fixed one test 3 to go

lib/til.ex

@@ -946,6 +946,7 @@ defmodule Tdd.Store do
 
   @doc """
   Updates a node's details directly. Used for knot-tying.
+  UNUSED RN
   """
   @spec update_node_in_place(
           non_neg_integer(),
@@ -1978,12 +1979,26 @@ defmodule Tdd.Compiler do
                 raise "Tdd.Compiler: Unbound type variable: #{inspect(var_name)}"
 
             {:mu, var_name, body_spec} ->
+              # Create a placeholder ID to represent the recursive reference.
               placeholder_id = Store.create_placeholder({:mu_knot_tying_for, var_name, body_spec})
+
+              # Compile the body using the placeholder in the context. The resulting TDD
+              # will have `placeholder_id` at its recursive leaves.
               new_context = Map.put(context, var_name, placeholder_id)
-              body_id = compile_normalized_spec(body_spec, new_context)
-              {:ok, body_details} = Store.get_node(body_id)
-              Store.update_node_in_place(placeholder_id, {:ok, body_details})
-              Algo.simplify(placeholder_id)
+              body_id_with_placeholder = compile_normalized_spec(body_spec, new_context)
+
+              # "Tie the knot": substitute the placeholder with the ID of the body's root.
+              # This correctly forms the cyclic TDD graph using the standard algorithm.
+              # The `substitute` function is designed for this and does not corrupt the store.
+              final_id =
+                Algo.substitute(
+                  body_id_with_placeholder,
+                  placeholder_id,
+                  body_id_with_placeholder
+                )
+
+              # The resulting graph may have new simplification opportunities after the knot is tied.
+              Algo.simplify(final_id)
 
             other_spec ->
               raw_id = do_structural_compile(other_spec, context)

test/til_test.exs

@@ -533,12 +533,6 @@ defmodule TddSystemTest do
       # list_of(integer & atom) is list_of(:none).
       # A list of :none can only be the empty list, as no element can ever exist.
       spec = {:list_of, {:intersect, [:integer, :atom]}}
-      Tdd.Store.init()
-      Debug.print_tdd_graph(Compiler.spec_to_id(spec))
-      Debug.print_tdd_graph(Compiler.spec_to_id({:literal, []}))
-
-      Process.get(:tdd_node_by_id) |> IO.inspect(label: ":tdd_node_by_id")
-      Process.get(:tdd_nodes) |> IO.inspect(label: ":tdd_nodes")
       assert_equivalent_specs(spec, {:literal, []})
     end
   end