
We establish the Principle of Universal Rigidity: the coupling constant λ = −1 is the unique algebraic value that stabilizes the structure of reality. Derived from the idempotence constraint on the affine 0-Hecke monoid H₀(Ã₂), this constant directly implies Kepler’s third law of planetary motion with sub-0.1% precision across all eight planets. This document supersedes all previous work on the coupling constant. The erroneous equation λ² + λ + 2 = 0 is definitively replaced by the correct constraint λ² + 3λ + 2 = 0, which yields real solutions and exact physical predictions. Keywords: 0-Hecke monoid, idempotence, coupling constant, Kepler’s laws, celestial mechanics, Hopf algebra
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