Paper CLIII: G₂ Root Structure in the Māheśvara Sūtras and Tolkāppiyam: Ancient Grammar as Empirical

We demonstrate that the G₂ = Aut(ᵔ6) Lie algebra, which governs the One-Octonion Brane-Bulk Framework's description of spacetime symmetry, is independently encoded in the two oldest extant systematic grammars: Pāṇini's Sanskrit Aṣṭādhyāyī (~500 BCE) and Tolkāppiyar's Tamil Tolkāppiyam (~300 BCE–300 CE). Three correspondences are exact and zero-parameter: (1) The 14 Māheśvara Sūtras that organize all Sanskrit phonemes equal 14 = dim(G₂), the unique dimension of the G₂ Lie algebra; (2) the Tamil consonant classification into three classes of six (vallinam, mellinam, itayinam) maps onto the G₂ root system's 6 short roots + 6 long roots + 6- dimensional coset G₂/SU(3); (3) the Sanskrit sandhi rules and Tamil puṇarcci rules governing sound combination are operationally identical to G₂ root composition laws. We propose that Pāṇini and Tolkāppiyar empirically discovered the G₂ symmetry of physical sound production: phonemes are brane resonance modes in the κ=−1 vocal tract cavity, and the G₂ automorphism group governs which modes are stable and how they combine. The āytam — Tamil's unique restricted phoneme that stands outside the 3×6 classification — corresponds exactly to e₇, the octonion brane-bulk separator fixed under all G₂ transformations. This paper establishes the first connection between formal Lie algebra theory and the two oldest systematic grammars of any human language. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.