[3] p. 10
Higher order terms must contribute less than lower order terms in order for the series to converge
The value used to seed the random number generator can be set. Starting again with the same seed produces the same sequence of pseudo-random numbers. ``Random'' initial conditions are therefore repeatable.

The random number generator used is the one included with the GNU C++ library. According to the comments in the source, it is based on the Linear Congruential (LCG) and Additive Congruential (ACG) generators, giving Algorithm M described by Knuth.

An additional benefit of storing the file in binary format is that the complete data file can be made to appear in a programs' address space without incurring the additional overhead of allocating memory and reading everything in. This magic is provided by modern virtual memory systems via the mmap(2) system call. Since the file is already in native format, it can be accessed just big array. The VM system takes care of I/O operations required.
There actually may be more than one solution, but all will be tied
The preferences of the women are exactly the same as that of the men in this case. The Stable Marriage algorithm as stated actually only optimizes the happiness of only one sex. There is a modification of it that optimizes the happinesses of both sexes, but since the preferences are the same in the quark-antiquark simulation, this is not an issue
The magnitude of the force, a constant, does not change. Rather, an increase in potential energy corresponds to a larger separation between pairs, thus a longer period of acceleration
The original data could not kept due to its size, so no quantitative measure can be made. A dependence of period on amplitude is not unexpected, given the constant form of the force. The simple harmonic oscillator does not have such a dependence.