In[]:=
SimpleGraph

Out[]=
In[]:=
ResourceFunction["TuringMachineCausalGraph"][2506,{1,{{},0}},30]
Out[]=
In[]:=
Graph[%,GraphLayout"SpringElectricalEmbedding"]
Out[]=
In[]:=
Graph[ResourceFunction["TuringMachineCausalGraph"][2506,{1,{{},0}},100],GraphLayout"SpringElectricalEmbedding"]
Out[]=
In[]:=
ResourceFunction["LogDifferences"][ResourceFunction["RaggedMeanAround"][Values@ResourceFunction["GraphNeighborhoodVolumes"][ResourceFunction["TuringMachineCausalGraph"][2506,{1,{{},0}},100]]]]
Out[]=
{1.491
±
0.020
,1.87
±
0.07
,1.87
±
0.14
,1.78
±
0.22
,1.66
±
0.31
,1.6
±
0.4
,1.4
±
0.5
,1.3
±
0.6
,1.2
±
0.7
,1.0
±
0.8
,0.9
±
0.9
,0.9
±
0.9
,0.6
±
1.1
,0.1
±
1.2
,-0.8
±
1.6
,-2.1
±
2.1
,-3.1
±
3.1
,-5.
±
5.
,-8.
±
4.
}
In[]:=
ListLinePlot[%,PlotRange{0,2}]
Out[]=
In[]:=
CausalDiamondDimensionEstimator[causalGraph_Graph,startVertex_,endVertex_]:=Module[{causalDiamond,d},causalDiamond=TransitiveClosureGraph[Subgraph[causalGraph,Intersection[VertexInComponent[causalGraph,endVertex],VertexOutComponent[causalGraph,startVertex]]]];​​If[EmptyGraphQ[causalDiamond],Infinity,Replace[d,FindRoot[{EdgeCount[causalDiamond]/((VertexCount[causalDiamond])^2)(Gamma[d+1]*Gamma[d/2])/(4Gamma[3d/2])},{d,1,0,Infinity}]]]]
In[]:=
With[{ag=ResourceFunction["TuringMachineCausalGraph"][2506,{1,{{},0}},30]},CausalDiamondDimensionEstimator[ag,First[VertexList[ag]],Last[VertexList[ag]]]]
Out[]=
1.05293
In[]:=
With[{ag=ResourceFunction["TuringMachineCausalGraph"][2506,{1,{{},0}},30]},CausalDiamondDimensionEstimator[ag,Echo@First[VertexList[ag]],Echo@Last[VertexList[ag]]]]
All these events are timelike separated....

Causal Graphs

What de-duplication is appropriate?

[Observer is local in branchial space?]

Branchlike fusion (cf. spacelike fusion with eyes)

[ fusion in the case of ants.... ]

MWTM universality

A given state entrains other states that are near it in branchial space....
Motion of head in physical space....
[branchial coordinate is an additional “state variable”]

s=1 DTM

Initial conditions