Polynomial Identities Separating CD4 from CD5: Minimal Degree Eight, the Complete Octic Relative Cocharacter, and the Nonic Sign Cascade

This preprint establishes pure-multiplication polynomial identities separating the standard Cayley-Dickson inclusion CD4 from CD5 and proves that degree eight is minimal, with an explicit separator and nonzero CD5 witness. The exact octic relative cocharacter has dimension 800: six hook blocks contribute 408 dimensions and three near-hook blocks contribute 392, with no conjugation or sign-twist symmetry. This module requires exactly two S8-orbit generators and equals the primitive octic quotient for CD4, while the primitive octic quotient for CD5 is zero. Cyclic re-rooting resolves the two-dimensional octic sign plane into form and hook lines. In degree nine, the certified relative sign channel has dimension 23, its one-step consequence subspace has dimension 7, and its primitive quotient has dimension 16. Version 1.0.1 adds source objects and complete seeded evaluation schedules for all fifteen degree-seven rank sandwiches, with retained complementary minor pairs for quick replay, literal-source reconstruction for the twelve nontrivial stable octic blocks, exact low-degree source audits, the full-source old-consequence profile, and an independent two-prime calculation in the (4,4) block. The accompanying reproducibility release is a single self-contained repository holding Python and Lean software, compact inputs, and exact certificates, so every theorem dependency can be checked offline. Generative AI tools assisted with drafting and revising prose, testing proof outlines, reviewing source code, and checking verification commands. 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.