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June 6, 20260 citationsOpen Access

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

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VIVali Ilyas

Key Points

  • The research aims to identify exceptional algebraic structures within a 29-symbol ancient linguistic system and explore their implications for unified field theory.
  • Analyzed a 29-symbol ancient discrete linguistic system against a verified corpus.
  • Verified algebraic structures like G2 and SO(8) through computational analysis and corpus frequency evaluation.
  • Derived predictions based on findings, achieving verifications of several predicted outcomes.
  • The algebra systematically undergoes spontaneous symmetry breaking from G2 symmetry to a rank-1 ground state.
  • The Casimir proxy in the broken phase is 0.931, correlating with the predicted 0.9375 from symmetry breaking mechanisms.
  • Five falsifiable predictions made; four of them have been verified.

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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Cite This Study

Vali Ilyas (2026) studied this question.

synapsesocial.com/papers/6a23bafd71a5da9775e769fdhttps://doi.org/10.5281/zenodo.20544282
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