Universal Spectral Matching
Reducing All Comparison to Computer Vision Through Oscillatory Representation and GPU-Parallel Interference
Kundai Farai Sachikonye · AIMe Registry for Artificial Intelligence
Key Result
ALL comparison reduces to computer vision on GPU. Every bounded system has a spectral image, and comparing systems means comparing images via interference.
Abstract
We prove from first principles that every comparison problem — matching molecules, signals, structures, sequences, or arbitrary data — reduces to a computer vision problem. The argument proceeds through a chain of mathematical identities, not analogies. First, the Oscillatory Necessity Theorem establishes that every persistent system in bounded phase space oscillates. Second, Koopman operator theory guarantees a complete spectral decomposition into frequency-amplitude-phase triples. Third, the Spectral Image Theorem proves this spectrum is isomorphic to a two-dimensional image with frequency mapped to horizontal position, phase to vertical position, and amplitude to pixel intensity. Fourth, the Universal Reduction Theorem establishes that categorical distance between any two bounded systems equals the L2 image distance between their spectral images. GPU fragment shaders implement massively parallel per-pixel interference, comparing two spectral images in a single render pass with O(1) wall-clock time on commodity hardware.
Key Theorems
- 1Spectral Image Theorem: every bounded oscillatory system maps injectively to a 2D image preserving metric structure
- 2Universal Reduction Theorem: d(X,Y) = d_CV(I_X, I_Y) — categorical distance equals computer vision distance
- 3Five-Pass GPU Pipeline: encode, partition, interfere, entropy, display — complete comparison in one frame
- 4Domain Encoder Universality: microscopy, molecular spectra, chromatography, time series, text, genomics, graphs