Prime Gaps, Fractal Geometry, and the Killer Lemma: A Spectral Framework for the Riemann Hypothesis

This paper formalizes and tests the Killer Lemma: a spectral instability argument for the Riemann Hypothesis. Assuming the Spectral Invariant Hypothesis—that prime gaps exhibit stable wavelet and fractal structure—it proves that off-line zeta zeros would induce detectable distortions in these invariants. Combining analytic models, simulations, and statistical validation, the framework transforms earlier observations into a conditional spectral proof strategy.