diff --git a/README.md b/README.md
index 4f16e99..73a5ab7 100644
--- a/README.md
+++ b/README.md
@@ -69,6 +69,7 @@ The CI workflow builds the native library on four runners, one per platform:
 | `macos-latest` | `native/arm64-darwin/` |
 | `macos-15-intel` | `native/x86_64-darwin/` |
 
+On each runner `sbt test` loads the fresh library and solves two small problems with known answers.
 A final job collects the four libraries into one jar and checks that each directory is present.
 On a push to `main` that job publishes the jar to GitHub Packages.
 That jar has no classifier.
diff --git a/build.sbt b/build.sbt
index 49ea973..b8cca47 100644
--- a/build.sbt
+++ b/build.sbt
@@ -18,7 +18,7 @@ lazy val githubRepository = "GitHub Package Registry" at s"https://maven.pkg.git
 lazy val commonSettings = Seq(
   javah / target := sourceDirectory.value / "native" / "include",
   // CI drops libraries from other runners into lib_native/<platform>/ before packaging.
-  // sbt-jni would also map lib_native/ under the host platform; turn that second mapping off.
+  // sbt-jni would also map lib_native/ under the host platform. Turn that second mapping off.
   Compile / unmanagedPlatformDependentNativeDirectories := Seq.empty,
   Test / unmanagedPlatformDependentNativeDirectories := Seq.empty,
   crossPaths := true,
@@ -30,6 +30,8 @@ lazy val root = (project in file("."))
   .settings(commonSettings:_*)
   .settings(
     name := "ecos",
-    libraryDependencies ++= Seq(breeze, jblas)
+    libraryDependencies ++= Seq(breeze, jblas, scalatest),
+    // The test loads the native library. A forked JVM keeps that out of sbt's class loaders.
+    Test / fork := true
   )
   .enablePlugins(JniNative)
diff --git a/project/Dependencies.scala b/project/Dependencies.scala
index 04636d2..656e4a5 100644
--- a/project/Dependencies.scala
+++ b/project/Dependencies.scala
@@ -3,4 +3,5 @@ import sbt._
 object Dependencies {
   lazy val breeze = "org.scalanlp"             %% "breeze"           % "2.0"
   lazy val jblas  = "org.jblas"                %  "jblas"            % "1.2.5"
+  lazy val scalatest = "org.scalatest"       %% "scalatest"        % "3.2.20" % Test
 }
diff --git a/src/test/scala/io/citrine/ecos/QpSolverSpec.scala b/src/test/scala/io/citrine/ecos/QpSolverSpec.scala
new file mode 100644
index 0000000..102467c
--- /dev/null
+++ b/src/test/scala/io/citrine/ecos/QpSolverSpec.scala
@@ -0,0 +1,83 @@
+package io.citrine.ecos
+
+import breeze.linalg.CSCMatrix
+import org.scalatest.flatspec.AnyFlatSpec
+import org.scalatest.matchers.should.Matchers
+
+/**
+  * Loads the native library and solves small problems with known answers.
+  * It runs on every CI platform. A library that builds but cannot load, or
+  * returns wrong numbers, fails that platform's build.
+  */
+class QpSolverSpec extends AnyFlatSpec with Matchers {
+
+  /** Each row holds coefficients on four variables, then a lower and an upper bound. */
+  private val boxAndSums: Seq[(Array[Double], Double, Double)] = Seq(
+    (Array(1.0, 1.0, 0.0, 0.0), 0.7, 0.8),
+    (Array(0.0, 0.0, 1.0, 0.0), 0.1, 0.4),
+    (Array(1.0, 0.0, 0.0, 0.0), 0.0, 1.0),
+    (Array(0.0, 1.0, 0.0, 0.0), 0.0, 1.0),
+    (Array(0.0, 0.0, 1.0, 0.0), 0.0, 1.0),
+    (Array(0.0, 0.0, 0.0, 1.0), 0.0, 1.0)
+  )
+
+  /** Each bounded row becomes two inequality rows: a x <= ub and -a x <= -lb. */
+  private def inequalities(rows: Seq[(Array[Double], Double, Double)], n: Int): (CSCMatrix[Double], Array[Double]) = {
+    val builder = new CSCMatrix.Builder[Double](2 * rows.size, n)
+    val h = Array.fill(2 * rows.size)(0.0)
+    rows.zipWithIndex.foreach { case ((coefficients, lower, upper), i) =>
+      coefficients.zipWithIndex.foreach { case (value, j) =>
+        if (value != 0.0) {
+          builder.add(2 * i, j, value)
+          builder.add(2 * i + 1, j, -value)
+        }
+      }
+      h(2 * i) = upper
+      h(2 * i + 1) = -lower
+    }
+    (builder.result, h)
+  }
+
+  /** Equalities: the variables sum to one, and the last variable is zero. */
+  private def equalities(n: Int): CSCMatrix[Double] = {
+    val builder = new CSCMatrix.Builder[Double](2, n)
+    (0 until n).foreach(j => builder.add(0, j, 1.0))
+    builder.add(1, n - 1, 1.0)
+    builder.result
+  }
+
+  "NativeECOS" should "report the ECOS version" in {
+    new NativeECOS().EcosVer() should not be empty
+  }
+
+  "QpSolver" should "project the origin onto the constraint set" in {
+    val n = 4
+    val (g, h) = inequalities(boxAndSums, n)
+    val solver = new QpSolver(nHessian = n, diagonal = true, Equalities = Some(equalities(n)), Inequalities = Some(g))
+    solver.updateEquality(Array(1.0, 0.0))
+    solver.updateInequality(g, h)
+
+    val (status, x) = solver.solve(Array.fill(n)(1.0), Array.fill(n)(0.0))
+
+    status shouldBe Optimal
+    val expected = Array(0.35, 0.35, 0.3, 0.0)
+    x.zip(expected).foreach { case (actual, want) => actual shouldBe want +- 1e-4 }
+  }
+
+  it should "report an infeasible problem" in {
+    val n = 2
+    // x0 must be 2, but the box keeps x0 within [0, 1].
+    val rows = Seq(
+      (Array(1.0, 0.0), 2.0, 2.0),
+      (Array(1.0, 0.0), 0.0, 1.0),
+      (Array(0.0, 1.0), 0.0, 1.0)
+    )
+    val (g, h) = inequalities(rows, n)
+    val solver = new QpSolver(nHessian = n, diagonal = true, Inequalities = Some(g))
+    solver.updateInequality(g, h)
+
+    val (status, _) = solver.solve(Array.fill(n)(1.0), Array.fill(n)(0.0))
+
+    status should (be(PrimalInfeasible) or be(PrimalInfeasibleInaccurate))
+  }
+}