# Non-Random Data Encodes its Geometric and Topological Dimensions

arXiv: https://arxiv.org/abs/2405.07803 · HTML: https://mlsanity.com/paper/2405.07803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 7 of 7)

- [Emergence and algorithmic information dynamics of systems and observers](https://mlsanity.com/paper/2105.14707/) (2021)
- [Minimal Algorithmic Information Loss Methods for Dimension Reduction, Feature Selection and Network Sparsification](https://mlsanity.com/paper/1802.05843/) (2018)
- [Algorithmic Complexity and Reprogrammability of Chemical Structure Networks](https://mlsanity.com/paper/1802.05856/) (2018)
- [An Algorithmic Information Distortion in Multidimensional Networks](https://mlsanity.com/paper/2009.05879/) (2020)
- [The Case for Technosignatures: Why They May Be Abundant, Long-lived, Highly Detectable, and Unambiguous](https://mlsanity.com/paper/2203.10899/) (2022)
- [An Optimal, Universal and Agnostic Decoding Method for Message Reconstruction, Bio and Technosignature Detection](https://mlsanity.com/paper/2303.16045/) (2023)
- [A Simplicity Bubble Problem in Formal-Theoretic Learning Systems](https://mlsanity.com/paper/2112.12275/) (2021)

## Abstract (arXiv)

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.