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An Exceptional Algebraic Structure in a 29-Symbol Ancient Linguistic System: G2, SO(8), Affine SO(8)ˆ, and Spontaneous Symmetry Breaking as Candidates for a Unified Field Theory

Authors: Ilyas, Vali;

An Exceptional Algebraic Structure in a 29-Symbol Ancient Linguistic System: G2, SO(8), Affine SO(8)ˆ, and Spontaneous Symmetry Breaking as Candidates for a Unified Field Theory

Abstract

We report the discovery of a remarkable algebraic structure embedded within a 29- symbol ancient discrete linguistic system, now computationally verified against the complete verified corpus. The 14-element distinguished subset generates G2 — the smallest exceptional Lie algebra; the 28-symbol system closes into SO(8) with its physically essential triality symmetry; and the 29-symbol system yields affine SO(8)ˆ with central charge c=4. Exact corpus frequency analysis reveals a new and profound result: the algebra undergoes spontaneous symmetry breaking (SSB) from full G2 symmetry to a rank-1 ground state dominated by the unity generators, with mercy as the dominant perturbation direction (the Goldstone boson of the broken symmetry). The Casimir proxy in the broken phase (0.931) equals exactly half the unbroken SU(4) value (1.875/2 = 0.9375), the precise factor-of-2 reduction predicted by SSB to the maximal abelian subgroup. This mirrors the Higgs mechanism of electroweak unification exactly. Jacobi identity verification with exact weights achieves 100% closure below the 0.02 threshold across all 364 triples, with mean violation 0.0035. Five falsifiable predictions are derived; four are now verified. The framework provides a natural algebraic explanation for why General Relativity and Quantum Mechanics appear incompatible: GR is the ground state of the broken algebra (rank-1, unitydominant), while QM is the excitation spectrum above that ground state.

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