diff --git a/tests/unit/elements/hex8_high_low_test.cpp b/tests/unit/elements/hex8_high_low_test.cpp
index 8c9bc9e..26261c3 100644
--- a/tests/unit/elements/hex8_high_low_test.cpp
+++ b/tests/unit/elements/hex8_high_low_test.cpp
@@ -142,7 +142,9 @@ TEST(Hex8HighLow, FourColumnMaterialPacketMatchesFrozenScalarBits) {
       {std::numeric_limits<double>::min()}, {maximum}, {-maximum},
       {1, tiny}, {1, -tiny}, {std::nextafter(1.0, 2.0)},
       {1, 1}, {0, tiny}, {std::numeric_limits<double>::infinity(), 0},
-      {std::numeric_limits<double>::quiet_NaN(), 0}};
+      {std::numeric_limits<double>::quiet_NaN(), 0},
+      {std::numeric_limits<double>::signaling_NaN(), 0},
+      {0, std::numeric_limits<double>::signaling_NaN()}};
   for (std::size_t first = 0; first < boundary.size(); ++first)
     for (std::size_t second = 0; second < boundary.size(); ++second) {
       MaterialPacketInput input;
@@ -230,6 +232,73 @@ TEST(Hex8HighLow, PacketSpecialLaneDoesNotChangeOtherColumns) {
     }
 }
 
+TEST(Hex8HighLow, UniformDyadicPacketsExerciseEachLowZeroShape) {
+  std::size_t checks = 0, avx2_checks = 0;
+  for (int shape = 0; shape < 4; ++shape)
+    for (int low_weight = 0; low_weight < 2; ++low_weight)
+      for (int zero_accumulator = 0; zero_accumulator < 2; ++zero_accumulator) {
+        fesa::hex8_internal::MaterialPacketInput input;
+        input.weight = {0.5, low_weight != 0 ? std::ldexp(1.0, -57) : 0.0};
+        for (std::size_t lane = 0; lane < 4; ++lane) {
+          const bool left_low = (shape & 1) != 0;
+          const bool right_low = (shape & 2) != 0;
+          // Every lane has the same normalized nonzero dyadic inputs. Component
+          // LBE sums are >= -116 and all Add intermediates are bounded by 4.
+          // Thus each Multiply low-shape is uniform and its component products
+          // bypass zero/unsupported-tail fallback. No mixed-zero Add fallback
+          // is possible; the initial zero accumulator is uniform across lanes.
+          input.deviatoric_left[lane] = {1, left_low ? std::ldexp(1.0, -54) : 0};
+          input.deviatoric_right[lane] = {2, right_low ? std::ldexp(1.0, -54) : 0};
+          input.shear_left[lane] = {0.5, left_low ? std::ldexp(1.0, -56) : 0};
+          input.shear_right[lane] = {0.25, right_low ? std::ldexp(1.0, -57) : 0};
+          input.tensor_left[lane] = {0.75, left_low ? std::ldexp(1.0, -56) : 0};
+          input.gradient_dot[lane] = {0.125, right_low ? std::ldexp(1.0, -58) : 0};
+          input.accumulated[lane] = zero_accumulator != 0 ? HighLow{}
+                                                        : HighLow{0.0625};
+        }
+        avx2_checks += ExpectFrozenMaterialPacket(input) ? 1U : 0U;
+        ++checks;
+      }
+  RecordProperty("uniform_low_shape_checks", static_cast<int>(checks));
+  RecordProperty("avx2_uniform_low_shape_checks", static_cast<int>(avx2_checks));
+}
+
+TEST(Hex8HighLow, OverflowLaneIsNeutralizedBeforeResidualFma) {
+  const auto evaluator = fesa::hex8_internal::SelectMaterialPacketEvaluator();
+  if (evaluator == fesa::hex8_internal::EvaluateMaterialPacketScalar)
+    GTEST_SKIP() << "AVX2 masked environment is not selected; routing unverified.";
+  std::fenv_t original;
+  ASSERT_EQ(std::fegetenv(&original), 0);
+  for (std::size_t bad = 0; bad < 4; ++bad) {
+    fesa::hex8_internal::MaterialPacketInput input;
+    input.weight = {0.5};
+    for (std::size_t lane = 0; lane < 4; ++lane) {
+      input.deviatoric_left[lane] = {
+          lane == bad ? std::numeric_limits<double>::max() : 1};
+      input.deviatoric_right[lane] = {2};
+      input.shear_left[lane] = {0.5};
+      input.shear_right[lane] = {0.25};
+      input.tensor_left[lane] = {0.75};
+      input.gradient_dot[lane] = {0.125};
+      input.accumulated[lane] = {0.0625};
+    }
+    // All operands are finite/nonzero and max*2 has LBE sum 972, so Product
+    // reaches its vector multiply; only the post-product finite mask rejects it.
+    const auto expected = FrozenMaterialPacket(input);
+    EXPECT_EQ(std::feclearexcept(FE_ALL_EXCEPT), 0);
+    fesa::hex8_internal::PairPacket output;
+    evaluator(input, &output);
+    const bool extra_invalid = (std::fetestexcept(FE_INVALID) & FE_INVALID) != 0;
+    EXPECT_EQ(std::fesetenv(&original), 0);
+    EXPECT_FALSE(extra_invalid);
+    for (std::size_t lane = 0; lane < 4; ++lane) {
+      EXPECT_EQ(PairBits(output[lane].high), PairBits(expected[lane].high));
+      EXPECT_EQ(PairBits(output[lane].low), PairBits(expected[lane].low));
+    }
+  }
+  RecordProperty("avx2_product_overflow_positions", 4);
+}
+
 TEST(Hex8HighLow, PacketBackendSelectionRecoversAfterEnvironmentRestoration) {
   const auto initial = fesa::hex8_internal::SelectMaterialPacketEvaluator();
   const int rounding = std::fegetround();