I've been building an external cognitive OS for LLMs called KIS (Knowledge Innovation System) for 18 months. The core argument:
As LLMs get smarter, they converge faster. This is the problem. Genuine inquiry requires non-convergent, open-ended exploration — which is structurally incompatible with how trained models work.
The math: question-space is a Colimit (open, non-convergent expansion). Model weights implement closure operators (Galois Connections), where φ(φ(q)) = φ(q). These two structures are fundamentally incompatible. Scaling won't fix this.
KIS operates upstream of LLMs — designing initial conditions before generation begins. Currently operational as WebKIS. Effect size d ≈ 0.8 in invention support experiments.
As LLMs get smarter, they converge faster. This is the problem. Genuine inquiry requires non-convergent, open-ended exploration — which is structurally incompatible with how trained models work.
The math: question-space is a Colimit (open, non-convergent expansion). Model weights implement closure operators (Galois Connections), where φ(φ(q)) = φ(q). These two structures are fundamentally incompatible. Scaling won't fix this.
KIS operates upstream of LLMs — designing initial conditions before generation begins. Currently operational as WebKIS. Effect size d ≈ 0.8 in invention support experiments.
Preprint: https://zenodo.org/records/19305025
Happy to discuss the category theory or architecture.