My remarks in various posts in this thread encompass all of the below.
1 year was used to illustrate that at the longest time of studies
comparing various diets with high protein/low carb results were similar
and could be explained by fewer calories consumed compared to daily
energy needs. Up to 6 months the high protein/low carb diets have a
small advantage as below. Thereafter differences start to disappear to
the 1 year point as above.

During those first 6 months it is reasonable to assume weight loss with
high protein/low carb has higher energy costs for metablizing the
different macronutrients, the energy costs of shifting to stored fat and
protein intake, plus differential water loss not discussed before. By 6
months those higher energy costs have been consumed and the advantage
starts to disappear.

Even considering the advantage for differing energy costs for different
ratios of macronutrients, weight loss in the end, the 1 year point used
as proxy for same, is because there was a deficit in energy as measured
by calories made up by stored energy sources. This is valid and
accounts for the loss inspite of the tinkering done to evoke differing
energy costs. Bty, exercise level can be one energy cost and is easily
added to the sum with ease.

Atkins wanted to distinguish his diet from others in part by suggesting
some magic was at hand that calorie deficit did not account for in his
results. High protein/low carb diets are now more generally accepted as
working with some caloric advantage over others but with no reason to
evoke some magical biophysics to describe the final result as compared
to other equally caloric deficit diets. The 4 percent advantage for the
first 6 months means for the same deficit another dieter will have to
consume less to have the same weight loss results. At one year things
have changed.


Notice how you're carefull to pick a specific time
frame in order to be
technically correct on your stated point while at the same time
ignoring the facts for earlier time frames.

In many studies, low carbers without caloric restriction lose 4%
more than low fatters with caloric restriction. The reason that loss
at twice that length of time has reached the same levels is the
metabolic advantage of ketosis is proportional to the amount of
excess fat remaining to lose. A year later so many test subjects
have bottomed out in both test groups that rates no longer
mismatch. What these studies show is that if you're willing to
stick with a low fat plus calorie restircted diet for longer than
someone on a low carb non-restricted diet, you'll lose anyways.

that is how in all diets works.

A stance you reach by carefully ignoring one set of facts and
selecting another set of facts without paying heed to why the
numbers start different and end different.

The details might vary to a degree but it is the calories in the
end. Any energy cost for different metabolic pathway engagment is a
detail and not an fundimental explanation.

That's also incorrect on several levels.

1) Different fuels are burned using different metabolic pathways and
they do have different efficiencies. Include digestion and calories
have even greater inefficiencies. Calories are a poor measurement
that happens to be easy to look up in a table. In a way, calories
are rather like the scale reading that way.

2) Weight is caused by amount of stored body fat plus amount of
lean plus other. If stored body fat is withdrwan from storage it
is weight lost whether it is burned for fuel or not. Low insulin and
high glucagon levels of ketosis draw fat from storage. Calories
get wasted. Do enough studies on where it goes and I suggest
you'll find where that 4% number above comes from. Also, low
carbers lose less lean that low fatters.

3) Calories-in is not all there is to the equation. Calories-out is
also a variable. It's why exercise is stressed. It's also why there
is so much discussion of "starvation mode". What "starvation
mode" is (other than something denied by folks who like to
define stuff out of existance) is a reduction in basal metabolism.
Carefully track basal metabolism in dieters and you'll discover some
fun stuff. For example low carb reduces it less than low fat. But
also extreme approaches to local carb reduce it more than mild
approaches to low carb.