Latent Mollification Bridge

We establish that Latent grade truncation—the foundational operation in the Latent framework—is mathematically equivalent to mollification in the spectral domain. Truncating a series at grade \(N\) corresponds to convolving with a mollifier whose bandwidth is controlled by the scale parameter \(\varepsilon\). This identification yields a metric space structure on distributions, where approximation error is bounded by \(\varepsilon\) and refines monotonically. We prove 38 theorems organized across seven clusters: convolution identities, error control, metric structure, embedding coherence, limit convergence, exponential decay properties, and Fourier-domain representations. All results are formally verified in the Platonic kernel (50 verification checks, 0 errors) and exported to Lean 4.