Topological Information Theory

Topological information theory is a proposed theoretical framework that would connect the topological structure of information networks to their epistemic outcomes. It seeks to extend the tools of network theory and differential geometry to the study of information ecosystems, treating information as a field on a network with its own dynamics, conservation laws, and phase transitions.

The central question of topological information theory is: how does the shape of an information network determine its capacity to produce reliable knowledge? This question connects information topology to epistemic entropy, mutual information, and the design of epistemic infrastructure.

The field remains speculative. No general formalism yet exists that would predict, for example, the critical threshold at which a network's topology shifts from epistemically productive to epistemically degenerate.