Red cones spectral sensitivity Most sources seem to give the spectral sensitivity of cones in the human eye as this: 
As you can see all three curves have one maximum at a specific frequency.
However some sources state that red cone sensitivity has another "bump" at short wavelengths: 
Note that in this second image the red (L) cones have a secondary maximum in the far left of the spectrum.
Which one is correct?
My hypotheses:

*

*the first one is correct, the second one came about as a confusion with the color matching functions of the 1931 CIE standard (this is the most likely thing imo)

*the second one is correct, the first one is simply an older, coarser version, and is outdated by now

*the signals that go from the eye to the brain are actually more complicated than that, each of them is actually a combination of the three cone stimuli, together with the stimulus from the rods, so no graph of this kind can ever be very accurate

 A: The first one is correct. There is no second peak in the cone fundamentals found here, which represent, if not the best data available today, at least fairly close to it.

the second one came about as a confusion with the color matching functions of the 1931 CIE standard

Maybe. Certainly there are web sites that show the CIE XYZ CMFs and misidentify them as cone sensitivity curves.
I think that the confusion in modern times comes from the vaguer idea that the three cones detect red, green, and blue (or specifically sRGB). If that were true, then the violet end of the spectrum would have to stimulate the "red" cones since it appears to have red in it.

the signals that go from the eye to the brain are actually more complicated than that, each of them is actually a combination of the three cone stimuli,

That's true; the optic nerve doesn't have enough bandwidth to carry all of the raw cone data, and there is significant postprocessing in the retina itself.
But as far as I know, there are no cells that compute a mix of the L and S cones that would resemble the CIE X CMF or the curve marked L on your second graph.

together with the stimulus from the rods,

I don't know whether cone and rod signals are mixed.

so no graph of this kind can ever be very accurate

The first graph is only meant to show the (normalized) responses of the three cone types to incoming light, and it shows that accurately as far as I know. That's a useful thing to know inasmuch as all later stages of the visual system have only those cone outputs to work with (well, and the rods).
The LMS space can be used to model chromatic adaptation and color blindness, and to define other color spaces like XYZ. XYZ was originally defined "directly" by CMFs, but you can get a somewhat more accurate color space by approximating those CMFs by linear combinations of the cone responses measured by modern techniques.
