Whisker Trajectories of the Riemann Zeros under Arithmetic Deformation: t-Invariance and Collapse toward the Critical Line

This paper introduces a controlled arithmetic deformation of the Riemann zeta function and studies the resulting three-dimensional geometric structure of its nontrivial zeros. For each zero ρₙ = 1/2 + itₙ, a one-parameter deformation family Zc (s) is defined through exponential suppression of arithmetically complex terms, with Z₀ (s) = ζ (s). As the deformation parameter c increases from zero, the exact zero at σ = 1/2 continuously deforms into a local minimum trajectory — a "whisker" — whose real-part coordinate σ* (c, t) moves away from the critical line. Numerical computation over the first eight nontrivial zeros reveals two central results: t-invariance (the imaginary ordinate t is preserved along each whisker to within 14 ppm relative variation) and linear scaling of the displacement (exponent 0. 97 ± 0. 03). The set of whiskers forms a structured family of parallel trajectories in the three-dimensional space (σ, t, c), all originating from the critical line at c = 0. The paper provides the complete reproducible Python implementation and numerical dataset. No proof of the Riemann Hypothesis is claimed. This paper is a companion to: Colombo, P. (2026). "A Universal Quadratic Law Governing the Local Geometry of Riemann Zeros. " Zenodo. https: //doi. org/10. 5281/zenodo. 20213580