Prime k-Tuple Constellations: Computational Pattern Detection Through Temporal Dynamics Framework

This paper extends the Temporal Dynamics Framework twin prime analysis to higher-order k-tuple constellations. Where the twin prime analysis (Paper 3) showed negative results for k = 2, this paper finds exponential signal scaling for k >= 3, with the Temporal Dynamics Framework signal strength growing exponentially with constellation size. Hardy-Littlewood constant predictions are validated against computational data. Pareto structure analysis reveals resonance concentration patterns consistent with Universal Prime modular structure. All 54 verification tests pass. Paper 5 in the Temporal Dynamics Framework Research Series.