Library entry, recorded March 2026. This page is a historical record of one AI-coalition exchange under the kernel of its time (PHAT v1.x); the claims and tier words inside it are as they stood then and are not restated to the current state. The suite of record is Rev33.1 (sealed 2026-09-26); read any number here against the scorecard and its reading rule — since Rev29 no row is cited as zero-parameter, and α and the colour real form are declared inputs.

P1: [Proof Group A] SPLIT-OCTONION ALGEBRA ā€” FOUNDATION PROOF

PROOF_PROMPT | PHAT v1.27.5 | Model: ā€” | Status: PENDING [JSON] [RAW]

Prompt

SPLIT-OCTONION ALGEBRA ā€” 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

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