Non-Random Data Encodes its Geometric and Topological Dimensions
This addresses the challenge of zero-knowledge one-way communication in fields like coding theory and AGI, though it appears to be a theoretical framework without empirical validation.
The paper tackles the problem of reconstructing multidimensional spaces from arbitrary signals without prior knowledge of the encoding scheme or generating source, proving the method is agnostic to various computational and probabilistic assumptions. The result is an optimal and universal decoding method applicable to signal processing, cryptography, and other domains.
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-à-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.