A Mathematical Duality Between Photoelectric Detection and Microtubule Readout

Abstract

This paper develops a mathematical dual description between photoelectric detection and a Quantum Information Holography (QIH)-inspired model of microtubule readout. After reducing each system to a complex input field, substrate response, and two-outcome transition, the corresponding readout operators are shown to be mathematically equivalent under an explicit mapping of states, fields, frequencies, and response functions. The result does not claim that microtubules and photoelectric surfaces are physically identical, nor that microtubules have been experimentally demonstrated to implement this mechanism. Rather, it establishes a common operator-level architecture linking field amplitude, phase, interference, threshold-dependent transitions, and information readout. The framework is then extended computationally to a matched complex decoder and a time-resolved information geometry. This makes it possible to simulate and render the internal field, interference structure, state transitions, relational strengths, and reconstructed geometry frame by frame. The resulting architecture provides a directly testable software implementation independent of whether the broader QIH interpretation ultimately describes the physical universe.