This paper applies the Temporal Dynamics Framework to the Erdos-Straus Conjecture (1948), which states that for every integer n >= 2, the equation 4/n = 1/x + 1/y + 1/z has a solution in positive integers. The computational solver finds solutions for 45, 041 of 49, 999 values tested, with remaining cases reflecting solver search-depth limitations rather than counterexamples (the conjecture is known to hold to 10¹4). Hard cases cluster at specific residues modulo K = 41. Universal Prime divisibility provides decomposition shortcuts. The n congruent to 1 modulo 4 class contains the hardest cases. Paper 28 in the Temporal Dynamics Framework Research Series.
James Norman Ibbotson (Mon,) studied this question.