ocaml: phase 5.1 count_inversions.ml baseline (12 inversions via merge sort)

Modified merge sort that counts inversions during the merge step:
when an element from the right half is selected, the remaining
elements of the left half (mid - i + 1) all form inversions with
that right element.

  count_inv [|8; 4; 2; 1; 3; 5; 7; 6|] = 12

Inversions of [8;4;2;1;3;5;7;6]:
  with 8: (8,4)(8,2)(8,1)(8,3)(8,5)(8,7)(8,6) = 7
  with 4: (4,2)(4,1)(4,3) = 3
  with 2: (2,1) = 1
  with 7: (7,6) = 1
                                        total = 12

Tests: let rec ... and ... mutual recursion, while + ref + array
mutation, in-place sort with auxiliary scratch array.

145 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.
+- 2026-05-10 Phase 5.1 — count_inversions.ml baseline (count
+  inversions of [|8;4;2;1;3;5;7;6|] = 12, via merge-sort). Modified
+  merge sort: when right element is taken, accumulate `mid - i + 1`
+  inversions for the remaining left half. Tests `let rec merge ...
+  and sort ...` mutually recursive bindings, complex while + ref
+  + array mutation, in-place sort with auxiliary array.
+  145 baseline programs total.
 - 2026-05-10 Phase 5.1 — topo_sort.ml baseline (Kahn's algorithm
   topological sort of a 6-node DAG → all 6 vertices ordered).
   Standard BFS approach: compute in-degrees, seed queue with zero-