The Manifold Hypothesis under Unknown Gaussian Noise:Conditional Certificates and Consistent Dimension Estimation
未知高斯噪声下的流形假说:条件性证书与一致维数估计
We study what noisy data can establish about the Manifold Hypothesis under explicit identification and regularity conditions. A population residual certificate combines independent-view localization, Gaussian concentration, membership uncertainty, and population transfer. Existing rectifiability criteria then yield a covered-scale consequence. For a local smooth manifold with positive Hölder density, the actual-ball covariance limit identifies the spectral crossing with…