SHEET 8 · IV
SERIES SO(8) / T⁴
STATUS ISSUED
CLASS EXEC
A · Governing Identity
¼ × 4 = 1
four quarter-planes, composed, constitute the whole 8-space rotation — T⁴ = SO(2)⁴ ⊂ SO(8)
B · Plate — The Four Quarters (live)
C · Detail — Composition / Assembly
D · Schedule — Plane Register
Plane
Coords
Fraction
Generator
Phase
Rate
General Notes
Real, standard structure. ℝ⁸ decomposes into four orthogonal 2-planes; rotating each independently is the maximal torus T⁴ = SO(2)⁴ of the group SO(8). This is textbook Lie-group geometry.
Each 2-plane spans two of the eight dimensions — a literal quarter of the space. Four quarters, jointly, span all eight.
The count 4 is not arbitrary: ⌊8/2⌋ = 4 is the maximum number of planes that can rotate simultaneously in 8-space (vs 2 in 4-space, 1 in 3-space).
Reading of the identity. "¼ × 4 = 1" denotes four quarter-planes composing the whole rotation — a structural statement, not merely the arithmetic, which is trivially true.
This sheet is a faithful schematic of the plane decomposition; it is not a full 8-cube projection, and the dials depict phase, not a machinable mechanism.