The Balance Law
The fundamental constraint that makes the geometry work
What is the Balance Law?
The Balance Law states that the four torsions at the diagonal positions of the triaxial dipyramid MUST sum to zero. This isn't an assumption - it's a mathematical necessity that emerges from the geometry itself.
The Four Torsions
Why Does This Matter?
The Balance Law is MANDATORY for any valid CEDGA derivation. If your geometry violates τ₁ + τ₂ + τ₃ + τ₄ = 0, you're not working within the framework.
The "silent fourth" (τ₄) automatically compensates for whatever values τ₁, τ₂, and τ₃ take:
Live Balance Law Demonstration
Watch how τ₄ (yellow) always compensates to maintain balance = 0
The Proof
The M4 simulator ran 1000 iterations with random input values. In every single case, the sum of torsions was essentially zero (max deviation: 1.42e-14, which is floating-point precision noise).
This validates that the Balance Law is not just a theoretical claim - it's a mathematical fact that holds under all tested conditions.