# P1: [Proof Group A] SPLIT-OCTONION ALGEBRA — FOUNDATION PROOF

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

## Prompt

SPLIT-OCTONION ALGEBRA — FOUNDATION PROOF
Using v1.27.5 Kernel: Prove that the split-octonion algebra Os (8-dimensional, signature (4,4), basis {1,e1,e2,e3,f1,f2,f3,l}) satisfies all four division-algebra axioms up to alternativity. Show explicitly: (a) Zorn matrix multiplication table reproduces correct signs, (b) the zero-divisor structure {f1,f2,f3,l} spans a 4D null cone, (c) the split signature distinguishes Os from Euclidean O. Assess readiness for peer review. #SuperGrokTOE #SplitOctonions