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
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