ocaml: phase 5.1 magic_square.ml baseline (5x5 Siamese, diag sum = 65)

Siamese construction for odd-order magic squares:

  - place 1 at (0, n/2)
  - for k = 2..n^2, move up-right with (x-1+n) mod n wrap
  - if the target cell is taken, drop down one row instead

  for n=5, magic constant = n*(n^2+1)/2 = 5*26/2 = 65

Returns the main-diagonal sum (65 by construction).

Tests 2D array via Array.init + Array.make, mod arithmetic with
the (x-1+n) mod n idiom for negative-safe wrap, nested begin/end
branches inside for-loop body.

166 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -81,6 +81,7 @@
   "lis.ml": 6,
   "list_ops.ml": 30,
   "luhn.ml": 2,
+  "magic_square.ml": 65,
   "mat_mul.ml": 621,
   "matrix_power.ml": 832040,
   "max_path_tree.ml": 11,

lib/ocaml/baseline/magic_square.ml

@@ -0,0 +1,27 @@
+let n = 5
+
+let make_magic () =
+  let m = Array.init n (fun _ -> Array.make n 0) in
+  let row = ref 0 in
+  let col = ref (n / 2) in
+  for k = 1 to n * n do
+    m.(!row).(!col) <- k;
+    let nr = (!row - 1 + n) mod n in
+    let nc = (!col + 1) mod n in
+    if m.(nr).(nc) <> 0 then begin
+      row := (!row + 1) mod n
+    end else begin
+      row := nr;
+      col := nc
+    end
+  done;
+  m
+
+;;
+
+let m = make_magic () in
+let sum_diag = ref 0 in
+for i = 0 to n - 1 do
+  sum_diag := !sum_diag + m.(i).(i)
+done;
+!sum_diag

plans/ocaml-on-sx.md

@@ -407,6 +407,15 @@ _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 — magic_square.ml baseline (5×5 Siamese
+  construction → main-diagonal sum 65, the magic constant for n=5).
+  Place k=1 at (0, n/2); for each next k, move up-right with wrap-
+  around; if that cell is taken, move down one row instead.
+  Magic constant for an n×n square is n(n²+1)/2 = 5·26/2 = 65.
+  Tests 2D array via Array.init + Array.make, mod arithmetic with
+  the `(x - 1 + n) mod n` idiom for negative-safe wrap, nested
+  begin/end branches inside for-loop body. 166 baseline programs
+  total.
 - 2026-05-10 Phase 5.1 — matrix_power.ml baseline (Fibonacci via
   2×2 matrix fast exponentiation, F(30) = 832040). [[1,1],[1,0]]^n
   has Fibonacci numbers in the top row; recursive O(log n) power