Topological QEC via Lattice Symmetry and SU(3) Mass Splitting — E8 Intelligence Research

FINDING: Topological quantum error correction leverages lattice symmetries and algebraic structures (root systems, Weyl groups) to encode logical qubits non-locally, with the hexaquark result revealing SU(3) antidecuplet mass-splitting governed by Gell-Mann–Okubo-type linearity. | MATH: Surface codes: stabilizer group \( S = \langle X_v, Z_p \rangle \) on a square lattice; logical operators are non-contractible loops — homology classes \( H_1(\text{torus}) \cong \mathbb{Z}^2 \). Non-Abelian codes: anyons with fusion rules \( a \times b = \sum_c N^c_{ab} c \), braiding matrices \( B \) satisfying Yang–Baxter \( R_{12}R_{13}R_{23}=R_{23}R_{13}R_{12} \). Hexaquark: SU(3) antidecuplet mass formula \( M = M_0 + aY + b[I(I+1) - Y^2/4] \) — linear in hypercharge \( Y \), quadratic in isospin \( I \). | CONNECTION: Surface codes are defined on square lattices — crystallographic symmetry \( p4m \) (wallpaper group). Root system \( A_2 \) (hexagonal) underlies SU(3) — the hexaquark antidecuplet Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com