Inconsistent Return String from WinRecreation

I am a bit confused by why WinRecreation generates two different code sequences to capture a graph. Here are the openings to the two different sequences.

Window Ba_IBAW_plot() : Graph
	PauseUpdate; Silent 1		// building window...
	String fldrSav0= GetDataFolder(1)
	SetDataFolder root:Ba_IBAW:
	Display /W=(56,385,585,885) theta vs tau as "Plot for Ba_IBAW"
	AppendToGraph :::Ba_IBAW:Ba_IBAW_results:fitvH,:::Ba_IBAW:Ba_IBAW_results:fitpl
	SetDataFolder fldrSav0

Window Cr3O4_IBAW_plot() : Graph
	PauseUpdate; Silent 1		// building window...
	Display /W=(41,253,578,753) :Cr3O4_IBAW:theta vs :Cr3O4_IBAW:tau as "Plot for Cr3O4_IBAW"
	AppendToGraph :Cr3O4_IBAW:Cr3O4_IBAW_results:fitvH,:Cr3O4_IBAW:Cr3O4_IBAW_results:fitLa,:Cr3O4_IBAW:Cr3O4_IBAW_results:fitIs

In the first case, the recreation moves into the source folder before Display. In the second case, the Display step references the files inside their source folder from root:.

I am creating the WinRecreation string using the method below.

	SetDataFolder root:
	DoUpdate // assure that all is updated (based on current data folder setting)
	wrec = WinRecreation(rgraph,0)

What is most confusing is that I can consistently obtain the second format for WinRecreation for two different starting folders (Cr3O4_IBAW and Fe2O3_IBAW). But I always obtain the first format when I start with the Ba_IBAW folder (and even renaming it to Ba3bbb_IBAW).

Am I missing a step to force a consistent code sequence approach from WinRecreation? Is it perhaps due to appending two waves in the first case but three in the second?

IP 9.06B01 (Build 56648), macOS 15.7.4

EDIT: Yes!!! It appears to depend on how many additional waves are appended to the graph. I redid a graph from Ba_IBAW with three appended waves instead of two. The WinRecreation string became as below.

Window Ba_IBAW_plot() : Graph
	PauseUpdate; Silent 1		// building window...
	Display /W=(65,376,594,876) :Ba_IBAW:theta vs :Ba_IBAW:tau as "Plot for Ba_IBAW"
	AppendToGraph :Ba_IBAW:Ba_IBAW_results:fitvH,:Ba_IBAW:Ba_IBAW_results:fitLa,:Ba_IBAW:Ba_IBAW_results:fitIs

The question remains ... Outside of appending a dummy wave (and removing it later), can WinRecreation be forced to return a string that takes a consistent approach in referencing the waves on the graph?