Misunderstanding section 2.7 of Wolfram physics project?

Questions
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1

(Edit - removing the bold accusation that this was a typo - but leaving the core of the question as it had me stumped and the answer below is worth thinking about)

Sorry if this is the wrong place to post this but I think (i.e. just a smidge over 50% sure) there might be a typo on the Physics Project docs - section 2.7

specifically in the second panel, when I work it through I get this pattern:

EVphOZ-VAAMtfq1.jpg
EVphOZ-VAAMtfq1.jpg964×527 35.2 KB

2

seem to be similar issues throughout the page - maybe just y and z got switched somewhere (or I’m being dense…)

3

i think maybe this was the intended rule:

EVpoNBCUwAMb9WX.jpg
EVpoNBCUwAMb9WX.jpg680×543 28.9 KB

4

Keep in mind, evolution is not unique (as this is not a causal invariant rule):

Specifically, in the default evolution order, we get the result from the paper:

In\[\] := WolframModel[{{x, y}, {x, z}} -> {{z, w}, {y, w}, {x, w}, {x, 
     y}}, {{1, 2}, {1, 3}}, <|"MaxEvents" -> 2|>]["StatesPlotsList", 
 VertexLabels -> Automatic]

AutomaticOrdering.png
AutomaticOrdering.png1241×334 22.4 KB

If, however, we use a different event ordering function, we get the evolution you found:

In\[\] := WolframModel[{{x, y}, {x, z}} -> {{z, w}, {y, w}, {x, w}, {x, 
     y}}, {{1, 2}, {1, 3}}, <|"MaxEvents" -> 2|>, 
  "EventOrderingFunction" -> "ReverseRuleOrdering"]["StatesPlotsList",
  VertexLabels -> Automatic]

ReverseRuleOrdering.png
ReverseRuleOrdering.png1241×216 17.9 KB

You can use MultiwaySystem to find these two are the only possibilities for the first two steps (up to isomorphisms):

In\[\] := ResourceFunction["MultiwaySystem"][
  "WolframModel" -> {{{x, y}, {x, z}} -> {{z, w}, {y, w}, {x, w}, {x, 
       y}}}, {{{1, 2}, {1, 3}}}, 2, "StatesGraph", 
  VertexSize -> 1.3] // LayeredGraphPlot

MultiwaySystem.png
MultiwaySystem.png615×864 18.7 KB

5

This helps make a lot of sense of it - thanks!

I need to think some more about rule-ordering perhaps

6

This sketch helped me make sense of it:

image.png
image.png1001×464 30.9 KB

7

To me this implies that the rule as presented is not a well defined function without designating the ordering used. Are evolution rules not supposed to be functions? Maybe i should try reading the paper and not the website technical introduction?

8

Yes, rules are not functions, that is, they are not necessarily deterministic. I’m not sure which papers you are referring to, but, maybe, the docs on event ordering and selection could be helpful.

9

I think you’re right. It’s looking like I just need to keep reading more sections, because this is addressed already. Thanks for the reply!