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We consider the set of simple-stable representations which are modelled on Minsky's primitive-stable representations. We prove that the set of conjugacy classes of simple-stable representations of $\\Gamma_g$ in $\\mathrm{PU}(2,1)$ is a domain of discontinuity for this action, strictly larger than the set of conjugacy classes of convex cocompact representations"},"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":"2605.28891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-27T07:51:28Z","cross_cats_sorted":[],"title_canon_sha256":"913e6619db2e816da8d0a2b0b5172dbce4cb1099130f5b38d4355a3ad5d3366e","abstract_canon_sha256":"28ab47abd788db67655113eb0f91a037a5349d24349fe244b8ec9f4a7a02b734"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T00:04:15.577854Z","signature_b64":"i0p1Fz7iO+R7yD0je4SX2zCCpWHoMUDQ/XzTz3FGFLRjo9b0KKNIfBBzTjeBK0Vof1Ftf4auM0I0UIyIK7UrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5deaf2367e45c119b9f96ad6931a4d6b88f795a709ea73fbb5ee1cae882285b5","last_reissued_at":"2026-05-29T00:04:15.577151Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T00:04:15.577151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple-stable representations of surface groups in $\\mathrm{PU}(2,1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ulysse Remfort-Aurat (I2M)","submitted_at":"2026-05-27T07:51:28Z","abstract_excerpt":"Let $\\Gamma_g$ be the fundamental group of a closed orientable surface of genus $g\\geqslant 2$. 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