diff --git a/ext/ExponentialUtilitiesStaticArraysExt.jl b/ext/ExponentialUtilitiesStaticArraysExt.jl
index 109e616e..f552386c 100644
--- a/ext/ExponentialUtilitiesStaticArraysExt.jl
+++ b/ext/ExponentialUtilitiesStaticArraysExt.jl
@@ -2,7 +2,7 @@ module ExponentialUtilitiesStaticArraysExt
 
 export default_tolerance, theta, THETA32, THETA64
 
-using StaticArrays
+using StaticArrays: StaticArrays, SMatrix, SVector
 import Base: @propagate_inbounds
 import LinearAlgebra: tr, I, opnorm, norm
 import ExponentialUtilities
diff --git a/test/qa/Project.toml b/test/qa/Project.toml
index d07cb06f..ebf799ee 100644
--- a/test/qa/Project.toml
+++ b/test/qa/Project.toml
@@ -6,6 +6,7 @@ JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SciMLTesting = "09d9d899-5365-40a9-917a-5f67fddea283"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
@@ -14,5 +15,6 @@ Aqua = "0.8"
 JET = "0.9, 0.10, 0.11"
 SafeTestsets = "0.1, 1"
 SciMLTesting = "2.4"
+StaticArrays = "1.9.8"
 Test = "1"
 julia = "1.10"
diff --git a/test/qa/qa.jl b/test/qa/qa.jl
index f60d679c..b7b8f73a 100644
--- a/test/qa/qa.jl
+++ b/test/qa/qa.jl
@@ -1,6 +1,11 @@
 using SciMLTesting, ExponentialUtilities, JET, Test, LinearAlgebra
 using AllocCheck: check_allocs
 
+# ExplicitImports only sees a package extension once its trigger weakdep is
+# loaded (`Base.get_extension` returns `nothing` otherwise), so loading
+# StaticArrays here is what puts ExponentialUtilitiesStaticArraysExt under QA.
+using StaticArrays
+
 run_qa(
     ExponentialUtilities;
     ei_kwargs = (;
@@ -8,10 +13,16 @@ run_qa(
         # LAPACK balancing wrapper `gebal_noalloc!` (which keeps the CPU matrix
         # exponential allocation-free), plus `Base.promote_op` used to infer the
         # exponential! workspace type at cache construction without allocating.
+        # `arithmetic_closure` (owned by StaticArrays) is the only spelling of
+        # "type you get from doing arithmetic on this eltype", which the
+        # StaticArrays extension needs to pick the working eltype for `expv` on
+        # an integer-valued `SMatrix`. It is documented -- its own docstring
+        # demonstrates `import StaticArrays.arithmetic_closure` -- but StaticArrays
+        # has not declared it `public`, and there is no public equivalent.
         all_qualified_accesses_are_public = (;
             ignore = (
-                Symbol("@blasfunc"), :BlasInt, :chkfinite, :chklapackerror,
-                :chkstride1, :libblastrampoline, :promote_op,
+                Symbol("@blasfunc"), :BlasInt, :arithmetic_closure, :chkfinite,
+                :chklapackerror, :chkstride1, :libblastrampoline, :promote_op,
             ),
         ),
         # `chkstride1` (owned by LinearAlgebra) and `libblastrampoline` (owned by