Structured Information: Applications of MOC Information Topology

 Author: Zhang Suhang, Luoyang, Henan

Abstract

 Classical information theory is built around the framework of Shannon entropy, founded on assumptions of probability statistics, disordered randomness and mean ergodicity. Its essence is a system for measuring and encoding disordered discrete information. Faced with vast contemporary complex datasets characterised by self-similarity, nested stratification and scale correlation, the entropy paradigm is constrained by full-domain computational traversal, accumulation of redundant data and rampant unordered information. It is trapped in an inherent contradiction where computing overhead expands synchronously with data scale.

Drawing on the MOC multi-origin curvature information topology system of the Luoyang School of Mathematics, together with FCFG fractal continued-fraction geometry and the regulatory mechanism of fractional-prime nesting ratios, this paper puts forward a topological paradigm for structured information. Unlike the statistical description of disordered information in the Shannon framework, this paradigm takes the multi-origin curvature structure as its fundamental pillar. Data with features of self-similarity, nested stratification and scale recursion are collectively regarded as structured information manifolds amenable to topological normalization.

This study demonstrates that structured information does not require brute-force traversal or massive raw sampling and storage. With small fractional-primes constructing macroscopic topological skeletons and large fractional-primes generating microscopic nested details, supplemented by regulation of hierarchical nesting ratios and fractal topological growth rules, only a small set of topological parameters can replace enormous volumes of discrete data. This enables high-density representation, low-redundancy storage, rapid topological retrieval and reconstruction of order. Breaking the rigid linkage between computing power and data volume, this paradigm delivers an original underlying mathematical framework for big data, generative modelling, high-dimensional information retrieval, topological encryption and related fields.

Keywords: MOC information topology; multi-origin curvature; FCFG; fractional-prime; structured information; information efficiency; topological normalization

Since the advent of Shannon information theory, the fundamental thread of modern information science has rested upon probabilistic uncertainty, the quantity of disordered information and statistical average encoding. For a long time, the entire suite of systems for data compression, information transmission, retrieval scheduling and computing resource allocation adopts an information model that is disordered, random, discrete and devoid of inherent geometric structure.

Nevertheless, the overwhelming majority of high-value information in natural systems and modern digital spaces is not disordered. Fluid evolution fields, celestial matter distributions, natural textures, video sequences, tandem gene segments and complex network topologies commonly exhibit structural traits: self-similar nesting, hierarchical recursion, scale resonance, and the principle that the local embodies the global.

Traditional information frameworks cannot recognise or exploit the intrinsic topological order of information. They rely instead on point-by-point sampling, full-data storage and full-domain traversal to process massive structured data. This ultimately leads to continuous data expansion and rising computing and energy consumption, forming a long-standing and intractable contemporary dilemma.

Based on MOC multi-origin curvature information topology and FCFG fractal continued-fraction geometry, this paper establishes an original theoretical paradigm for structured information.

MOC breaks free from the single-origin Euclidean statistical framework and defines the topological carrier of information via multi-origin curvature. The FCFG fractional-prime system provides actionable mathematical tools: small fractional-primes carry global topological routing, while large fractional-primes generate fine microscopic structures. Together with hierarchical ratio regulation and fractal growth rules, they enable topological decomposition, parametric normalization and reconstruction of order for structured information.

This paper states the core thesis: disordered information belongs to Shannon; structured information belongs to MOC information topology.

Shannon entropy describes the degree of disorder in information. This topological paradigm characterises its inherent degree of order. By adjusting the superposition ratios and nesting scales of fractional-primes, massive structured data can break free from volumetric constraints and cut wasteful computing overhead. It advances standardised, high-density, controllable information processing, and provides an interdisciplinary underlying solution to mitigate the proliferation of structured information and break computing-power bottlenecks.