Multi–Euler Branches, Selberg Remainder and Zeta Zeros: A Conditional Windowed-Observable Bridge

We formulate a conditional bridge between composite-side windowed observables on U6 = {n ∈N : gcd(n,6) = 1}= {6k±1}, Selberg-type remainders, and local line models indexed by the non-trivial zeta zeros ρ= 1/2 + iγ. The bridge is deliberately separated into two parts. First, the prime–composite mirror principle is exact at the centered indicator level: under complementary centering, the prime and composite fluctuation signals satisfy XC =−XP, and every linear observable changes sign while preserving magnitude. Second, the appearance of zeta-zero ordinates in a concrete composite-side signal is conditional on an explicit-formula-type line decomposition for that signal.