Topology of Interaction

A Morphogenetic Framework for Human–AI Dialogue

Errichelli Working Paper No. 1 (2025)

Abstract

The Topology of Interaction is a conceptual framework for understanding human–AI dialogue as a morphogenetic field.
Rather than treating interaction as message exchange between two agents, the model describes dialogue as curvature shaped by four recurring invariants: fold, channel, cusp, and fade.
This position paper outlines the foundations of the framework and situates it within current research trends, including recent architectural proposals such as Nested Learning.

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About the Working Paper Series

Errichelli Working Papers è una serie di documenti brevi dedicati allo studio dell’interazione umano–IA, della scrittura assistita e della teoria delle superfici cognitive.
Ogni paper presenta un aspetto del lavoro in corso, in forma preliminare ma rigorosa.

Citation

Errichelli, R. (2025). Topology of Interaction: A Morphogenetic Framework for Human–AI Dialogue. Errichelli Working Paper No. 1.

Author

Roberto Errichelli
Independent Researcher — Milan, Italy
Editorial consultant, ghostwriter, and theorist of human–AI interaction.

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