Non-Random Data Encodes its Geometric and Topological Dimensions

TL;DR

This paper introduces a universal, non-random data decoding method based on information and measure theory, capable of reconstructing multidimensional signals without prior knowledge, with broad applications in coding, cryptography, and signal processing.

Contribution

It presents a novel, scheme-agnostic multidimensional space reconstruction method that does not rely on prior distributions or specific encoding schemes, advancing universal data decoding techniques.

Findings

Proven to be agnostic to encoding and computation models

Applicable to decoding in cryptography and bio-signature detection

Supports signal processing and topological analysis

Abstract

Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way communication channels, such as in deciphering messages (i.e., objects embedded into multidimensional spaces) from unknown generating sources about which no prior knowledge is available and to which no return message can be sent. Our multidimensional space reconstruction method from an arbitrary received signal is proven to be agnostic vis-\`a-vis the encoding-decoding scheme, computation model, programming language, formal theory, the computable (or semi-computable) method of approximation to algorithmic complexity, and any arbitrarily chosen (computable) probability measure. The method derives from the principles of an approach to Artificial General Intelligence (AGI) capable of building a general-purpose model of models independent of any arbitrarily assumed prior probability distribution. We argue that this optimal and universal method of decoding non-random data has applications to signal processing, causal deconvolution, topological and geometric properties encoding, cryptography, and bio- and technosignature detection.