The Computability Filter

Bilar, Daniyel Yaacov · 2026-10-08 · publication/preprint · cc-by-4.0

Abstract

The map from string-theory compactification data to cosmologically observable outcomes is well-defined as a function, but we argue that some of its values cannot be proved from the axioms theorists work in, and that on an infinite set of specifications it is not computable. Drawing on the undecidability of spectral gaps (Cubitt, Perez-Garcia, and Wolf 2015), the undecidability of quantum thermalisation (Shiraishi and Matsumoto 2021), and the meta-theoretical limits established by Faizal, Krauss, Shabir, and Marino (2025), we conjecture that some thermalisation values of the compactification map are independent of the theorist's axioms (Conjecture 1a), and uncomputable if the specification set is infinite (Conjecture 1a'). A separate conjecture (1b) treats the anthropic patch as the recursively enumerable subset of compactification specifications on which a thermalisation-decision procedure halts with a positive answer: a conjectural computability filter, independent of 1a. None constitutes a sharp prediction at present. Nine open problems are identified.

Keywords

string theory · landscape · computability · undecidability · anthropic selection · spectral gap · thermalisation · Kolmogorov complexity · CMB spectral distortions

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