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diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 7285d4a..b8ceda8 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,3 +1,19 @@
+A. Add tests for orthogonality in the Peirce decomposition.
+
+B. Add support for a symmetric positive-definite bilinear form in
+   the JordanSpinEJA.
+
 1. Add CartesianProductEJA.
 
 2. Check the axioms in the constructor when check != False?
+
+3. Add references and start citing them.
+
+4. Implement the octonion simple EJA.
+
+5. Factor out the unit-norm basis (and operator symmetry) tests once
+   all of the algebras pass.
+
+6. Can we make the minimal and characteristic polynomial tests work
+   for trivial algebras, too? Then we wouldn't need the "nontrivial"
+   argument to random_eja().