diff --git a/README.md b/README.md
index e7bb74f..8c086aa 100644
--- a/README.md
+++ b/README.md
@@ -272,11 +272,11 @@ All three distance functions are **lower-is-closer**:
 
 | SQL function | Index metric | Kernel |
 |---|---|---|
-| `l2_distance(a, b)` | `L2sq` | `sqrt(sum((a_i - b_i)^2))` (UDF) / `sum((a_i - b_i)^2)` (index) |
+| `l2_distance(a, b)` | `L2sq` | `sum((a_i - b_i)^2)` |
 | `cosine_distance(a, b)` | `Cos` | `1 - dot(a,b) / (norm(a) * norm(b))` |
 | `negative_dot_product(a, b)` | `IP` | `-(a . b)` |
 
-Note: `l2_distance` UDF returns actual L2 (with sqrt) for human-readable distances; USearch uses L2sq internally (no sqrt). The sort order is identical.
+`l2_distance` returns squared L2 (no sqrt), matching USearch's `MetricKind::L2sq`. This ensures numeric consistency between the UDF, the rewritten index path, and the brute-force path.
 
 ### Running tests
 
diff --git a/src/lib.rs b/src/lib.rs
index 538752d..5aee261 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -93,7 +93,7 @@ use datafusion::prelude::SessionContext;
 /// Register all extension components with a DataFusion [`SessionContext`].
 ///
 /// Registers:
-/// - `l2_distance(col, query)`          — Euclidean distance (L2)
+/// - `l2_distance(col, query)`          — squared Euclidean distance (L2sq)
 /// - `cosine_distance(col, query)`      — cosine distance
 /// - `negative_dot_product(col, query)` — negated inner product
 /// - `vector_usearch(table, query, k)`  — explicit ANN table function
diff --git a/src/udf.rs b/src/udf.rs
index 226c89c..233fcc1 100644
--- a/src/udf.rs
+++ b/src/udf.rs
@@ -22,12 +22,13 @@ use datafusion::scalar::ScalarValue;
 
 type Kernel = fn(&[f32], &[f32]) -> f32;
 
+// Returns L2sq (no sqrt) — matches USearch MetricKind::L2sq and keeps numeric
+// values consistent between the UDF path and the optimizer-rewritten index path.
 fn l2_kernel(a: &[f32], b: &[f32]) -> f32 {
     a.iter()
         .zip(b.iter())
         .map(|(x, y)| (x - y) * (x - y))
         .sum::<f32>()
-        .sqrt()
 }
 
 fn cosine_kernel(a: &[f32], b: &[f32]) -> f32 {
diff --git a/tests/execution.rs b/tests/execution.rs
index 8d6c5e8..542b5fe 100644
--- a/tests/execution.rs
+++ b/tests/execution.rs
@@ -19,7 +19,7 @@
 use std::sync::Arc;
 
 use arrow_array::builder::{FixedSizeListBuilder, Float32Builder};
-use arrow_array::{FixedSizeListArray, RecordBatch, StringArray, UInt64Array};
+use arrow_array::{FixedSizeListArray, Float32Array, RecordBatch, StringArray, UInt64Array};
 use arrow_schema::{DataType, Field, Schema};
 use datafusion::execution::session_state::SessionStateBuilder;
 use datafusion::prelude::SessionContext;
@@ -453,3 +453,60 @@ async fn exec_parquet_native_where_no_matches() {
     let ids = collect_ids(&ctx, &sql).await;
     assert!(ids.is_empty(), "no rows should match; got {ids:?}");
 }
+
+// ═══════════════════════════════════════════════════════════════════════════════
+// Numeric regression — l2_distance must return L2sq (no sqrt)
+// ═══════════════════════════════════════════════════════════════════════════════
+
+/// l2_distance must return squared L2, not actual L2.
+/// Row 1 = [1,0,0,0], query = [1,0,0,0] → L2sq = 0.0
+/// Row 2 = [0,1,0,0], query = [1,0,0,0] → L2sq = 2.0 (L2 would be ~1.414)
+#[tokio::test]
+async fn exec_l2_distance_returns_l2sq() {
+    let ctx = make_exec_ctx("items::vector").await;
+    let sql =
+        format!("SELECT id, l2_distance(vector, {Q}) AS dist FROM items ORDER BY dist ASC LIMIT 4");
+    let df = ctx.sql(&sql).await.expect("sql");
+    let batches = df.collect().await.expect("collect");
+
+    let mut dists: Vec<(u64, f32)> = vec![];
+    for batch in &batches {
+        let id_idx = batch.schema().index_of("id").unwrap();
+        let dist_idx = batch.schema().index_of("dist").unwrap();
+        let ids = batch
+            .column(id_idx)
+            .as_any()
+            .downcast_ref::<UInt64Array>()
+            .unwrap();
+        let ds = batch
+            .column(dist_idx)
+            .as_any()
+            .downcast_ref::<Float32Array>()
+            .unwrap();
+        for i in 0..batch.num_rows() {
+            dists.push((ids.value(i), ds.value(i)));
+        }
+    }
+
+    // Row 1: exact match → 0.0
+    let row1 = dists
+        .iter()
+        .find(|(id, _)| *id == 1)
+        .expect("row 1 missing");
+    assert!(
+        (row1.1 - 0.0).abs() < 1e-6,
+        "row 1 distance must be 0.0 (L2sq); got {}",
+        row1.1
+    );
+
+    // Row 2: [0,1,0,0] vs [1,0,0,0] → L2sq = 2.0, NOT sqrt(2) ≈ 1.414
+    let row2 = dists
+        .iter()
+        .find(|(id, _)| *id == 2)
+        .expect("row 2 missing");
+    assert!(
+        (row2.1 - 2.0).abs() < 1e-6,
+        "row 2 distance must be 2.0 (L2sq), not {:.4} (would be ~1.414 if L2)",
+        row2.1
+    );
+}