Modular Period Structure, Fractal Laws, and Algebraic Universality of the Affine Sequence T_k = 6*2^k + 1

A comprehensive number-theoretic study of the integer sequence T_k = 6*2^k + 1 (OEIS A004119). All 28 modules of the OmarwaCore Lean 4 formalization are covered: Core Reduction Theorem P(m) = ord(2, m/gcd(m,6)), Fractal Period Laws P(p^n) = d_0 * p^(n-1), Product Theorem via CRT, Super-Period L = 30 with three independent derivations, GCD Law, Palindromic Involution, Pascal-Sierpinski-Fibonacci bridge, and Grand Synthesis five-way theorem. 956 theorems, 0 sorry axioms. 13 pages.