Image Harmonic Matching Circuits
Oscillatory Pixel Dynamics and Interference-Based Visual Comparison Without Algorithmic Computation
Kundai Farai Sachikonye · AIMe Registry for Artificial Intelligence
Key Result
Image comparison IS interference, not computation. Constructive interference signals a match, destructive interference signals a mismatch — O(1) wall-clock time.
Abstract
We establish a framework in which image comparison is performed by physical interference rather than algorithmic computation. Starting from two axioms — bounded phase space for persistent dynamical systems and finite-resolution categorical observation — we prove by elimination that oscillatory dynamics is the unique valid mode for bounded persistent systems. This Oscillatory Necessity Theorem implies that the fundamental constituents of any physical representation are oscillators. Each pixel in a digital image is mapped to an information gas molecule inheriting thermodynamic and oscillatory properties — frequency, phase, and a partition signature. Image comparison then reduces to superposition of pixel wavefunctions: constructive interference signals a match and destructive interference signals a mismatch, with no sequential instruction execution required. Harmonically coupled pixel-oscillations form networks whose closed loops constitute matching circuits — wallless resonant cavities where the round-trip phase condition distinguishes sustained resonance from radiative decay.
Key Theorems
- 1Oscillatory Necessity Theorem: oscillatory dynamics is the unique valid persistent mode in bounded phase space
- 2Triple Equivalence: oscillation, categorical enumeration, and partition function evaluation yield identical entropy S = k_B M ln n
- 3Von Neumann Bottleneck Elimination: O(n^2 d) algorithmic comparison replaced by O(1) wall-clock interference
- 4Matching Circuit Theorem: closed harmonic loops with round-trip phase 2pi*n sustain resonance (verified match)