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Whether this holds, and how steep the slope must be, is unknown.","posed_since":"2018","precise":"The refined de Sitter conjecture (2018) states that in asymptotic, weakly coupled regions of moduli space, $\\mid \\operatorname{grad} V \\mid \\ge c V/M_{P}$ or $\\mathrm{min}\\ \\mathrm{eigenvalue}(\\operatorname{grad}\\ \\operatorname{grad} V) \\le -c' V/M_P^{2}$ with c, c' of order 1. Determine whether this holds in all asymptotic regions of string moduli spaces and find the optimal value of c in d dimensions.","problem_ref":"d3fbc8a6c40f3be18419d69e29fe70ba88e095e64e47cd9febc0549aea079f1c","references":"","settled_by":"A proof over all asymptotic limits of string compactifications with the sharp constant, or an explicit asymptotic counterexample.","status_note":"Candidate sharp values are $c = 2/\\sqrt{(d-1)(d-2)}$ from the trans-Planckian censorship conjecture (Bedroya, Vafa 2019) and $c = 2/\\sqrt{d-2}$ (Rudelius 2021), tested in many but not all asymptotic limits (2021-2025).","title":"Bound on scalar potential slopes in asymptotic field 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