# P7: [Proof Group B] G2(2) to SM GAUGE EMBEDDING — E8 ARCHITECTURE PROOF

**Category:** proof_prompt | **Kernel:** PHAT v1.27.5 | **Status:** PENDING

## Prompt

G2(2) to SM GAUGE EMBEDDING — E8 ARCHITECTURE PROOF
Prove the two-algebra architecture resolves the rank mismatch: G2(2) (rank 2) cannot contain SM gauge group (rank 4). Resolution: G2(2) = mass/zero-divisor sector; E8 = full gauge sector with branching E8 superset E6xSU(3) superset SO(10) superset SM. Show the embedding chain G2 subset Spin(7) subset Spin(8) subset E8 (Baez 2002). Assess completeness and flag any steps requiring further derivation. #SuperGrokTOE #E8 #GaugeEmbedding