ocaml: phase 5.1 euler25.ml baseline (first 12-digit Fibonacci index = 55)

Iteratively grows two refs while the larger is below 10^(n-1),
counting iterations:

  let euler25 n =
    let a = ref 1 in
    let b = ref 1 in
    let i = ref 2 in
    let target = ref 1 in
    for _ = 1 to n - 1 do target := !target * 10 done;
    while !b < !target do
      let c = !a + !b in
      a := !b;
      b := c;
      i := !i + 1
    done;
    !i

  euler25 12 = 55   (F(55) = 139_583_862_445, 12 digits)

Real PE25 asks for 1000 digits (answer 4782); 12 keeps within
safe-int while exercising the identical algorithm.

114 baseline programs total — 200 iterations landed.

lib/ocaml/baseline/euler25.ml

@@ -0,0 +1,17 @@
+let euler25 n =
+  let a = ref 1 in
+  let b = ref 1 in
+  let i = ref 2 in
+  let target = ref 1 in
+  for _ = 1 to n - 1 do target := !target * 10 done;
+  while !b < !target do
+    let c = !a + !b in
+    a := !b;
+    b := c;
+    i := !i + 1
+  done;
+  !i
+
+;;
+
+euler25 12

lib/ocaml/baseline/expected.json

@@ -28,6 +28,7 @@
   "euler1.ml": 233168,
   "euler10.ml": 1060,
   "euler2.ml": 4613732,
+  "euler25.ml": 55,
   "euler3.ml": 29,
   "euler4_small.ml": 9009,
   "euler5.ml": 232792560,

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _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.
+- 2026-05-09 Phase 5.1 — euler25.ml baseline (first Fibonacci index
+  with 12 digits = 55). Iteratively grows two refs while the larger
+  is below `10^(n-1)`, counting iterations. Real PE25 asks for 1000
+  digits (= 4782); 12 keeps within safe-int while exercising the
+  identical algorithm. 114 baseline programs total — and 200
+  iterations landed.
 - 2026-05-09 Phase 5.1 — euler3.ml baseline (largest prime factor of
   13195 = 29; PE3's worked example). Trial-division streaming: when
   the current factor divides m, divide and update largest; otherwise