Prime-Support Totient Recurrences: Structure, Exact Computation, Super-Polynomial Growth, and a General PSTR Family

This paper introduces and analyzes Prime-Support Totient Recurrences (PSTR), a novel class of nonautonomous arithmetic dynamics generated by coupling Euler's totient function to the prime support across short integer intervals. We establish the mathematical framework for the primary sequence $a_n$, prove its initial structural properties, and analyze its super-polynomial growth regime. In addition to exact numerical computations and empirical prime factorizations for the first several terms, we formulate the generalized PSTR family, explore its dynamic prime-factor dependence, and outline key open problems regarding term density and asymptotic bounds.