C02.1 · Source basis/status

**Registrar: `NONE/files-only` — standalone foundation gap**, explicitly identified by the D1258 Registrar README. No neighbouring identity is borrowed as a Registrar entry for this construction. The following are fully specified calculations, not a rewrite of the Registrar.

Appendix A §A.1, sealed Rev32.7 PDF p.135:

> All split-octonion products in the current suite are taken in Cayley–Dickson form. Writing elements as pairs (p, q) over the compact octonions,

**Sealed wording defect:** the halves in the formula must be **quaternions**, not compact octonions. D1258 reports this as house-confirmed **REV32.9_CHANGELOG S310.2 (landed in Rev32.9)**, a wording repair without a numerical change. The quotation above remains uncorrected; the explicitly defined carrier below is the correct one.

Appendix A §A.5, sealed Rev32.7 PDF p.138:

> The numerically correct route is the linear operator lift Appendix A §A.5, Proposition 0.2, sealed Rev32.7 PDF p.138:

> The earlier objection to eigvalsh applies only to naive octonionic matrix diagonalization, not to the lifted linear operator LA .

**Scope defect to review:** real matrix entries alone do not justify a symmetric-matrix eigensolver. The exact controls below show that a general split-Hermitian element has a real lift that is not Euclidean symmetric and can have nonreal eigenvalues. This does not challenge using a symmetric solver on a separately demonstrated symmetric special case, such as a diagonal vacuum.

Appendix L §2.1, Proposition 2.2, sealed Rev32.7 PDF p.236:

> The raw split algebra J3 (Os ) has signature (15, 12) (indefinite, not formally real)

The March P3 prompt's requests for formal reality and universally real Hermitian spectra are dated prompts, not established premises. This article tests them rather than adopting them.