Kim's Isotropic Number 𝐼 ( 𝑠 ) = 𝜁 ( 𝑠 ) ⋅ 𝜁 ( 1 − 𝑠 ) : Geometric Foundation of the KIT Unified Framework

We define and analyze Kim's Isotropic Number I(s)=ζ(s)⋅ζ(1−s), a fundamental invariant of the Riemann zeta function that serves as the geometric seed of the KIT unified framework. The isotropic number exhibits four-fold cruciform symmetry, ensuring space-time parity and matter-antimatter conjugation. On the critical line, I(s)=∣ζ(s)∣2≥0, enforcing real positive particle masses and establishing the Riemann Hypothesis as a physical law. Spectral stiffness ∣ζ′(ϱN)∣2 determines particle masses with zero free parameters, while trivial zeros anchor the strong force and CP conservation. At the saturation boundary N=7, stochastic fluctuations of 0.06% unify Newton’s constant scatter and the neutrino mass scale. This work provides a parameter-free mathematical bridge between number theory and fundamental physics.