diff --git a/lib/ocaml/baseline/binary_heap.ml b/lib/ocaml/baseline/binary_heap.ml
new file mode 100644
index 00000000..108d8ca5
--- /dev/null
+++ b/lib/ocaml/baseline/binary_heap.ml
@@ -0,0 +1,47 @@
+let parent i = (i - 1) / 2
+let lchild i = 2 * i + 1
+let rchild i = 2 * i + 2
+
+let swap a i j =
+  let t = a.(i) in
+  a.(i) <- a.(j);
+  a.(j) <- t
+
+let rec sift_up a i =
+  if i > 0 && a.(parent i) > a.(i) then begin
+    swap a i (parent i);
+    sift_up a (parent i)
+  end
+
+let rec sift_down a n i =
+  let l = lchild i and r = rchild i in
+  let smallest = ref i in
+  if l < n && a.(l) < a.(!smallest) then smallest := l;
+  if r < n && a.(r) < a.(!smallest) then smallest := r;
+  if !smallest <> i then begin
+    swap a i !smallest;
+    sift_down a n !smallest
+  end
+
+let push a size x =
+  a.(!size) <- x;
+  size := !size + 1;
+  sift_up a (!size - 1)
+
+let pop a size =
+  let m = a.(0) in
+  size := !size - 1;
+  a.(0) <- a.(!size);
+  sift_down a !size 0;
+  m
+
+;;
+
+let a = Array.make 20 0 in
+let s = ref 0 in
+List.iter (fun x -> push a s x) [9; 4; 7; 1; 8; 3; 5; 2; 6];
+let total = ref 0 in
+for _ = 1 to 9 do
+  total := !total * 10 + pop a s
+done;
+!total
diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 6b361776..d521d489 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/lib/ocaml/baseline/expected.json
@@ -11,6 +11,7 @@
   "bf_full.ml": 6,
   "bisect.ml": 141,
   "bigint_add.ml": 28,
+  "binary_heap.ml": 123456789,
   "bits.ml": 21,
   "balance.ml": 3,
   "base_n.ml": 17,
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index 97c7934e..ee42b769 100644
--- a/plans/ocaml-on-sx.md
+++ b/plans/ocaml-on-sx.md
@@ -407,6 +407,14 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-10 Phase 5.1 — binary_heap.ml baseline (array-backed
+  binary min-heap, push 9 random values then pop in sorted order
+  → digits concat to 123456789). Standard heap mechanics: parent
+  /lchild/rchild index arithmetic, sift-up after push, sift-down
+  after pop. Push [9;4;7;1;8;3;5;2;6], pop returns 1..9 in order;
+  fold-as-decimal yields 123456789. Tests recursive sift_up /
+  sift_down, ref-tracked external size, in-place array swap,
+  combined push/pop with mutable closure. 152 baseline programs total.
 - 2026-05-10 Phase 5.1 — rolling_hash.ml baseline (Rabin-Karp
   rolling hash for substring matching, count "abc" in
   "abcabcabcabcabcabc" = 6). Polynomial hash mod 1000003 with