C08.2 · 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.

- C08.2-PA01 — The Zorn product, trace-zero subspace and commutator used in the calculation. | STANDARD | [NV] §3.2; [E18] Proposition 2.2 for the composition structure. The article declares its signs rather than copying an incompatible table. - C08.2-PA02 — Compatibility of the composition trace form with multiplication and the induced commutator identities. | STANDARD | [S61] Chapter III, equations (33)–(34); [E18] Proposition 2.2. This general invariant-form mechanism is not a programme discovery. - C08.2-PA03 — The exact registered two-weight Frobenius test has twelve nonzero defects proportional to a−b. | PROGRAMME | LIB2-053; Rev32.7 Appendix K §4 Theorem 4.3 p.232; target article’s exhaustive symbolic run. - C08.2-PA04 — The registered reflected trace readout becomes 7/3 while its common scale remains free and nonzero. | PROGRAMME | LIB2-053; Appendix K p.232. This classification covers the specified normalization/readout, not every use of an invariant bilinear form. - C08.2-PA05 — Removing the positive identity line from the split composition norm leaves the imaginary signature (3,4). | STANDARD | [E18] §2, real split classification and Proposition 2.2; [S61] Chapter III. The signature calculation is a direct restriction. - C08.2-PA06 — Exclusion of positive seven in the specified unit-weight orthonormal-channel residue route. | PROGRAMME | LIB2-107; Rev32.7 Appendix I §8 Lemma 8.3 p.212. The source-specific residue class is the content of the application. - C08.2-PA07 — Raw matrix trace is not congruence-invariant; weighting channels changes the allowed signed sum. | STANDARD | [E18] §2 definition of the polar norm and its classification; both controls follow directly from the declared diagonal quadratic form. No claim about arbitrary residues is licensed. - C08.2-PA08 — The corpus explicitly withholds an LSZ, mass or physical-export theorem from the finite trace ratio. | PROGRAMME | LIB2-053 and LIB2-107; Appendix K p.232 and Appendix I p.212. The article performs no two-point or pole calculation. - C08.2-PA09 — The symbolic closure and exhaustive channel-subset enumeration in this implementation. | PROGRAMME | Target article’s script/stdout. Execution verifies the stated finite objects, not the missing banked-array bytes. - C08.2-PA10 — A non-residue physical realization and the precise external priority of the registered trace prescription. | UNRESOLVED | The supplied records do not construct the former; this targeted literature pass does not establish the latter. Neither absence is an assertion that the mathematics has not been studied.

**Attribution note.** The finite compatibility calculation is useful as explicit exposition even though the underlying composition-algebra identities are standard. PROGRAMME identifies the registered two-weight prescription and the application-specific exclusion, not a claim that invariant forms or signed signatures originate here.

**References inspected.**

[NV] Gábor P. Nagy and Petr Vojtěchovský. *Octonions, simple Moufang loops and triality*. Quasigroups and Related Systems 10 (2003), 65–93; arXiv:math/0701707v1. **Locator:** §3.1–§3.2 (Cayley–Dickson and split octonions); §7.1 (automorphisms). https://arxiv.org/pdf/math/0701707 Access scope: Relevant text; PDF extraction is damaged. No exact displayed Zorn signs are borrowed from its damaged extraction.

[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.