Introduction: After my three false starts with my very first attempt to do a pre-registration with Claude, Meta, and Google Search AI, I have been trying to define “the description of the problem as given.”

Today I might say, “The hexarchon, pictured here — https://81018.com/octahedron-dynamics/ — is an octahedron with the first level of structure reveal.” By dividing each edge in half and connecting those vertices, you see six smaller octahedrons, one in each corner and a tetrahedron, one in each face, and four hexagonal plates connecting bisecting the eight faces. I then provide a tool (within the prior link) to manipulate and explore it. In March 2026 Claude (AI) described it — https://81018.com/2026/03/18/claude-hexarchon/ The description given was ad hoc. I believe for a formal “Pre-Registration” it should be more formally defined.

Given my own personal lack of clarity with Claude [1] [2] and Meta [1], I will re-write Claude’s description so it’s much tighter and has guidelines that do not give away too much. Thinking about that, is it a fair question to ask, “How many possible answers are there?” I am rather sure that it is not an infinite number.

I would then go on with the pre-registration description. To date, this seems to be the best description that has emerged: “Please identify as many geometric constructions as possible and explain the potential dynamics. You can manipulate the model. Ideally, you will be able to name a process or construction you can envision. Perhaps if you start with a specific, named feature of the Hexarchon — a ratio of edge lengths, a ratio of face diagonals, an angle between symmetry axes, a ratio of volumes of inscribed solids, a cross-sectional area ratio, or a ratio of the radii of inscribed and circumscribed spheres. The construction must be specific enough that I can reproduce it without ambiguity.”

It seems framing this question is not a straightforward thing. It is certainly part of the magic to inspire the most creativity.