In[]:=
ResourceFunction["MultiwayFunctionSystem"][n|->{n+1,2n+1},{1},5,"EvolutionEventsGraphStructure",AspectRatio->1,GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
ResourceFunction["MultiwayFunctionSystem"][n|->{n+1,2n+1},{1},5,"CausalGraphStructure",AspectRatio->1,GraphLayout->"LayeredDigraphEmbedding"]
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In[]:=
ResourceFunction["MultiwayFunctionSystem"][n|->{n+2,2n+1},{1},5,"EvolutionEventsGraphStructure",AspectRatio->1,GraphLayout->"LayeredDigraphEmbedding"]
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In[]:=
ResourceFunction["MultiwayFunctionSystem"][n|->{n+2,2n+1},{1},7,"StatesGraphStructure",AspectRatio->1,GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
ResourceFunction["MultiwayFunctionSystem"][n|->{n+1,n-1},{1},7,"StatesGraphStructure",AspectRatio->1,GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
ResourceFunction["MultiwayFunctionSystem"][n|->{n+2,n-3},{1},7,"StatesGraphStructure",AspectRatio->1,GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
Graph[ResourceFunction["MultiwaySystem"][{"A"->"BBB","BB"->"A"},"A",6,"EvolutionEventsGraph"],AspectRatio->1]
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using so far: the events we the "states" (just integers) are all considered indivisible. And this means that So the only way one state---or the update events that can be applied to it---can "causally depend" on another So what about Later on we'll see how If we explicitly show events in this case we don't see anything new:
But essentially this is because the “states” of the system---here just numbers---are effectively indivisible, and are always used in their entirety to provide the expressions to which the rule is applied.
​
But in the string multiway system we considered above, the story is different. Because here, for example,

Token Events Graph

Single history (with a maxscan)

No tokens deduplicated.....
If the tokens were collected into states, one can tell what can be deduplicated based on isomorphism

Branched code

Another branch:
Latest master branch:

With branch

This picks a “random” set of events:
Only one token on LHS, so no conflicts....
Full event set produces all combinatorially possible events (i.e. all reachable tokens)
(Map of all possible events) [For a given history, only a particular multipath will be chosen]
[[ there should be dangling events to indicate events that can happen, whose output tokens we have not yet generated ]]
To get evolution, run this as a Petri net (AKA token flow automaton) (occupancy flow automaton)
[ Place an indicator / marker / chip ... / occupancy ]

WM case

This is like lemmas ; i.e. a new collection of rules for specific tokens.... Eventually this maps out all tokens that can ever occur.
To reconstruct our experience as an observer: we must knit tokens into states ; we see what tokens exist at a given “moment” based on which ones have markers.....

Spacelike vs. branchlike

Tokens are spacelike separated.... [output tokens of a single event are spacelike separated]
Spacelike only:
[[ Includes all conceivable events, even ones not reachable from the init cond here ]]
Some pairs can’t appear together; as the markers “wash into” this structure, they can only get to certain places simultaneously....