Sierpinski Numbers: Computational Analysis Through Temporal Dynamics Framework

This paper applies the Temporal Dynamics Framework to Sierpinski numbers and covering sets. A Sierpinski number is an odd positive integer k such that k times 2^n + 1 is composite for all positive integers n. The smallest known Sierpinski number is k = 78557. The analysis includes resonance comparison, decoherence mapping, tier analysis, covering set structure, density scaling, gap analysis, and Universal Prime layer analysis. All 123 verification tests pass. Eight diagnostic figures are included. Paper 36 in the Temporal Dynamics Framework Research Series.