Why it is a question
THEORY-160 holds the symmetry–conservation equivalence for a bracket with unique flows. If the bracket is antisymmetric, “a generates symmetries of b” holds exactly when “b generates symmetries of a” does. The record re-derived that from Baez’s Theorems 3, 4, 8 and 10. Where observables and generators are different kinds of thing, the equivalence needs a map ψ : O → L. Baez quotes Alfsen and Shultz (1998): for unital JB-algebras, a map with ψ_a(a) = 0 and a second condition exists exactly when O is the self-adjoint part of a C*-algebra. Until 2026-10-19 THEORY-160’s promote_when offered a checked reading of that theorem as one way to promote it. At the owner’s direction, from the promotion audit’s batch 008 (ADR-047), the THEORY was narrowed to the bracket equivalence, and this clause moved here.
It is open because the record holds the theorem only as Baez quotes it.
What would answer it
A checked reading of Alfsen and Shultz (1998), showing that a dynamical correspondence’s condition (A) is exactly what gives the equivalence for JB-algebras.