Many scientific models are completely unproven (but not disproven) and are accepted and used because they just seem to fit to reality. Until it is proven that they are wrong, we assume that they are true. That I know of, I can quote the Big Bang theory, the Quantum Theory, the String Theory, the black hole models. In the past, the atom theory (2000 years old, proven since 100).

There is no necessity for a model to be proven true to be accepted. Sometimes proof is just very hard to pin down.

So here is an unproven theory that fits reality quite well:

Let us state that there is, within each human being, a sort of capital or energy available for disposal. A unit that would be very hard to define scientifically for now, as its existence is not proven, but that allows us to construct a striking little model. This "energy", that we shall call "fluid" in the future for the sake of clarity (we can always rename it more conveniently later), would be available to all humans in sensibly the same amounts and everyone unsuspectingly spends it at his will, by undertaking activities that require focus.

Mathematically, Focus would be a derivative of Fluid.

Basically, this "fluid" would be the fuel of our capacity to focus our minds. If an individual keeps on needing focus after his daily capital of "fluid" is spent, he will feel nervous fatigue. If another goes to bed without having spent much of it, he will sleep poorly. One complete sleep cycle refills the fluid to its original level (minus an infinitesimal quantity that we will come back to later).