⊙ Hypercube Dimensions

Why 64 States Require 6 Dimensions — Not 5

25 = 32   │   26 = 64

Each dimension doubles the vertices

5D Hypercube (Penteract)
2⁵ vertices
32 states
drag to rotate
⚠ Missing half the Standard Model
6D Hypercube (Hexeract)
2⁶ vertices
64 states
drag to rotate
✓ Complete dual trinity

64 States → Standard Model

48
Fermions
12
Gauge Bosons
4
Higgs

48 + 12 + 4 = 64 = 2³ × 2³ = Input Trinity × Output Trinity

The Pattern: Braid → Field → Boundary

Tier Braid Field Boundary (Closure)
Spatial 1D Line 2D Surface 3D Volume — ⊙₁ locks
Temporal 4D Worldline 5D Config Space 6D Dual Trinity — ⊙₂ locks

Same pattern. Same roles. Why would nature change the rule after 4D?

The Question for Solomon

If you cap at 5D, you have 2⁵ = 32 vertices. That's half the states needed for the Standard Model.

Where do your other 32 states live?

The 6th dimension isn't a patch — it's where the dual trinity (input × output) completes. 2³ × 2³ = 64. Not 32. Not 128. Exactly 64.