C02.2 · 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.

- C02.2-PA01 — The diagonal frame, Peirce spaces and their multiplication rules. | STANDARD | [S61] Chapter IV, Peirce decomposition; [K04] §2.4 Example 5. The basis-product census executes these rules. - C02.2-PA02 — The diagonal adjoint is the quadratic map (x,y,z) to (yz,xz,xy). | STANDARD | [K04] Example 5, adjoint formula restricted to diagonal elements. - C02.2-PA03 — The sphere restriction factors through the antipodal quotient and is the Roman-surface parametrization. | STANDARD | [CSS] “Background” and “Equations and Graphics”, entry 1. The slot permutation equivariance is an elementary property of the same formula. - C02.2-PA04 — The Roman quartic, its double lines and the extra real-axis pieces of the implicit equation. | STANDARD | [CSS] “Background” explicitly discusses the extra “whiskers”; entry 1 supplies the implicit equation. These image-versus-variety distinctions are already in the literature. - C02.2-PA05 — The Roman surface has six pinch-image points and a triple point; the sphere parametrization has antipodal preimages. | STANDARD | [CSS] entry 1. The article’s tangent-rank calculation is a check of the standard parametrization. - C02.2-PA06 — Evaluation of the chosen golden vacuum, its adjoint and the normalization needed before using the sphere restriction. | PROGRAMME | LIB2-047; Rev32.7 Paper 1 §3, PDF pp.24–25; target article’s exact normalization outputs. - C02.2-PA07 — The programme’s Peirce/Roman comparison is restricted to its declared maps and does not supply the physical spinor identification. | PROGRAMME | Rev32.7 Paper 1 §3.1, PDF p.25. The standard Roman map is not relabeled a programme discovery. - C02.2-PA08 — The basis-product and permutation checks in this implementation. | PROGRAMME | Target article’s script/stdout. Those checks do not certify an unavailable global physical bundle. - C02.2-PA09 — The proposed spinor-bundle interface and banked-frame equivalence. | UNRESOLVED | Paper 1 p.25 explicitly leaves the former open; the original frame certificate is not supplied.

**Attribution note.** The restricted sphere map and its homogeneous extension must remain separate. This prior-art pass locates prior discussion of the implicit equation’s extra axis pieces; it does not suggest removing the article’s useful counterexample.

**References inspected.**

[K04] Sergei Krutelevich. *Jordan algebras, exceptional groups, and higher composition laws*. arXiv:math/0411104v1 (2004). **Locator:** §2.3, Proposition 3 (cubic norm construction); §2.4, Example 5 (Hermitian Jordan algebra); §3.1, Definition 17 and Proposition 18 (Freudenthal module and invariant group). https://arxiv.org/pdf/math/0411104 Access scope: Relevant sections and displayed quartic on PDF p.19 inspected. Quartic normalizations must be compared explicitly.

[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.

[CSS] Adam Coffman; linked paper with Arthur J. Schwartz and Charles M. Stanton. *Steiner Surfaces (author’s mathematical exposition); The algebra and geometry of Steiner and other quadratically parametrizable surfaces*. Author webpage; linked paper, Computer Aided Geometric Design 13(3) (1996), 257–286. **Locator:** “Background”; “Equations and Graphics”, entry 1: Roman surface. https://users.pfw.edu/CoffmanA/steinersurface.html Access scope: Author webpage read. The journal paper’s theorem numbering was not inspected and is not asserted.