ocaml: phase 5.1 floyd_cycle.ml baseline (tortoise-hare, mu=0 lam=8 -> 8)

Floyd's cycle detection on a numeric function f(x) = (2x + 5) mod 17.
Three phases:

  Phase 1: advance slow/fast until collision inside the cycle
            (fast double-steps, slow single-steps)
  Phase 2: restart slow from x0; advance both by 1 until they
            meet — count is mu (length of tail before cycle)
  Phase 3: advance fast around cycle once until it meets slow
            — count is lam (cycle length)

For x0 = 1, the orbit visits 1, 7, 2, 9, 6, 0, 5, 15 then returns
to 1 — pure cycle of length 8, mu = 0, lam = 8. Encoded as
mu*100 + lam = 8.

Tests three sequential while loops sharing ref state,
double-step `fast := f (f !fast)`, meeting-condition flag.

185 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,17 @@ _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.
+- 2026-05-11 Phase 5.1 — floyd_cycle.ml baseline (Floyd's tortoise
+  -and-hare cycle detection on f(x) = (2x+5) mod 17; μ=0 λ=8 →
+  encoded 8). Three phases: (1) advance slow/fast until they
+  collide inside the cycle, (2) restart slow from x0 and advance
+  both by 1 until they meet — the count is μ (tail length),
+  (3) advance fast around the cycle once until it meets slow — the
+  count is λ (cycle length). For x0=1, f(1)=7, f(7)=2, … cycles
+  through all 8 distinct values 1,7,2,9,6,0,5,15 before returning
+  to 1, so μ=0 λ=8 → 0*100+8=8. Tests three sequential while
+  loops sharing ref state, double-step `fast := f (f !fast)`,
+  meeting-condition flag pattern. 185 baseline programs total.
 - 2026-05-11 Phase 5.1 — kth_two.ml baseline (8th smallest in
   merged [1;3;5;7;9;11;13] ∪ [2;4;6;8;10;12] = 8). Two-pointer
   merge that advances the smaller-head pointer k times. Pick rule: