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A classical solution of string theory with a 4d de Sitter space-time could provide a simple and well-controlled setting to establish a connection to cosmological models. So far however, it has proven very difficult to find any example of such a solution. As will be recalled, attempts in this direction are plagued by many no-go theorems, or by the difficulty for concrete 10d supergravity solutions to fit in the classical stringy regime. This situation agrees with the recent claims of de Sitter swampland conjectures. These conjectures can actually be verified quantitatively, with a surprisingly good agreement, as will be shown. This may hint at a deep reason against classical de Sitter background, possibly to be found within the web of swampland conjectures, and the relation to the distance conjecture will briefly be commented on.