C01.2 · Prior art

Classification inserted by the house from the D1259 prior-art addendum (contract §8). STANDARD = established mathematics, cited. PROGRAMME = corpus-specific construction, application or audit — NOT a claim of historical originality. UNRESOLVED = a source or identification boundary. These are provenance classifications, not scientific tiers.

- C01.2-PA01 — A unital algebra automorphism fixes the identity and preserves the Cayley norm. | STANDARD | [E18] Proposition 2.2 and §2; [BH] §6. The quadratic identity determines trace and norm intrinsically. - C01.2-PA02 — The derivation algebra of a Cayley algebra is of type G2; compact and split real forms have different Killing signatures. | STANDARD | [S61] Chapter III, concluding derivation-algebra discussion; [BM] §5.2–5.3 and Appendix B. The nullspace calculation is an explicit presentation of this established algebra. - C01.2-PA03 — Cartan decomposition, the compact subalgebra and the intrinsic Killing-form test for the split real form. | STANDARD | [BM] §5.2–5.3, Proposition 3; Appendix B. The article computes its normalization, rather than importing a table of signs. - C01.2-PA04 — The split rank-two G2 root system and its long/short-root distinction. | STANDARD | [BM] Appendix B. Recovering the roots from the solved matrices is exposition and an implementation test. - C01.2-PA05 — The faithful quaternion-pair action has a diagonal central kernel, yielding SO(4), not an unqualified faithful product of two SU(2) groups. | STANDARD | [E18] §1.2; [BM] Appendix A. The article’s action is expressed in its declared doubling convention. - C01.2-PA06 — The full split-octonion automorphism group and the distinction from its covering group are known. | STANDARD | [BH] §6, especially PDF p.13; [BM] Appendix A. This supplies literature support for the classification that the old article did not independently prove. It does not make its Lie-algebra code a global-group proof. - C01.2-PA07 — The declared compact-part colour obstruction in the loaded split real form. | PROGRAMME | LIB2-096; Rev32.7 Appendix N §2, PDF p.253. Its application is narrower than the standard automorphism classification. - C01.2-PA08 — The exact ranks, root weights and implementation controls reported by this script. | PROGRAMME | Target article and its executed stdout. They certify the stated presentation, not equivalence with unavailable frozen matrices. - C01.2-PA09 — The precise theorem/page in Jacobson’s 1958 original intended by the March prompt, and the map to the banked arrays. | UNRESOLVED | Jacobson’s bibliographic identity is located, but the original text was not successfully inspected. Cite [BH]/[BM] for the standard statement; do not invent a Jacobson theorem number.

**Attribution note.** Documentation of a known global result and a complete independent proof are different. The literature boundary can now be narrowed; the old implementation’s missing global proof and frozen-frame alignment are not retroactively filled by its rank computation.

**References inspected.**

[E18] Alberto Elduque. *Composition algebras*. arXiv:1810.09979v1 (2018). **Locator:** §1.2; §2, Proposition 2.2, Theorems 2.5 and 2.11, Corollary 2.12. https://arxiv.org/pdf/1810.09979 Access scope: Full relevant text sections; the author expressly does not treat the Zorn vector-matrix model.

[S61] Richard D. Schafer. *An Introduction to Nonassociative Algebras*. Stillwater lecture notes, 1961; Project Gutenberg ebook 25156 (not the pagination of the 1966 book). **Locator:** Chapter III, printed pp.25–28; Chapter IV, especially the Jordan identity/linearization, Peirce decomposition, and exceptional type-E discussion, printed pp.29–37. https://www.gutenberg.org/files/25156/25156-pdf.pdf Access scope: Title and cited chapters inspected; references use this notes edition.

[BH] John C. Baez and John Huerta. *G2 and the rolling ball*. arXiv:1205.2447; Transactions of the AMS 366 (2014), 5257–5293. **Locator:** §6, “Split octonions and the rolling ball”, especially PDF pp.12–13. https://arxiv.org/pdf/1205.2447 Access scope: Relevant text and PDF p.13 image inspected; distinction between the automorphism group and its double cover.

[BM] Gil Bor and Richard Montgomery. *G2 and the “rolling distribution”*. arXiv:math/0612469; L’Enseignement Mathématique 55 (2009), 157–196. **Locator:** §5.2–§5.3, Proposition 3; Appendix A (covering groups); Appendix B (root basis). https://arxiv.org/pdf/math/0612469 Access scope: Relevant prose and formulas; no unrendered root table is transcribed.