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The Celestial Sphere as an Ideal Benchmark for Quantum Gravity: Null-Geodesic Universality, Mass Generation, and Theory Discrimination with Existing Data
Every conventional route to Planck-scale observables is physically blocked: collider access requires galactic-scale infrastructure; primordial B-modes probe tensor amplitudes, not propagator structure; the Kamionkowski-Loeb method [1] is foreground-limited in practice. We show that \sigma^2 = 0 (the null boundary I^{-}\cup I^{+}) is the unique open window, where the bandlimited Green's function- derived from G\in L^2 and \dim \mathcal{H} = 1 - satisfies G|_{I^{\pm}} = 1 exactly. This is a removable singularity of \sin (z) / z at z = 0; the real and imaginary axes of z correspond to timelike and spacelike propagation respectively, both analytically determined by the null value. The completeness identity \sum_{l}(2l + 1)j_{l}(x)^{2} = 1 confirms global consistency; the conformal dimensions \Delta_{l} = l + 1 emerge from the rescaled boundary limit (\Omega r)^{2\Delta_{l}}G_{l}|_{\Omega r\to \infty}. Mass generation is geometrically the displacement of z from 0 into \mathbb{R}^{+}: the Higgs mechanism removes W^{\pm},Z from I^{\pm}, leaving exactly l = 0,1,2 on the celestial sphere. This parameter-free prediction is an ideal benchmark against which competing quantum-gravity theories are immediately testable with existing public data.
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