Question:
for GTO preflop defending range against 3bet, is it simply depend on Hero's equity vs. 3 bettor's range(plus position, but i assume it wouldnt change a lot)?

Why I ask this question:
im reading this book"modern poker theory" by michael acevedo, and it gives a fixed open size and 3bet size, which is 2.5bb for all position expect SB, and 8.5bb when in position. it doesnt really relate to my question, so i will keep long story short, it gives CO 27.8% opening range, and gives BN 11.7% 3bet against CO. CO need to 4bet 20.6% and Call 20.4%(out of its opening range)

Mathematically speaking, CO needs to defend 32%, because of the pot odd:3:6.25. but the GTO play is 40%. so i assume the frequency its depends on how well the card value against BN's 3bet range? in other words, your defending range must be able to realize 32% equity.

does it have something to do with the card performance against BN's range in later straight as well? which is basically unsolvable for human brain. or it just simply goes" here is BN's range, here is our range, it has 32% raw equity against BN's range "

Mathematically speaking, you don't have the required conditions to apply mdf and get the correct result. Mdf only works on the river against a polar range. You won't see it working on situations like these. The issue here is that from the point of view of the 3bettor bluffs, if your opponent defends at mdf, we still gain a fraction of the pot when he calls and we flop something, so CO needs to defend at a higher rate to make us remain indifferent

Yes, more or less, except the range as a whole doesn't have 32% equity. It's every hand in the continuance range must be able to win at least that much of the pot. You continue with the hands that will be profitable given the pot odds offered (given an estimation of how well they will play or realize their equity post-flop in position). i.e. If it happens that 40% of your range will make money (or at least breakeven) vs villain's range at this sizing, then you should continue with 40% of your range.
In the long run, every hand in your continuance range has to be able to recoup at the least the cost of calling the 3-bet. So if the pot lays odds that require you to win at least 32% of the time, then you should continue with all the hands that will do that (because it's +EV to do so), and fold all the ones that will not.
Depending on the exact positional (and range) situation the "fold to 3-bet" frequency will vary somewhat, because it's not strongly correlated with MDF. The calling range depends more on the pot odds and how often you'll win, given the exact situation.

Arty really hit the nail on the head. I’ll offer a couple of other points that drive this. A solver will play all continuing hands optimally. So when it suggests calling a three bet OOP vs BN with hands like 22-66 and small suited connector 54s-76s and small suited aces like A5s you have to ask honestly can you make money doing it? His charts recommend calling some of 44 and folding. If I understand this correctly, that means this play is break even for the solver (same EV of calling as folding). Might be unlikely you can make money doing it or you might be able to make more than the solver as it’s derived from BN playing perfectly as well.
To expound on that point, if you put the best player in the world in CO against the worst on the BTN, it is likely the best player could make more money with more hands than the solver output. As the player on the BTN progressively gets better the less money the best player should make to the point he’s playing against the solver and the best he can do is the same as solver vs solver.
The other point to consider is that the output on the charts is based on optimal play against a specific counter range that is being played optimally. As soon as your opponent deviates from that it changes your response. For instance the charts for say HJ vs CO will not necessarily be an accurate response to many players that are playing more of a calling/3b strategy from CO instead of the threebet or fold strategy recommended in the book.
I say all that to caution blind use of charts. They are a good starting point but should be used as a guide. Ultimately you want to understanding why they are constructed the way they are. The most important thing to ask yourself is what is my opponent raising me with range wise and how do I construct my range against that? Most importantly if you do not know how your hand is going to make money postflop against that range you need to figure that out first.

The open raise Range is metered by The number of players that can 3 bet. Since the opening range is quite linear this lends itself to contain a fraction of hands that can continue profitably vs a 3 bet, that fraction is larger than the fraction which corresponds with mdf.

I think this effect is prominent until someone makes a heads up reraise.

I am confused by the inclusion of this statement. I can’t think of any opening range that doesn’t contain a fraction of hands that can continue profitably vs a 3 bet.

The comma implies that the idea is not complete without this part.

There's no short answer to this question, really the answer is "construct a defense range that best maximizes EV against your opponents range and strategy", which is obviously a little vague.

The reasons why you construct your range in a particular way have to do with a lot of factors, equity being a major component, but it is not the entire picture. Just to prove this point, let's say you open from the CO with a range of only 77, and are 3bet by a standard button 3bet range such as the one in the book. If you put this into a preflop solver, you will see that the CO will fold the majority of the time, though 77 clearly has enough equity to continue here (probably like 45%). This is because your lack of range diversity will allow your opponent to prevent you from realizing your equity over multiple streets of betting, polarizing over your very capped range on most boards and winning the pot with a massive portion of his range.

Ultimately, it is too hard to find a "pen-and-pencil" type reasoning for these types of problems. That's why we use the solver in the first place. Most of the "GTO frequencies" and "MDF" rules are just a general guideline to help get you close to the correct frequencies, but they are not truly factors in why ranges are constructed the way they are.

This is wrong, it has nothing to do with having better hands, it's because our calls don't fully deny that we defend more often. If it were because we have better hands to defend villain would just 3bet righter and we are back to mdf

In 3+ handed game the buttons open range and the sb 3bet range are both metered by the presence of the big blind.

If the sb folds, bb 3bets, button will continue more often than mdf suggests because of this.

If sb is sitting out, like in a tourney, then button should play mdf exactly because of what lazaleas just said. If btn isn’t forced to fold mdf %, then bb isn’t 3 betting enough.