diff --git a/crates/bgz-tensor/tests/palette_multihop_error_probe.rs b/crates/bgz-tensor/tests/palette_multihop_error_probe.rs
new file mode 100644
index 000000000..ec7a6da51
--- /dev/null
+++ b/crates/bgz-tensor/tests/palette_multihop_error_probe.rs
@@ -0,0 +1,46 @@
+//! Quantized XOR composition is exact only when the frozen codebook is closed.
+//! A table lookup does not itself assert correctness of a multi-hop inference.
+use bgz_tensor::{Base17, ComposeTable, WeightPalette};
+
+fn value(n: i16) -> Base17 {
+    let mut dims = [0i16; 17];
+    dims[0] = n;
+    Base17 { dims }
+}
+
+fn frozen(values: &[i16]) -> WeightPalette {
+    WeightPalette {
+        entries: values.iter().copied().map(value).collect(),
+        radii: vec![0; values.len()],
+        counts: vec![1; values.len()],
+    }
+}
+
+#[test]
+fn closed_codebook_64_hops_are_exact_and_leave_frame_unchanged() {
+    let palette = frozen(&[0, 1]);
+    let snapshot = palette.entries.clone();
+    let table = ComposeTable::build(&palette);
+    let mut got = 0u8;
+    let mut exact = value(0);
+    for hop in 1..=64 {
+        let input = if hop % 2 == 0 { 0 } else { 1 };
+        got = table.compose(got, input);
+        exact = exact.xor_bind(&palette.entries[input as usize]);
+        assert_eq!(palette.entries[got as usize], exact, "hop {hop}");
+    }
+    assert_eq!(palette.entries, snapshot);
+}
+
+#[test]
+fn immutable_but_nonclosed_codebook_has_a_three_hop_counterexample() {
+    let palette = frozen(&[0, 1, 2]); // 1 XOR 2 = 3 is not in the codebook
+    let table = ComposeTable::build(&palette);
+    let direct = value(1).xor_bind(&value(2)).xor_bind(&value(2));
+    assert_eq!(direct, value(1)); // XOR is associative and self-inverse
+    let first = table.compose(1, 2); // missing 3 snaps to nearest 2
+    assert_eq!(first, 2);
+    let quantized = table.compose(first, 2); // then 2 XOR 2 returns 0
+    assert_eq!(quantized, 0);
+    assert_ne!(palette.entries[quantized as usize], direct);
+}