C05.1 · 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.

- C05.1-PA01 — The quadratic relation for the golden unit and its elementary reciprocal-power identities. | STANDARD | [KC] Theorem 1.1 and §2 Table 1, d=5, identifies the unit; the identities are direct algebraic consequences. The bare identity is not specific to this programme. - C05.1-PA02 — The chosen golden Jordan vacuum and its evaluated Gram/mismatch chain. | PROGRAMME | LIB2-046, LIB2-047, LIB2-048 and LIB2-356; Rev32.7 Appendix E pp.163–165 and Paper 3 p.59. These labels concern the registered vacuum application, not ownership of golden-ratio arithmetic. - C05.1-PA03 — A normalized positive diagonal element need not have the selected spectrum. | STANDARD | [K04] Example 5 restricted to its diagonal subalgebra. The article’s reciprocal-family control is a direct evaluation of this standard cubic norm. - C05.1-PA04 — The equal-norm shorthand omits a selector premise although the norm-product mismatch identity survives. | PROGRAMME | LIB2-356 and Rev32.7 Paper 3 p.59; target article’s exact countermodel; D1259 dispatch reports the house-confirmed S310.6 correction. - C05.1-PA05 — The dimensions of the Cayley algebra and the degree/rank of the Albert algebra, and their arithmetic ratio. | STANDARD | [S61] Chapters III–IV; [K04] Proposition 3 and Example 5. No physical exponent follows from division of these dimensions. - C05.1-PA06 — Use of that dimension ratio in the programme’s mass-exponent discussion. | PROGRAMME | LIB2-049; Rev32.7 Appendix A §A.9 p.148. The source itself separates the exact ratio from a derived mass exponent. - C05.1-PA07 — Multiplying the stated trace-block and normalized equal-copy weights. | STANDARD | [K04] Example 5 fixes the trace form; normalization of a declared equal-copy vector is elementary linear algebra. The square-root identity is not a selection theorem. - C05.1-PA08 — Registration of those factors as the chosen first-row weight. | PROGRAMME | LIB2-050; Rev32.7 Paper 3 p.46. The use of the factors and the readout route are separate premises. - C05.1-PA09 — The specified half-weight coefficient and sector-relative invariant-generator uniqueness. | PROGRAMME | LIB2-051 and LIB2-052; Rev32.7 Appendix B §B.5 p.153. Their original A558 and A603/E110 proofs remain [NOT VERIFIED] in the article. - C05.1-PA10 — The reflected-module trace ratio and its Frobenius closure in the registered normalization. | PROGRAMME | LIB2-053; Rev32.7 Appendix K Theorem 4.3 p.232; expanded in C08.2. - C05.1-PA11 — Historical mathematical priority of the exact registered generator normalization, and the missing physical readout map. | UNRESOLVED | No exact external match or complete original generator payload was recovered. PROGRAMME above specifies corpus provenance and makes no priority claim.

**Attribution note.** A single formula can have a standard algebraic part and a programme-specific use, but these are distinct results in this table. The table does not assign two labels to one predicate. In particular, the golden unit’s elementary identity is STANDARD; the chosen vacuum/Gram/readout construction is PROGRAMME.

**References inspected.**

[KC] Keith Conrad. *Dirichlet’s Unit Theorem*. Author’s notes, no publication date inferred. **Locator:** Theorem 1.1; §2, Table 1, row d=5. https://kconrad.math.uconn.edu/blurbs/gradnumthy/unittheorem.pdf Access scope: Text and the table on PDF p.2 inspected. Positivity at one embedding is distinguished from total positivity.

[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.