ac1942fe199f","last_reissued_at":"2026-05-17T23:46:11.363867Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:11.363867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measure rigidity for solvable group actions in the space of lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Manfred Einsiedler, Ronggang Shi","submitted_at":"2017-02-10T07:30:23Z","abstract_excerpt":"We study invariant probability measures on the homogeneous space $\\mathrm{SL}_n(\\mathbb R)/\\mathrm{SL}_n(\\mathbb Z)$ for the action of subgroups of $\\mathrm{SL}_n(\\mathbb R)$ of the form $SF$ where $F$ is generated by one parameter unipotent groups and $S$ is a one parameter $\\mathbb R$-diagonalizable group normalizing $F$. 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