A Geometric Resolution of the Riemann Function and the Emergence of the Prime Code

This work is divided into two parts.

The first part resolves the behavior of the Dirichlet partial sums on the critical line using an On-the-Go cancellation identity, showing that sustained index-by-index cancellation — and therefore the vanishing of the zeta function — can occur only when Re(s)=1/2. This yields a geometric understanding of the critical line and produces a stable three-dimensional structure we call the Riemann helix.

The second part uses this geometric structure to build an alphabetic model of the integers.

From the helix we extract two geometric quanta (one angular, one radial) and use them to construct an empirical prime-prediction rule. The full algorithm and code implementation are included, and the method is tested numerically on the first 10,000 primes with perfect accuracy. While no formal proof is claimed, the results reveal a strong geometric resonance between the Riemann helix and the prime sequence.