ocaml: phase 5.1 euler14.ml baseline (longest Collatz under 100, starting n = 97)

collatz_len walks n through n/2 if even, 3n+1 if odd, counting
steps. Outer loop scans 2..N tracking the best length and arg-best:

  let euler14 limit =
    let best = ref 0 in
    let best_n = ref 0 in
    for n = 2 to limit do
      let l = collatz_len n in
      if l > !best then begin
        best := l;
        best_n := n
      end
    done;
    !best_n

  euler14 100 = 97   (97 generates a 118-step chain)

Real PE14 uses limit = 1_000_000 (answer 837799); 100 exercises the
same algorithm in <2 minutes on our contended host.

116 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _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 — euler14.ml baseline (longest Collatz chain
+  starting under N=100 → 97). collatz_len walks n through the
+  iteration n/2 if even, 3n+1 if odd, counting steps. Outer loop
+  scans 2..N tracking best length and arg-best. n=97 generates the
+  118-step chain. Real PE14 uses N=1,000,000 (answer 837799); N=100
+  exercises the same algorithm in <2 minutes. 116 baseline programs
+  total.
 - 2026-05-09 Phase 5.1 — euler16.ml baseline (digit sum of 2^15 =
   26). Computes 2^n via for-loop accumulation, then walks the digits
   via mod 10 / div 10 to sum them. Real PE16 asks for 2^1000 which