TWIST-J
A finite rule with unbounded evolution.
One equation: J = 1 + j², where j is the twist unit.
Multiplication by J is a 4×4 integer matrix
over {−1, 0, 1}. Galois structure yields an exact
3+1+0 decomposition. Time is a counter. Space is a commutator. Curvature is what remains.
axiom
J = 1 + j² = (1, 0, 1, 0)
polar
J = (1/φ) · ei · 2π/5
inverse
J⁻¹ = −j − j² = (0, −1, −1, 0)
golden
φ = −j² − j³ = (0, 0, −1, −1)
bridge
J · φ = j
cubic
(J − 1)³ = j
quintic
J⁵ = φ⁻⁵
norm
N(J) = det(MJ) = 1
trace
Tr(J) = 3
engine
4 additions per step. Zero multiplications.
drift
Zero. Exact integer arithmetic.
Ansatz: if the algebra maps to physics, it reproduces weak-field General Relativity with zero free parameters.
Predicts g00 grr = 1 exactly. General Relativity: g00 = 1 − 2GM/rc². Experiment decides.