Positivity of gravitational path integral inner products requires non-perturbative instabilities in axion wormholes that break shift symmetry, implying a sharp axion weak gravity conjecture with precise constants.
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The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.
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Positivity of the gravitational path integral implies the axionic weak gravity conjecture
Positivity of gravitational path integral inner products requires non-perturbative instabilities in axion wormholes that break shift symmetry, implying a sharp axion weak gravity conjecture with precise constants.
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M\"obius randomness in the Hartle-Hawking state
The Hartle-Hawking state for toroidal quantum cosmologies is expressed in the Langlands decomposition as a sum over zeta zeros whose near-singularity dynamics follow the Hilbert-Pólya Hamiltonian and as a Möbius average of CFT partition functions.