Sheaf Theory · the H¹ Inconsistency Index PATENT PENDING

A numerical measure
of where your models disagree

Multi-agent AI is a consistency problem — and consistency is a branch of mathematics. Sheaf theory is the math of how local pieces glue into one coherent global whole, and how to detect precisely when they don't. Your agents are locally confident and globally blind; Sheaf measures exactly where they cohere — and where they contradict each other without any of them noticing.

H⁰ what they all agree on H¹ the obstruction — where they don't Sheaf makes the gap computable
Penrose stairs: a staircase that appears to rise continuously and return to where it started.
Every step is sound. The staircase goes nowhere. Check any two neighbouring steps and one is higher than the other, exactly as it should be. Every local check passes. There is still no consistent height you can assign to the whole flight, and no single step tells you that — the contradiction only exists in how they fit together. That failure has a name and a number: it is a non-zero H¹. Your agents fail the same way, and it is the thing Sheaf measures. Figure: Impossible staircase, Sakurambo, public domain.

Patent pending · Read the technical whitepaper → · Published (DOI ↗)

the desk · Fundamental · Macro · Quant · Technical · Risk

Independent AI analysts answer your question separately — the local sections. A market question convenes a five-discipline desk (Fundamental, Macro, Quant, Technical, Risk); any other question, a panel of frontier models. We then run a genuine first-cohomology computation: if the answers can't glue into one consistent whole (a cyclic contradiction), that's a true H¹ obstruction; when they can, H¹ is zero and we report the deterministic H⁰ disagreement over the overlap graph. Computed, not a model guessing a score. AI agents modeling analytical frameworks — for research, not investment advice.