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Osmosis produces water from external oxygen
The adsorbed water-phase that forms at contact zones separates water into its ionic constituents, the hydroxide forms a crystalline structure closest to the membrane, (H3O2-)n, and the protons form a layer of H3O+ on top of it. The ordering of water at contact zones is a colligative property, and is promoted in the water compartment and impaired in the salt compartment. It is the asymmetry in the adsorbed water phase on either side of a membrane that causes a transfer of protons to the hyperosmotic compartment during osmosis. The protons reorder around the combined charge of the hydroxide layer on both sides of the membrane, that acts like a motor. (Zhao, 2009; Pollack, 2013)
The loss of protons from the water compartment forces water to decompose into dioxide, there is not enough hydrogen to sustain the water. This reaction releases one electron per water, and the electrons will move towards a region of lower negative charge, the salt compartment. This electrical potential was measured by Jaques Loeb in 1921, and corroborated by Gerald Pollack in 2009.
When external oxygen is supplied to the salt compartment, it will combine with the protons and electrons that were transferred from the water compartment, and produce water. Water itself does not move across the membrane. It only appears to move.
That external oxygen is required for osmosis is a hypothesis that can be easily tested experimentally by performing a standard osmosis experiment without external oxygen in the salt compartment. The author has not done so.
References
Zhao, Q., Ovchinnikova, K., Chai, B., Yoo, H., Magula, J., & Pollack, G. H. (2009). Role of Proton Gradients in the Mechanism of Osmosis. The Journal of Physical Chemistry B, 113(31), 10708 10714. https://doi.org/10.1021/jp9021568
Pollack, G., 2013. The Fourth Phase Of Water. Seattle: Ebner and Sons.
Loeb, J. (1921). THE ORIGIN OF THE POTENTIAL DIFFERENCES RESPONSIBLE FOR ANOMALOUS OSMOSIS. Journal of General Physiology, 4(2), 213 226. https://doi.org/10.1085/jgp.4.2.213