← twistj.com
The kernel
The starting identities, in one place.
This page is reference, not argument. For an orientation to the
program, read Canon Core.
For the authority, read the
Canon.
No claim on this page is stronger than its row in the registry.
axiom
J = 1 + j² = (1, 0, 1, 0)
unit
j = ζ₅ = e2πi/5 j⁵ = 1
polar
J = (1/φ) · ei · 2π/5
inverse
J⁻¹ = −j − j² = (0, −1, −1, 0)
bridge
J · φ = j
cubic
(J − 1)³ = j
quintic
J⁵ = φ⁻⁵
matrix
MJ = [1 0 −1 1; 0 1 −1 0; 1 0 0 0; 0 1 −1 1] basis (1, j, j², j³)
step
(a, b, c, d) ↦ (a−c+d, b−c, a, b−c+d)
norm
N(J) = det(MJ) = 1
trace
Tr(J) = 3
engine
4 additions per step, zero multiplications: the step rule above, exactly.
drift
Zero. Exact integer arithmetic.
canon
Public Canon · ACTIVE · repository head
Verify it yourself:
kernel_identities.py,
Python standard library, exact arithmetic, no float in any assertion.