Hello there! Brace yourself as we dive into a tantalizing problem that involves vector manipulation, combinatorial logic, and some C++ mastery. This problem centers around finding combinations in a given list whose sum is equivalent to a specified target value. Are you ready for a thrilling endeavor? Great! Let's jump into the world of C++ and number theory.

Here's the task at hand: You have to write a C++ function that accepts a vector of distinct integers and a target sum as input. The aim is to identify exactly four numbers in the vector that, when summed, equal this target. Should there be multiple sets that meet this condition, your function should return any one of them. If no such quad exists, the function should return an empty vector.

Consider this vector as an example: {5, 15, 2, 7, 8, 4}. If your target sum is 24, a four-number set that adds up to this value could be {5, 7, 4, 8}.

The input vector will contain at least 4 and at most 1,000 distinct integers. The input integers will be in the range $-10^6$ to . The target sum will also be in the range of to . There is a time limit for the solution to evaluate within 3 seconds.