Polynomial Identities Separating CD4 from CD5: Minimal Degree Eight and Relative Structure in Degrees Eight and Nine

This preprint establishes the first pure-multiplication polynomial identities separating the standard Cayley-Dickson inclusion CD4 from CD5. It proves equality through degree seven and strict separation in degree eight, with an explicit separator and nonzero CD5 witness. Exactly 11 of the 22 degree-eight isotypic blocks are determined; the remaining 11 are open. The degree-nine result is restricted to the sign-isotypic component, whose certified relative dimension is 23; its one-step operadic-consequence subspace has dimension 7 and the corresponding primitive quotient has dimension 16. The accompanying reproducibility release provides Python and Lean software, compact inputs, and full exact certificates. Generative AI tools, including OpenAI Codex, assisted with drafting and revising prose, exploring proof and implementation strategies, source-code review, and verification-workflow support. No model output is treated as mathematical evidence; the author reviewed and validated all claims, proofs, computations, references, code, and final wording and takes full responsibility. AI tools are not authors or contributors.