This is a speculative but falsifiable proposal for how large language models might recursively restructure their internal problem space—not based on surface similarity, but based on reasoning transferability.

The idea is simple: if models can evaluate which problems lie close together in the space of reasoning (rather than co-occurrence), and cluster accordingly, then they might construct their own topology of cognition—a geometry of what generalizes, transfers, or connects.

The paper outlines a recursive loop:

• Estimate reasoning-based proximity between problems,
• Transform the embedding space accordingly,
• Cluster into conceptual neighborhoods,
• Feed that structure back into inference,
• Iterate.

This mechanism, if successful, could allow models to structure how they think—not just what they predict. It confronts objections by Chomsky (structure cannot emerge from statistics) and Vapnik (learning without theory is epistemic alchemy), and offers a framework by which we can either validate or falsify the possibility of emergent structure in LLM cognition.

I invite criticism on all fronts, particularly:

• Is there any real pathway by which recursive behavioural feedback can extract topology from surface-level sequence models?
• Does this framework misunderstand the depth of Chomsky’s or Vapnik’s objections?
• Could a failure of this process reveal something even deeper about the topological void of current AI architectures?

Full paper below. Feedback, falsification, or fire welcome.

In the Topology of Thought - A Proposal for Recursive Cognitive Structuring in Language Models.docx - Google Docs