A Mathematical Curiosity — II : The Extended Monoid M_ext = H₀(A₃) × H₀(A₃)ᵒᵖ

Description / Abstract: We report the isolation of a closed algebraic structure, $M_{ext}$, possessing a cardinality of exactly 576 elements. This document serves as a proof of existence for a system exhibiting three distinct invariant signatures: Binomial Spectral Decomposition: The charge operator yields a strict $(1, 6, 15, 20...)$ distribution. Geometric Confinement: The discrete curvature is strictly positive ($\kappa > 0$) and correlated with pair creation. Fermionic Limit: A specific deformation parameter $q$ induces a transition to a nilpotent state ($M^2=0$) satisfying Pauli exclusion.