A geometric approach to zero-free regions for the Riemann zeta function via transverse curvature of log|ξ(s)|

We introduce a geometric approach to zero-free regions for the Riemann zeta function based on the transverse curvature of log|ξ(s)|. We prove that an off-axis zero at distance δ from the critical line creates a band of negative curvature of width exactly 2δ (the "tidal dichotomy"), and that under a Strong Spacing Conjecture (SSC) preventing arbitrary clustering of zeros, this negative band cannot be compensated by on-line zeros. Combining this geometric constraint with L² energy bounds (Parseval's identity and the Montgomery–Vaughan large sieve), one obtains a formal bound δ ≤ C/(log T)². However, we then show that this bound is illusory: the mollification required to apply L² methods destroys the geometric signal. The tidal curvature O(1/δ²) is reduced to O(1/η²) by convolution, where 1/η is the mollification scale. We further demonstrate, via a differential mollifier (band-pass wavelet) that perfectly cancels the archimedean background, that the barrier is intrinsic to the Fourier resolution limit — not an artifact of the competition with log T. The Fourier uncertainty principle prevents any mollifier from resolving structure at scale δ without requiring a Dirichlet polynomial of length N ≥ exp(c/δ), which collapses the bound. The tidal dichotomy itself is a genuine geometric result about the curvature landscape of ξ. Its inability to produce a 1/(log T)² zero-free region is a concrete, geometrically transparent manifestation of the mean-to-max barrier: L² energy methods cannot capture pointwise geometric information destroyed by the smoothing they require. This analysis complements the systematic cartography of structural obstructions in "Twenty-five ways not to prove the Riemann Hypothesis" (doi:10.5281/zenodo.18986272), providing a 26th documented path and the most geometrically explicit demonstration of the barrier to date.