To simplify this expression, we need to follow the order of operations: parentheses, exponents, multiplication and division, and addition and subtraction. We also need to use the distributive property and the fraction rules. Here are the steps:

First, we simplify the innermost parentheses using fraction arithmetic. We have:

4−[25−{34+(31+(31−41×64))}]

= 4−[25−{34+(31+(31−61))}]

Next, we simplify the remaining parentheses by adding or subtracting the fractions. We need to find the common denominators and adjust the numerators accordingly. We have:

= 4−[25−{34+(62+61)}]

= 4−[25−{34+63}]

= 4−[25−{68+63}]

= 4−[25−611]

Then, we simplify the brackets by subtracting the fractions. We need to find the common denominator and adjust the numerators accordingly. We have:

= 4−[615−611]

= 4−64

Finally, we simplify the expression by subtracting the fraction from the whole number to a fraction with the same denominator and then subtract the numerators. We have:

= 624−64

= 620

We can also reduce the fraction by dividing the numerator and denominator by their greatest common factor, which is 2. We have:

= 310

Therefore, the simplified expression is 310

or 331