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Context. There are significant amounts of H2 in the Milky Way. Due to itssymmetry H2 does not radiate at radio frequencies. CO is thought to be a tracerfor H2, however CO is formed at significantly higher opacities than H2. Thus,toward high Galactic latitudes significant amounts of H2 are hidden and calledCO-dark. Aims. We demonstrate that the dust-to-gas ratio is a tool to identifylocations and column densities of CO-dark H2. Methods. We adopt the hypothesisof a constant E(B-V)/NH ratio, independent of phase transitions from HI to H2.We investigate the Doppler temperatures TD, from a Gaussian decomposition ofHI4PI data, to study temperature dependencies of E(B-V)/NHI. Results. TheE(B-V)/NHI ratio in the cold HI gas phase is high in comparison to the warmerone. We consider this as evidence that cold HI gas toward high Galacticlatitudes is associated with H2. Beyond CO-bright regions we find for TD < 1165K a correlation (NHI + 2NH2 )/NHI prop -log T_D. In combination with a factorXCO = 4.0 10 20 cm^-2 (K km s^-1 )-1 this yields for the full-sky NH /E(B-V)sim 5.1 to 6.7 10^21 cm^-2 mag^-1, compatible with X-ray scattering and UVabsorption line observations. Conclusions. Cold HI with T_D < 1165 K containson average 46% CO-dark H2. Prominent filaments have TD < 220 K and typicalexcitation temperatures Tex sim 50 K. With a molecular gas fraction of > 61%they are dominated dynamically by H2.

HI filaments are cold and associated with dark molecular gas. HI4PI based estimates of the local diffuse CO-dark H2 distribution