C02.1 · 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.

- C02.1-PA01 — The split Albert algebra, its cubic norm, adjoint and element characteristic identity. | STANDARD | [K04] §2.3 Proposition 3 and §2.4 Example 5; [S61] Chapter IV, exceptional type-E discussion. - C02.1-PA02 — The Jordan identity, power-associative element powers and linearized multiplication-operator identities. | STANDARD | [S61] Chapter IV, opening equations and their linearization. The generic symbolic residuals execute these established identities. - C02.1-PA03 — The trace bilinear form on the split Hermitian algebra is indefinite. | STANDARD | [K04] Example 5 gives the trace form; [S61] Chapter III supplies the split norm. The displayed signature is their blockwise consequence. - C02.1-PA04 — A nonzero sum of Jordan squares equal to zero obstructs formal reality. | STANDARD | [S61] Chapter IV, formal reality and Hermitian construction; the article exhibits a direct counterexample in that construction. - C02.1-PA05 — A diagonal element acts by its diagonal entries and pairwise means on its Peirce spaces. | STANDARD | [S61] Chapter IV, Peirce decomposition; [K04] Example 5. The displayed failure of the cubic on an off-diagonal block is an elementary consequence, not a separate spectral discovery. - C02.1-PA06 — Hermitian terminology over a split composition algebra does not impose Euclidean spectral positivity. | STANDARD | [K04] Example 5 with an isotropic/split composition algebra; [S61] Chapters III–IV. The displayed cubic is a worked example of those formulas. - C02.1-PA07 — The suite’s real-lift/eigvalsh sentence needs its symmetry qualification. | PROGRAMME | NONE/files-only foundation gap; Rev32.7 Appendix A §A.5, PDF p.138; D1259 dispatch reports house confirmation and REV32.9_CHANGELOG S310.5 (landed in Rev32.9). This is a source correction, not a newly discovered restriction of symmetric eigensolvers. - C02.1-PA08 — The half-algebra wording defect in the quoted Cayley–Dickson paragraph. | PROGRAMME | Rev32.7 Appendix A §A.1, PDF p.135; D1258 dispatch and its queued S310.2 correction. Keep the sealed quote unchanged. - C02.1-PA09 — The generic polynomial certificate and the explicit counterexample runs. | PROGRAMME | Target article’s complete script and stdout. They are an implementation record of standard algebra and a programme-source audit. - C02.1-PA10 — A map from this mathematical spectrum to physical mass eigenstates and equivalence to all banked arrays. | UNRESOLVED | No such map or alignment certificate is supplied. The dedicated foundation Registrar gap remains NONE/files-only.

**Attribution note.** The split algebra is not an unexplored replacement for the established Albert algebra. Its familiar non-Euclidean properties explain why the March prompt’s formal-reality and universal-real-spectrum demands were inappropriate.

**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.