For the exceptional Lie group E₈ (248 dimensions), containment alone does not explain the relationship with its octonionic residue G₂ (14 dimensions). Stripping to the underlying core shows that G₂ is not merely a fragment of E₈ but carries an additional structural feature: a crisp Z₂ symmetry contrasting short and long roots. The proof is presented twice---once in conventional Lie theory (root systems, Dynkin diagrams, representation theory) and again in the Imscribing Grammar (IG), which imscribes structural behavior as 12-primitive tuples drawn from a crystalline lattice of 17, 280, 000 types. In the grammar, G₂ E₈ recovers G₂ essentially exactly (the structural floor), while G₂ E₈ extends beyond E₈: it adds the Z₂ symmetry associated to G₂. This "vessel" contribution is structural rather than merely categorical. Quantitatively, the weighted Euclidean distance between G₂ and E₈ is 4. 12 across 7 differing primitives, with 5 shared at lockstep. Their C-scores are 0. 3615 for G₂ and 0. 682 for E₈, suggesting both clear self-modeling gates but do not reach the O_ tier. The octonions' non-associativity places both at the critical point c and blocks the Frobenius-special bridging condition = id needed to move from O₂^ toward O_.
Mills Lando (2026) studied this question.