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We argue that the topological string partition function, which has been knownto correspond to a wave-function, can be interpreted as an exact``wave-function of the universe'' in the mini-superspace sector of physicalsuperstring theory. This realizes the idea of Hartle and Hawking in the contextof string theory, including all loop quantum corrections. The mini-superspaceapproximation is justified as an exact description of BPS quantities. Moreoverthis proposal leads to a conceptual explanation of the recent observation thatthe black hole entropy is the square of the topological string wave-function.This wave-function can be interpreted in the context of flux compactificationof all spatial dimensions as providing a physical probability distribution onthe moduli space of string compactification. Euclidean time is realizedholographically in this setup.Comment: 37 pages, 2 figure

Hartle–Hawking Wave-Function for Flux Compactifications: the Entropic Principle