diff --git a/skainet-backends/skainet-backend-cpu/src/commonMain/kotlin/sk/ainet/exec/tensor/ops/DefaultCpuOps.kt b/skainet-backends/skainet-backend-cpu/src/commonMain/kotlin/sk/ainet/exec/tensor/ops/DefaultCpuOps.kt
index 2f7b15b37..66bcbdbc3 100644
--- a/skainet-backends/skainet-backend-cpu/src/commonMain/kotlin/sk/ainet/exec/tensor/ops/DefaultCpuOps.kt
+++ b/skainet-backends/skainet-backend-cpu/src/commonMain/kotlin/sk/ainet/exec/tensor/ops/DefaultCpuOps.kt
@@ -1031,8 +1031,15 @@ public open class DefaultCpuOpsBase(protected val dataFactory: TensorDataFactory
      */
     /** The heap packed data types whose kernels read input-block-major bytes. */
     private fun isHeapPackedWeight(data: sk.ainet.lang.tensor.data.TensorData<*, *>): Boolean =
-        data is Q4_KTensorData || data is Q5_KTensorData || data is Q6_KTensorData ||
-            data is Q5_1TensorData || data is Q5_0TensorData || data is Q8_0TensorData || data is Q4_0TensorData
+        // Any packed block storage, not an enumeration of formats (#1136 physiology: kernels are
+        // selected by the weight's storage format, and so is the Wᵀ-marker path that reaches them).
+        // The hardcoded Q-list this replaces silently excluded the ternary types
+        // (BitNetB158TensorData, BitNetPlanesTensorData), so `transpose` dense-copied them through
+        // a decoding get() that returns CODES, not values — a ClassCastException at best. The JVM
+        // tier keeps its own narrower list (isHeapPackedWeightForJvm) for the formats its
+        // relayout-and-cache kernels actually read; everything else lands in
+        // matmulWeightTransposedViaViews, which serves any encoding through KernelDispatch.
+        data is sk.ainet.lang.tensor.storage.PackedBlockStorage
 
     /**
      * The block relayout by its own name (#973/#1096) — what `transpose` used to do to a packed
diff --git a/skainet-backends/skainet-backend-cpu/src/commonTest/kotlin/sk/ainet/exec/tensor/ops/TernaryWeightTransposeDispatchTest.kt b/skainet-backends/skainet-backend-cpu/src/commonTest/kotlin/sk/ainet/exec/tensor/ops/TernaryWeightTransposeDispatchTest.kt
new file mode 100644
index 000000000..0443bcc94
--- /dev/null
+++ b/skainet-backends/skainet-backend-cpu/src/commonTest/kotlin/sk/ainet/exec/tensor/ops/TernaryWeightTransposeDispatchTest.kt
@@ -0,0 +1,84 @@
+package sk.ainet.exec.tensor.ops
+
+import sk.ainet.context.DirectCpuExecutionContext
+import sk.ainet.lang.memory.ExperimentalMemoryApi
+import sk.ainet.lang.memory.TernaryCodec
+import sk.ainet.lang.tensor.Shape
+import sk.ainet.lang.tensor.data.BitNetB158TensorData
+import sk.ainet.lang.tensor.data.BitNetPlanesTensorData
+import sk.ainet.lang.types.FP32
+import kotlin.math.abs
+import kotlin.random.Random
+import kotlin.test.Test
+import kotlin.test.assertTrue
+
+/**
+ * The consumer-shaped path for packed ternary weights (#1136): `ops.matmul(x, ops.transpose(W))`
+ * — what every dense-layer `linearProject` does — must route a `[out, in]` packed ternary weight
+ * through the Wᵀ marker into `KernelDispatch`, never through a dense decode-copy transpose.
+ *
+ * Before `isHeapPackedWeight` was broadened from the hardcoded Q-format list to
+ * `PackedBlockStorage`, `transpose` dense-copied these tensors through their decoding `get()` —
+ * which returns ternary CODES, not values — and threw `ClassCastException` (Byte → Float) on the
+ * JVM. The oracle here is the decoded matmul.
+ */
+@OptIn(ExperimentalMemoryApi::class)
+class TernaryWeightTransposeDispatchTest {
+
+    private val ctx = DirectCpuExecutionContext()
+
+    private fun ternaryValues(count: Int, seed: Int): FloatArray {
+        val rng = Random(seed)
+        return FloatArray(count) { (rng.nextInt(3) - 1) * 0.25f }
+    }
+
+    private fun assertMatmulTransposedMatchesDecode(
+        n: Int,
+        k: Int,
+        weightData: sk.ainet.lang.tensor.data.TensorData<FP32, Float>,
+        decoded: FloatArray,
+        seed: Int,
+        tol: Float,
+    ) {
+        val w = ctx.fromData(weightData, FP32::class)
+        val rng = Random(seed)
+        val x = ctx.fromFloatArray<FP32, Float>(Shape(1, k), FP32::class, FloatArray(k) { rng.nextFloat() - 0.5f })
+
+        val out = ctx.ops.matmul(x, ctx.ops.transpose(w))
+
+        for (o in 0 until n) {
+            var want = 0f
+            for (i in 0 until k) want += x.data.get(0, i) * decoded[o * k + i]
+            val got = out.data.get(0, o)
+            assertTrue(
+                abs(got - want) <= tol * maxOf(1f, abs(want)),
+                "[$o]: matmul(x, transpose(W))=$got decoded-matmul=$want",
+            )
+        }
+    }
+
+    @Test
+    fun bitNetB158WeightDispatchesThroughTheTransposeMarker() {
+        val n = 5; val k = 32
+        val values = ternaryValues(n * k, seed = 3)
+        val data = BitNetB158TensorData.fromFloats(Shape(n, k), values)
+        val decoded = TernaryCodec.decodeBitNet(data.packedData, n * k)
+        @Suppress("UNCHECKED_CAST")
+        assertMatmulTransposedMatchesDecode(
+            n, k, data as sk.ainet.lang.tensor.data.TensorData<FP32, Float>, decoded, seed = 7, tol = 1e-4f,
+        )
+    }
+
+    @Test
+    fun bitNetPlanesWeightDispatchesThroughTheTransposeMarker() {
+        val n = 4; val k = 32
+        val rng = Random(11)
+        val values = FloatArray(n * k) { (rng.nextFloat() - 0.5f) * 2f }
+        val data = BitNetPlanesTensorData.fromFloats(Shape(n, k), values)
+        val decoded = TernaryCodec.decodeBitNetPlanes(data.packedData, n, k)
+        @Suppress("UNCHECKED_CAST")
+        assertMatmulTransposedMatchesDecode(
+            n, k, data as sk.ainet.lang.tensor.data.TensorData<FP32, Float>, decoded, seed = 13, tol = 1e-3f,
+        )
+    }
+}