I've seen many a 'green' magnitude off by a magnitude or more from contemporaneous visual and purported V magnitudes in databases.
Consequently my cynicism knows no bounds when people tell me something unfiltered (especially if unclear NIR and UV ends potential leakages have to be considered) is the same as using a monochrome device with proper Johnson V filter AND Johnson B filter so that proper transformations can be done on stars that are not white.
Best bet is to suck it and see.
Pick some reference stars from somewhere, constant stars, measure a star in whatever way you wish whether letting the machine do it all, via imaging two stars and setting one as the reference value against which the other will be measured, or using some sort of ensemble approach, then check your result and see if it agrees with the catalogued Johnson V magnitude for the star, THEN tell yourself if you are just getting green channel magnitudes or sufficiently proximate Johnson V ones.
Too much theory and not enough primary testing with personalised practical calibration against valid reference objects in amateur times series photometry.
Mathematics isn't a science, you can give proof of anything using algorithms irrespective of any reality.