Rotation as Invertible Noise: Geometry, Stabilizers, and Multi-view Identification on the Sphere

We study a generative model in which noise is a random rotation R ∈ SO(3) applied to a band-limited field f on the sphere S^2. (i) The cumulative effect of any number of local strikes on S^2 collapses to a single rotation with only 3 degrees of freedom. (ii) With R known, recovery is information-theoretically optimal (slope 1.04 against the Cramer-Rao proxy). (iii) With R unknown, a single view leaves an SO(3)-torsor gauge that no amount of data can resolve. (iv) With two views of the same f, the residual ambiguity is exactly the stabilizer Stab(f) of the field. This contrasts with Gaussian diffusion: rotations preserve information but induce a group-theoretic gauge, not information destruction. Source: https://github.com/mablue/sphere-noise Author: https://masoudsoft.ir