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We propose a resolution to the "soft omission" problem in Celestial Holography by mapping the boundary correlators of the massless S-matrix onto the arithmetic murmurations of a topological informational space. We demonstrate that a Somos-8-like Phase Transition (N≈200,000) triggers a Schramm-Loewner Evolution (SLE) process with a fractal dimension d=1.326, which acts as the natural smoothing scale for the Inverse Mellin Transform required to resolve non-singular celestial amplitudes. By identifying the Geometric Friction constant (λF = 34/13) as the diffusivity parameter (κ) of the vacuum interface, we show that the dissipative central charge of the early vacuum (c≈-0.0995) is lifted to unity (c=1) via the Arithmetic Gain of the murmuration spectral peaks. This mechanism provides a formal link between the aperiodic order of the Einstein Monotile and the analytic stability of the physical vacuum.