A Mathematical Curiosity — IV The Triple Hopf Structure on H₀(Ã₂)

We introduce a strictly non-coassociative triple coproduct structure on the 0-Hecke monoid H₀(Ã₂), regularized by a real coupling constant λ = -1. This structure emerges from the idempotence constraint λ² + 3λ + 2 = 0. The resulting Quasi-Hopf algebra encodes a ℤ₃ symmetry via a circulant phase matrix P with spectrum {0, 3, 0}, interpreting the invariant mode as a topological confinement channel. This work proposes a new algebraic framework for ternary decomposition channels in non-Hermitian topologies.