What is the meaning of light cones in MM space?

Things that can be proved equal symbolically
Incompleteness: causally disconnected parts of the MM universe
(If have to consider paths of infinite length, potentially cannot ever reach them with a finite number of added axioms)

Accumulation of theorems: relation to causal connections?

In[]:=
With[{g=ResourceFunction["MultiwaySystem"][{"A""AB","BB""A"},{"A"},5,"EvolutionCausalGraph"]},HighlightGraph[g,Subgraph[g,PathGraph[FindShortestPath[g,"A","ABBA"]]]]]
Out[]=
In[]:=
With[{g=ResourceFunction["MultiwaySystem"][{"A""AB","BB""A"},{"A"},5,"EvolutionEventsGraph"]},HighlightGraph[g,Subgraph[g,PathGraph[FindShortestPath[g,"A","ABBA"]]]]]
Out[]=
In[]:=
LayeredGraphPlot[With[{g=ResourceFunction["MultiwaySystem"][{"A""AB","BB""A"},{"A"},7,"EvolutionCausalGraphStructure"]},HighlightGraph[g,Style[Subgraph[g,PathGraph[FindShortestPath[g,"A","ABAA"]]],Red,Thick]]],AspectRatio1/2]
Out[]=
In[]:=
LayeredGraphPlot[With[{g=ResourceFunction["MultiwaySystem"][{"B""ABA","AA""B","BB""A"},{"B"},7,"EvolutionCausalGraphStructure"]},HighlightGraph[g,Style[Subgraph[g,PathGraph[FindShortestPath[g,"B","BAB"]]],Red,Thick]]],AspectRatio1/2]
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In[]:=
FindShortestPath[ResourceFunction["MultiwaySystem"][{"B""ABA","AA""B","BB""A"},{"B"},7,"EvolutionCausalGraphStructure"],"B","BAB"]
Out[]=
{B,{BABA,B,{,}},{AAB,AA,{,AB}},BAB}

What is the meaning of dimension/growth rate in MM space?

Branchial graph

Known relationships in mathematics at a given time..... [at least for 2-way edges]

Causal invariance

In a branch pair .... are the two branches “equal” ?
{xa,xb},{ay,by}
Is the key axiom that then a is equal to b? [Cinv  any branch pair is equal .... i.e. that connected parts of the branchial graph are equal]
[[[ Euclid: Things that are equal to the same thing are also equal to one another (the Transitive property of a Euclidean relation) ]]]
​

Euclid

[[ partly copied from MM...-11.nb ]]
In[]:=
ResourceObject["Theorem Network from Euclid's Elements"]
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ResourceObject
Name: Theorem Network from Euclid's Elements
»
Type: DataResource
Description: A graph of the theorems from Euclid's Elements and their logical dependencies
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In[]:=
euclid=ResourceData["Theorem Network from Euclid's Elements"]
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Dimensions

Statistics etc.

Dependence on continuity of space....

Longest path

Platonic solids

Entity Version