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Namely, let $G := SL_2(\\mathbb{R}) \\times \\dots \\times SL_2(\\mathbb{R}) $ and $\\Gamma$ be a lattice in $G$. We show that the set of points on $G/\\Gamma$ whose forward orbits under a one parameter Ad-semisimple subsemigroup of $G$ are bounded, form a hyperplane absolute winning set."},"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":"1611.06470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-20T05:01:47Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"fbf168e45d3269d30418fb7b050434054f7f10059b5f3b0be8958b1968c6a1f8","abstract_canon_sha256":"ac0d1fa7b6f805fb4840eeab0838575969b82fb2dfc6542e79cbf78f2bbecb3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:26.981972Z","signature_b64":"pj+WCTvv7LAg+vJ8YjhfdUvN5kCSh2iGq08NqmTq/fHKcwh55slld6wvAorROmDF6K+uiS52/gKUHLH3QylsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5be71415e3bf87fedf572fbf3f0d4001368ccda3b12705041174bf78c3adc32a","last_reissued_at":"2026-05-17T23:40:26.981266Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:26.981266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded orbits of Diagonalizable Flows on finite volume quotients of products of $SL_2(\\mathbb{R})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Anish Ghosh, Jinpeng An, Lifan Guan, Tue Ly","submitted_at":"2016-11-20T05:01:47Z","abstract_excerpt":"We prove a number field analogue of W. 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