vCF-1 Demo: Linear Curvature-Change Denoising for 2D Astronomical Maps (Medley 2025)

vCF-1 (Variable Curvature Filter – Version 1) is a linear, prior-minimal denoising method developed by Michael Medley as part of the Echo Lattice Theory Family v2. This record provides a safe, simplified demonstration of how the vCF-1 curvature-change operator can be applied to 2D scientific images such as comet frames, sky maps, and astronomical data products. This demo does not include the full proprietary vCF-1 implementation. Instead, it shows a transparent, reproducible subset of the method using: 1D first-order and second-order finite-difference operators A 2D curvature-change operator constructed via Kronecker products A linear solve of the form(I + λE) x = ywhere E is the curvature-change operator and λ controls smoothing strength A synthetic test image (Gaussian source + noise) to illustrate performance What This Demo Shows How vCF-1 removes high-frequency noise while maintaining large-scale structures How the method applies to 2D arrays (e.g., FITS-loaded maps) How the curvature-change framework differs from traditional wavelet or Gaussian filters A fully reproducible workflow using only NumPy, SciPy, and Matplotlib What This Demo Does Not Reveal No full Echo Lattice engine No production-level 2D operator No HEALPix or domain-specific CMB code No proprietary optimizations