> Something in biological systems is capable of defying the conservation of matter and energy
> Somewhere in the spaghetti bowl, matter or energy are being wicked away or added in a fashion so subtle that it has never, ever been observed.
Well, being that I'm anonymous, you are welcome to think that I measured incorrectly, (and whatever else you come to think of). I accept that.
However, the statements I quoted above indicate that you're following religion while you believe you have a scientific world view. So, I will not try to convince you of my measurements (which I admit could be very erroneous, even though they are based on food labels, which are an accepted, if idiotic, method of measurement).
However:
There is NO law of conservation of matter or mass. If you believe there is one, you should revisit your physics; There is conservation of energy, (and depending on how your system is modeled, probably momentum as well). But no such thing as conservation of matter or mass.
There IS a law of conservation of energy, but it does NOT in any way apply to the question at hand -- except at the tautological sense which I pointed in the first place. To wit:
1. Cellulose (paper, wood) is a carbohydrate. You can eat 1kg of paper a day, which is thus assumed to have 4000kcal, and all the vitamins you need, plus 20 gram of protein (a suboptimal, yet generally livable diet) - and you will die of starvation. Yet, exchange the paper with 1kg of sugar, and you won't die of starvation (you will eventually of diabetes).
Now, if this "energy balance" you allude to meant anything in this context, the paper<->sugar exchange would not have made a difference. But it does. And the reason that it does is that enzymes in our body know how to break up sugar, but not cellulose - and cellulose, DESPITE ITS ENERGY CONTENT, gets out the same way it came in. So atwater (the guy who set up the food energy system we now use) added a "per food factor" to say how much we can derive from it, and paper gets 0. Great - but it has been shown (see below) that his numbers are far from precise.
Furthermore, the 4kcal/edible carbohydrate gram is available only through cellular respiration (oxidation). However, the body can get energy through fermentation (glycolisys) as well (which it does under some oxygen stress conditions, and which is what many cancers do because their oxidation mechanism, the mitochondria, is borked). And fermentation produces about 1/8th of the energy that oxidation does.
Furthermore again, some energy production is "learned" - the first time you try to digest sorbitol or xylitol, you derive exactly 0 kcal/gram from them. After a few weeks, you max out at ~2.5kcal/gram. After a few months of not digesting either, you're back to 0 (I read conflicting reports, the minimum of which is 3 months, the maximum of which is over a year - but apparently, the required enzyme production eventually winds down when you do not need them).
Furthermore, atwater factors (the way all caloric content is computed these days) have been shown to be 20% wrong for nuts (and have similar errors for every other group that was tested recently; not many have been. atwater factors are now 140 years old. They're bad, but no better system has been devised).
So, "energy balance" is not a balance unless you know:
a) you know how much of your food is actually digested
b) you know how much of your energy production is done by respiration as opposed to fermentation (about 99% when you are healthy. But are you healthy?)
c) you know you are in a steady state for your diet (so that, e.g. you get 2.4 kcal/g from xylitol and not 1.2)
d) you know your so-called BMR (which is not constant, and is in fact dependent on your food intake)
e) know your biome and how it effects your food (about 10% of your weight, 1000% of your cells by number, and about 30% of your feces are bacteria that are not the same in other people. Do you know how to account for them?)
I could go on for hours. You're repeating misguided religious arguments, believing that you're speaking science.
I obviously can't measure anything, per your conclusion. But you should study your body chemistry/physics/biology better. Because your option (1) above implies significant misunderstanding.
References:
How labels are computed: https://en.wikipedia.org/wiki/Food_energy
One example of how imprecise this system is: http://www.foodnavigator-usa.com/Science/Study-Almonds-may-h...