Static Power Dynamics and Harmony Cycles:Universal Convergence and Attractor Classification in Iterated Digit-PowerMappings We introduce and investigate Static Power Dynamics, a novel class of iterated digit-power mappingsdefined by the transformationfP(n) = Σ di^P,where di are the decimal digits of n ∈ ℕ and P ≥ 2 is a fixed integer parameter applied uniformly andstatically to all digits. Utilizing a dedicated iterative computational engine (the Sufi Cycle Finder [10]), wesystematically classify all periodic attractors — termed Harmony Cycles — for parameters P ∈ {2, 3, 4, 5,6, 7, 8, 9, 10, 11, 12, 13, 15, 100} across ranges up to 100,000. The mapping recovers the classical HappyNumbers system as the special case P = 2, and its non-trivial fixed points at each P are precisely thegeneralized narcissistic (Armstrong) numbers (Theorem 1). We prove analytically that n = 1 is a universalfixed point for all P ≥ 2, establish a boundedness theorem guaranteeing eventual periodicity, and documenta striking even/odd parity pattern in attractor counts. A complete attractor landscape is provided for eachtested parameter, revealing rich non-monotone structural complexity as P varies.