Sheaf Labs · the H¹ Inconsistency Index, live PATENT PENDING

A number
for where your models disagree

When several AI agents work together, the question is whether their answers fit together. There is a branch of mathematics for exactly that. Sheaf theory is the mathematics of how small pieces join into one whole picture, and of finding exactly where they do not. Each of your agents is sure of its own piece and cannot see the whole. Sheaf measures exactly where the pieces fit, and where they contradict each other without any agent noticing.

H⁰ what they all agree on H¹ where they do not fit together Sheaf turns that into a number
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

Separate AI analysts answer your question on their own. In the mathematics these are the local sections. A market question goes to a desk of five specialists (Fundamental, Macro, Quant, Technical, Risk). Any other question goes to several leading AI models. We then run the calculation: if the answers cannot be joined into one consistent whole (a contradiction that runs in a circle), that is a true H¹ result. When they can, H¹ is zero and we report the H⁰ disagreement, the plain differences between answers that overlap. The score is calculated the same way every time. These are AI agents applying analysis methods, for research. This is not investment advice.