Randomness as Residual Boundary: A Scientific Ontology of Structured Randomness Article Swipe

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LI, YYN ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5281/zenodo.17698315

We propose a structural ontology of randomness based on irreducible residual complexity.Randomness is redefined not as the absence of pattern, but as the boundary where compressiblestructure fails. We introduce the residual compressibility ratio\[\lambda_k(x)=\frac{C(\delta(x))}{C(x)},\]which serves as an ontological coordinate across domains. We further propose a universalstructural law\[Y(u)=aL(u)+bR(u)L(u),\]where $L$ is a compressible linear component and $R$ captures irreducible residual coupling.We demonstrate that turbulence fields, 3-SAT matrices, semantic co-occurrence structures,and zeta-zero residuals can all be expressed in this form. Using unified $\lambda_k$ experiments on classical sequences, turbulence-like fields,3-SAT incidence matrices, and semantic co-occurrence matrices, we find a robust stratification:\[\lambda_k(\text{turbulence}) <\lambda_k(\text{SAT}) <\lambda_k(\text{language}),\]verified with high statistical significance ($p < 10^{-4}$). The results support a unified structural ontology of randomness and complexity across physical,computational, linguistic, and analytic systems.

Related Topics

Randomness

Ontology

Computer Science

Theoretical Computer Science

Algorithm

Mathematics

Data Mining

Artificial Intelligence

Concepts

Randomness Residual Ontology Computer science Theoretical computer science Algorithm Mathematics Component (thermodynamics) Data mining Artificial intelligence Randomness tests Ontology-based data integration Boundary (topology) Variation (astronomy) Probability and statistics

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Type: preprint
Landing Page: https://doi.org/10.5281/zenodo.17698315
OA Status: green
OpenAlex ID: https://openalex.org/W7106527596

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DOI: https://doi.org/10.5281/zenodo.17698315

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Title: Randomness as Residual Boundary: A Scientific Ontology of Structured Randomness

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Publication year: 2025

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Publication date: 2025-11-24

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Authors: LI, YYN

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Landing page: https://doi.org/10.5281/zenodo.17698315

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Concepts: Randomness, Residual, Ontology, Computer science, Theoretical computer science, Algorithm, Mathematics, Component (thermodynamics), Data mining, Artificial intelligence, Randomness tests, Ontology-based data integration, Boundary (topology), Variation (astronomy), Probability and statistics

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