diff --git a/include/rabitqlib/quantization/rabitq_impl.hpp b/include/rabitqlib/quantization/rabitq_impl.hpp
index a59a698..bd05ee3 100644
--- a/include/rabitqlib/quantization/rabitq_impl.hpp
+++ b/include/rabitqlib/quantization/rabitq_impl.hpp
@@ -434,10 +434,10 @@ inline T ex_bits_code(
         ipnorm_inv = quantize_ex(abs_res.data(), ex_code, dim, ex_bits);
     }
 
-    // revert codes for negative dims
+    // Revert codes for negative or zero dims
     int32_t mask = (1 << ex_bits) - 1;
     for (size_t j = 0; j < dim; ++j) {
-        if (res_arr.data()[j] < 0) {
+        if (res_arr.data()[j] <= 0) {
             TP tmp = ex_code[j];
             ex_code[j] = (~tmp) & mask;
         }
diff --git a/tests/unit/rabitqlib/quantization/rabitq_test.cpp b/tests/unit/rabitqlib/quantization/rabitq_test.cpp
index 22231be..f8103a4 100644
--- a/tests/unit/rabitqlib/quantization/rabitq_test.cpp
+++ b/tests/unit/rabitqlib/quantization/rabitq_test.cpp
@@ -6,6 +6,7 @@
 #include <cmath>
 #include <cstdint>
 #include <limits>
+#include <string>
 
 namespace rabitqlib::quant {
 namespace {
@@ -92,5 +93,80 @@ TEST(RabitqOneBitTest, FullQuantizationInitializesCodesAndFactors) {
     EXPECT_TRUE(std::isfinite(f_error));
 }
 
+// An exactly-zero residual coordinate must be encoded consistently by both halves of
+// the split code. one_bit_code() uses (residual > 0) and so calls zero negative; if
+// ex_bits_code() calls it positive, the assembled code lands 2^ex_bits away from where
+// the factors assume it is. The <c*xu_cb, r> == ||r||^2 invariant cannot see this,
+// because a zero coordinate contributes nothing to that inner product.
+TEST(RabitqSignConventionTest, ZeroResidualCoordinateGetsSmallestMagnitudeCode) {
+    constexpr size_t kDim = 64;
+    constexpr size_t kTotalBits = 8;
+    constexpr size_t kExBits = kTotalBits - 1;
+
+    std::array<float, kDim> data{};
+    for (size_t i = 0; i < kDim; ++i) {
+        data[i] = static_cast<float>(i % 7) - 3.0F;  // zero at i % 7 == 3
+    }
+
+    std::array<uint8_t, kDim> code{};
+    float f_add = 0;
+    float f_rescale = 0;
+    float f_error = 0;
+    quantize_full_single(
+        data.data(), kDim, kTotalBits, code.data(), f_add, f_rescale, f_error
+    );
+
+    // centered code is code + cb, cb = -(2^total_bits - 1)/2
+    const float cb = -((1 << kExBits) - 0.5F);
+    size_t n_zero = 0;
+    for (size_t i = 0; i < kDim; ++i) {
+        if (data[i] != 0.0F) {
+            continue;
+        }
+        ++n_zero;
+        EXPECT_FLOAT_EQ(static_cast<float>(code[i]) + cb, -0.5F)
+            << "zero residual at dim " << i << " encoded as " << +code[i];
+    }
+    ASSERT_GT(n_zero, 0U) << "test vector must contain exact zeros";
+}
+
+TEST(RabitqSignConventionTest, ZeroResidualDoesNotInflateReconstructionNorm) {
+    constexpr size_t kDim = 64;
+    constexpr size_t kTotalBits = 8;
+    constexpr size_t kExBits = kTotalBits - 1;
+
+    std::array<float, kDim> data{};
+    for (size_t i = 0; i < kDim; ++i) {
+        data[i] = static_cast<float>((i * 37) % 23) - 11.0F;  // zeros at rem 11
+    }
+
+    std::array<uint8_t, kDim> code{};
+    float f_add = 0;
+    float f_rescale = 0;
+    float f_error = 0;
+    quantize_full_single(
+        data.data(), kDim, kTotalBits, code.data(), f_add, f_rescale, f_error
+    );
+
+    const double cb = -((1 << kExBits) - 0.5);
+    const double c = f_rescale / -2.0;
+    double nsq = 0;
+    double qq = 0;
+    size_t n_zero = 0;
+    for (size_t i = 0; i < kDim; ++i) {
+        const double q = static_cast<double>(code[i]) + cb;
+        nsq += static_cast<double>(data[i]) * data[i];
+        qq += q * q;
+        n_zero += (data[i] == 0.0F);
+    }
+    ASSERT_GT(n_zero, 0U) << "test vector must contain exact zeros";
+
+    // ||c*xu_cb||^2 / ||r||^2 - 1 == tan^2 of the angle between the residual and its
+    // reconstruction. A mismatched sign convention inflates this by orders of magnitude.
+    const double tan_sq = ((c * c * qq) / nsq) - 1.0;
+    EXPECT_LT(tan_sq, 1e-3) << "reconstruction norm inflated, tan^2 = "
+                            << std::to_string(tan_sq);
+}
+
 }  // namespace
 }  // namespace rabitqlib::quant