ocaml: phase 5.1 tail_factorial.ml baseline (12! via tail-recursion = 479001600)

Single-helper tail-recursive loop threading an accumulator:

  let factorial n =
    let rec go n acc =
      if n <= 1 then acc
      else go (n - 1) (n * acc)
    in
    go n 1

  factorial 12 = 479_001_600

Companion to factorial.ml (10! = 3628800 via doubly-recursive
style); same answer-shape, different evaluator stress: this version
has constant stack depth.

130 baseline programs total — milestone.

lib/ocaml/baseline/expected.json

@@ -114,6 +114,7 @@
   "simpson_int.ml": 10000,
   "stable_unique.ml": 46,
   "subseq_check.ml": 3,
+  "tail_factorial.ml": 479001600,
   "subset_sum.ml": 8,
   "tic_tac_toe.ml": 1,
   "word_freq.ml": 8,

lib/ocaml/baseline/tail_factorial.ml

@@ -0,0 +1,10 @@
+let factorial n =
+  let rec go n acc =
+    if n <= 1 then acc
+    else go (n - 1) (n * acc)
+  in
+  go n 1
+
+;;
+
+factorial 12

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.
+- 2026-05-10 Phase 5.1 — tail_factorial.ml baseline (12! via tail
+  recursion = 479001600). Single-helper tail-recursive loop
+  threading an accumulator. Companion to factorial.ml (10! via
+  doubly-recursive style); same answer-shape, different evaluator
+  stress (tail-call optimisation if any, or pure constant stack
+  depth otherwise). 130 baseline programs total — milestone.
 - 2026-05-10 Phase 5.1 — zerosafe.ml baseline (Option-chained safe
   division, sum 10 + (-1) + (-1) + 20 = 28). safe_div returns None
   on division by zero; safe_chain stitches two divisions, propagating