The κ Constant
The ONE input from which all geometry derives
What is κ?
Kappa (κ) is the fundamental angular unit of the Epoch Model. It represents one degree expressed in radians - the smallest meaningful angular step in the geometric framework. Everything in CEDGA must trace back to this single constant.
The Derivation Chain
This is the ONLY assumed input.
180 κ-steps complete a half-toroidal rotation.
The tetrahelix naturally divides into 4 transforms at diagonal positions.
Four torsions at 45° intervals MUST sum to zero. Mathematical necessity.
The tetrahelix edge-to-edge angle emerges from geometric constraint.
Why 2π/180?
The choice isn't arbitrary. 180 is the number of degrees in a half-circle (π radians). This makes κ the bridge between degree-based and radian-based geometry - the conversion factor that allows us to work in either system.
More importantly, 180 = 4 × 45 = 2 × 90 = 3 × 60. These divisions give us:
Four-fold symmetry (180/4)
The four transforms T₁, T₂, T₃, T₄ at 45° diagonal positions.
Two-fold inversion (180/2)
The [1 = -1] principle - facing and inverted views sum to zero.
Three-fold structure (180/3)
Connection to base-60 mathematics: 60 = 180/3 = 2² × 3 × 5.
The silent fourth
Three visible + one compensating. τ₄ = -(τ₁+τ₂+τ₃).