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ehrlich-b/euclidean-jordan

Bryan Ehrlich

Palomar Registrypalomar/PALOMAR-2026-08-29-000001Aug 29, 2026math.RAscore 0

The Jordan trace form tau(x,y) = tr(L_{x*y}), constructed from the multiplication rather than assumed: symmetric, associative, and positive definite. Symmetry and associativity need neither finite dimensionality nor formal reality; positive definiteness needs both, and runs through the spectral theorem. The carrier is not assumed unital, so this supplies the Euclidean form itself and does not by itself establish a unital Euclidean Jordan algebra. Sits directly on Mathlib's IsCommJordan. Coordinatization is absent. Machine checked, not peer reviewed, no priority claim.

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