Refined positional evaluations of the first move:
Re: post #1 (LSB control of a6)
Is this not partial control (threatening)?
Yes, but I think that the effective control is a more appropriate notion. [The white LSB partially controls a6, but it can't move there without the material loss.] It's necessary to consider more examples in order to formulate an exact definition of this effective control. It's discussable, what do U think?
The words/terms partial, total, single, shared came to mind. Maybe valued differently vs all or none?
Different positional evaluation types are certainly possible and maybe reasonable. However, in the case of 1. e4, nobody would say that white controls a6. Do U agree?
On the other hand, the original definition of pev (without "effectiveness") is easier and clearer. 
I would say the bishop is "eyeing" the square. Just as if the bishop were on g2, eyeing b7.
My point is that later on, beyond move 1 for white, we will need to address anyway. At least I think so.
Let's continue for now. We can go back and revisit later as additional criterion arise.
All right, it's reasonable. I'll come back to the original definition of pev and the corresponding Pev using the notion of partial control. When we will be able to clearly define the notion of effective control then we could define the effective pev too. I'll make corrections right now. 
Is e3 still same as e4?
Yes. In principle, we could/should introduce a multiplicative coefficient k > 1 for squares controlled at the opposite side. But the exact value of such coefficient is unclear to me so far. So, at the moment, I'd prefer to work with current definitions. What do U think?
Thank you for one more completely pointless and useless thread Yigor.
LoL I'm gifted to create a lot of abstract nonsense. 
I would like to add:
Since the sqaures have a value of 1. All squares are equal (for now).
Do we have values defined for each piece?
At the moment, any controlling piece has also the value equal to 1.
Maybe a big problem, but ok...
Value did not increase (in case of d4) for queen?
No, I don't think so. Sometimes, it might be even more important to control a square with a pawn than with a queen !?! 
I've corrected calculations for the 1st move (post #2), returning back to the notion of partial control.
@DeirdreSkye Go to learn the true meaning of transpositions in chess before trying to criticize others.
What are the standard elements/characteristics of a positional evaluation? We need to define what it is we will measure, how we measure it, and why that is the best method of measuring.
Originally, my idea was to define evaluations from positions alone (without using engines and statistics) such that these evaluations are nonetheless comparable to engine evaluations. U can also notice that formulas defining the positional evaluation are inspired by my formulas for the statistical evaluation :
https://www.chess.com/forum/view/chess-openings/statistical-sharpness-and-evaluation
@DeirdreSkye has shown in his numerous posts that for him "learning chess openings" amounts to memorising as many theoretical lines as possible.
In mathematics, the category theory is often called "abstract nonsense". However, it permits to prove some important results difficult to prove by other methods. 
I can find a million nonsense that neither I nor you can reject with proof. That is why humans have something called : Common sense. It helps them reject things without the need of concrete proof.
If people were always guided by "common sense", the theory of relativity or quantum physics could be never discovered. "Common sense" is an enemy of great discoveries.
Chess example: if Blackburne were motivated only by "common sense", he could never play the Jerome gambit, sacrificing the queen and both rooks in order to put one of most incredible mates in the chess history. 
Yigor,
Maybe this should be initialized elsewhere. After some conclusions or progress is made, then made available for anyone (aliens included) to contribute their thoughts.
Oh, well, let's just ignore aliens and they will go away very soon.
I could also block aliens from participating in this thread but it would be against so-called "freedom of speech".
I take a break and will calculate
Well, thanks to suggestions by @DanlsTheMan, I'll make some corrections to my original definition:
https://www.chess.com/forum/view/chess-openings/numerical-criterion-of-positional-evaluation
First of all, I'll make the kingside/queenside division:
W=WK+WQ, B=BK+BQ
pevK = (WK/BK - 1)/2 if WK >= BK
pevK = (1 -BK/WK)/2 if BK >= WK
pevQ = (WQ/BQ - 1)/2 if WQ >= BQ
pevQ = (1 - BQ/WQ)/2 if BQ >= WQ
Pev = (pevK, pevQ)
while pev is defined as before. Attention: in general, pev ≠ pevK+pevQ.
Example 1 (King's Pawn opening).
At the kingside, the pawn e4 controls f5 and the white queen controls g4 and h5 (=+3 to the initial 11 controlled squares). At the queenside, the pawn e4 controls d5 and the white LSB controls c4, b5 and a6.
WK=14, WQ=15, W=29; BK=BQ=11, B=22
pevK = (14/11-1)/2 =+0.14, pevQ = (15/11-1)/2 =+0.18
Pev = (+0.14, +0.18); pev = (29/22-1) = +0.32
Example 2 (Sicilian defense).
WK=14, WQ=15, W=29; BK=11, BQ=14, B=25
pevK=(14/11-1)/2=+0.14, pevQ=(15/14-1)/2=+0.04
Pev = (+0.14, +0.04) while pev=(29/25-1)=+0.16
So, we see that Pev describes better the positional situation showing that white has an advantage at the kingside and almost no advantage at the queenside.