ocaml: phase 5.1 matrix_power.ml baseline (F(30) = 832040 via 2x2 matrix pow)

Fibonacci via repeated-squaring matrix exponentiation:

  [[1, 1], [1, 0]] ^ n = [[F(n+1), F(n)], [F(n), F(n-1)]]

Recursive O(log n) power:

  let rec mpow m n =
    if n = 0 then identity
    else if n mod 2 = 0 then let h = mpow m (n / 2) in mul h h
    else mul m (mpow m (n - 1))

Returns the .b cell after raising to the 30th power -> 832040 = F(30).

Tests record literal construction inside recursive function returns,
record field access (x.a etc), and pure integer arithmetic in the
matrix multiply.

165 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -82,6 +82,7 @@
   "list_ops.ml": 30,
   "luhn.ml": 2,
   "mat_mul.ml": 621,
+  "matrix_power.ml": 832040,
   "max_path_tree.ml": 11,
   "max_product3.ml": 300,
   "max_run.ml": 5,

lib/ocaml/baseline/matrix_power.ml

@@ -0,0 +1,20 @@
+type m22 = { a : int; b : int; c : int; d : int }
+
+let mul x y =
+  { a = x.a * y.a + x.b * y.c;
+    b = x.a * y.b + x.b * y.d;
+    c = x.c * y.a + x.d * y.c;
+    d = x.c * y.b + x.d * y.d }
+
+let rec mpow m n =
+  if n = 0 then { a = 1; b = 0; c = 0; d = 1 }
+  else if n mod 2 = 0 then
+    let h = mpow m (n / 2) in mul h h
+  else
+    mul m (mpow m (n - 1))
+
+;;
+
+let fib_matrix = { a = 1; b = 1; c = 1; d = 0 } in
+let r = mpow fib_matrix 30 in
+r.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 — 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
+  via repeated squaring on even n, multiply by base on odd n.
+  Records `{a; b; c; d}` standing in for matrix entries. F(30) =
+  832040 matches the closed form. Tests record literal construction
+  inside recursive function returns, record field access (x.a etc),
+  arithmetic on integers (no float). 165 baseline programs total.
 - 2026-05-10 Phase 5.1 — bipartite.ml baseline (BFS 2-coloring on
   7-node cycle-rich graph → bipartite with 4 vertices in color 0).
   Edges: 0-1, 0-3, 1-2, 1-4, 2-5, 3-4, 3-6, 5-6. This forms a