Hypergeometries / exhibit 01

The dimension ladder

A point becomes a segment, a square, a cube—and then a tesseract. This is not a museum of names. It is one object you can count, turn, and slice with care.

The instrument

A changing projection

Honesty check: the drawing is a 2D projection of a rotating representation. It is a shadow-like view, not the higher-dimensional object itself.

Choose a dimension 4A 4-cube is called a tesseract. Slice position w = 0.0Fixing w = 0 leaves a cube in the remaining x, y, z coordinates.

16verticesV = 2⁴

32edgesE = 4 · 2³

24square facesF₂ = C(4,2) · 2²

Worked case

From copying outward to counting exactly

1. CopyMake two copies of an object.
2. JoinConnect corresponding points.
3. CountEach new dimension doubles vertices and adds one edge direction.

Prediction checkpoint

How many edges does a tesseract have?

Use the ladder: E = n · 2^(n−1).

Replay provenance

Built from two historical Claude Code Hypergeometries sessions. The source paths, original repository revision, and recoverable context are recorded in provenance.json.