{"id":"66bc1408-d87b-4ce9-b0ab-14aaa9265762","arxiv_id":"2411.08000","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Projection onto the epigraph of the perspective of any convex lower semicontinuous function reduces to solving two scalar equations involving that function's proximity operator.","lead":"This paper gives a formula for projecting any point onto the cone formed by the epigraph of a perspective function, using only two scalar equations built from the proximity operator of the original function. The result gives a unified way to compute projections onto exponential, power, and hyperbolic cones, which are useful in conic optimization.","discovery_kind":"new_method","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-12T22:04:52.715288+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}