In[]:=
SetDirectory[NotebookDirectory[]]
Out[]=
/Users/sw/Dropbox/Physics/WorkingMaterial/2022
In[]:=
setmm=Import["DATA/setmm-basic.wxf"];
In[]:=
metamathGraph=Graph[Flatten@KeyValueMap[{label,thm}Map[label#&,TakeWhile[Rest@thm〚-1〛,#=!=")"&]],Select[setmm["Statements"],MatchQ["Theorem"[__]]]]];
In[]:=
VertexCount[metamathGraph]
Out[]=
42127
In[]:=
ResourceFunction["WolframHausdorffDimension"][metamathGraph,#,{0,10}]&/@RandomSample[VertexList[metamathGraph],200]
Out[]=
{2.33565,2.14743,1.69817,1.91486,2.52019,2.05977,1.65271,1.97283,2.55331,2.9885,2.27604,2.01014,2.09935,1.0383,2.81428,1.79465,3.84135,2.32888,2.27892,2.25584,1.05293,2.19062,2.10762,2.06394,2.20255,1.33109,2.56022,2.83853,1.98972,2.44667,2.025,2.80266,2.60657,2.26251,2.61086,1.25245,2.03647,1.19399,2.73217,2.41485,0.877196,2.14928,1.36214,2.276,2.09078,2.004,1.22803,2.21778,2.62904,3.2271,2.20283,1.7552,1.98301,2.36577,2.39561,2.30392,1.81752,2.62354,2.60626,1.92852,0.,2.26216,2.28449,2.04059,2.22865,2.45245,2.19531,2.05246,2.0068,2.56718,1.00072,2.00902,3.27826,2.28896,1.6748,2.26312,2.93388,2.4753,2.09575,1.87273,2.13393,1.33567,2.10563,2.31424,2.44034,2.56495,2.08706,2.65452,1.6145,1.80986,2.78345,2.88674,2.03626,2.3137,3.70535,2.33329,1.81996,2.23881,1.52042,2.48705,1.95761,2.29623,0.,2.55624,2.4411,0.,1.85972,2.28396,2.09161,2.80339,2.17925,2.16432,2.18296,2.03414,2.73726,2.33927,2.1624,0.,2.08024,1.97517,2.6532,2.05791,2.18322,2.26815,2.83722,1.89049,1.68053,2.53957,2.67231,1.97533,2.52863,2.04667,1.76578,1.99879,1.88007,2.22612,0.,1.65876,2.82173,0.,2.66515,2.263,2.12222,1.7023,2.17909,1.91734,2.18625,2.25209,2.82094,1.60776,1.73358,3.27707,2.33021,2.6134,1.75212,2.30863,1.45673,1.88427,2.27396,2.67321,1.42421,2.8745,1.48899,1.64845,2.01035,1.58087,2.56537,2.00108,1.74446,1.16511,2.00833,1.75624,1.64157,2.36674,1.66198,2.08835,2.0443,1.90672,2.32819,1.98064,2.47312,2.02026,0.,2.25606,2.27624,3.78177,2.15236,0.,2.25185,0.,2.43869,2.68742,1.11652,2.76476,2.08722,2.59684,1.79086,2.10285,1.64696,2.07922}
In[]:=
Histogram[%]
Out[]=
In[]:=
ResourceFunction["WolframHausdorffDimension"][metamathGraph,#,{0,10}]&/@RandomSample[VertexList[metamathGraph],2000];
In[]:=
Histogram[%]
Out[]=
In[]:=
ResourceFunction["WolframHausdorffDimension"][metamathGraph,#,{0,20}]&/@RandomSample[VertexList[metamathGraph],1000];
In[]:=
Histogram[%]
Out[]=
In[]:=
ResourceFunction["WolframHausdorffDimension"][UndirectedGraph[metamathGraph],#,{0,10}]&/@RandomSample[VertexList[metamathGraph],500];
Out[]=
$Aborted
In[]:=
ResourceFunction["WolframHausdorffDimension"][UndirectedGraph[metamathGraph],#,{0,10}]&/@RandomSample[VertexList[metamathGraph],20];
In[]:=
Histogram[%]
Out[]=
In[]:=
ResourceFunction["WolframHausdorffDimension"][UndirectedGraph[metamathGraph],#,{0,15},"Volume","VolumeMethod"->Identity]&/@RandomSample[VertexList[metamathGraph],10]
Out[]=
{{1,50,37261,42035,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,29,34108,40804,42117,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,74,34554,41603,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,16,33642,40716,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,102,14652,41075,42114,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,43,35505,39465,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,31,35159,41891,42043,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,27,34420,41679,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,40,24699,41724,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127},{1,29,35049,41928,42123,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127,42127}}
In[]:=
ResourceFunction["WolframHausdorffDimension"][metamathGraph,#,{0,15},"Volume","VolumeMethod"->Identity]&/@RandomSample[VertexList[metamathGraph],10]
Out[]=
{{1,22,51,138,261,284,439,610,1407,1407,1407,1407,1407,1407,1407,1407},{1,41,109,212,328,1408,1408,1408,1408,1408,1408,1408,1408,1408,1408,1408},{1,39,155,363,726,2379,2379,2379,2379,2379,2379,2379,2379,2379,2379,2379},{1,23,71,369,6303,6303,6303,6303,6303,6303,6303,6303,6303,6303,6303,6303},{1,55,136,347,641,3187,3187,3187,3187,3187,3187,3187,3187,3187,3187,3187},{1,38,100,3752,3752,3752,3752,3752,3752,3752,3752,3752,3752,3752,3752,3752},{1,44,159,496,1129,5273,5273,5273,5273,5273,5273,5273,5273,5273,5273,5273},{1,29,71,138,237,240,748,748,748,748,748,748,748,748,748,748},{1,4,7,16,22,31,41,49,78,78,78,78,78,78,78,78},{1,38,120,284,2948,2948,2948,2948,2948,2948,2948,2948,2948,2948,2948,2948}}
In[]:=
ResourceFunction["WolframHausdorffDimension"][ReverseGraph[metamathGraph],#,{0,15},"Volume","VolumeMethod"->Identity]&/@RandomSample[VertexList[metamathGraph],10]
Out[]=
{{1,4,14,25,36,48,58,82,100,107,119,123,123,123,123,123},{1,13,79,179,339,451,539,593,772,772,772,772,772,772,772,772},{1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},{1,2,3,4,5,6,7,10,14,18,24,32,46,70,139,255},{1,3,5,8,9,9,9,9,9,9,9,9,9,9,9,9},{1,6,32,99,321,867,2226,2228,4003,8494,27036,27036,27036,27036,27036,27036},{1,12,22,29,37,40,42,52,52,52,52,52,52,52,52,52},{1,3,6,8,10,11,19,19,19,19,19,19,19,19,19,19},{1,18,83,165,244,297,448,448,448,448,448,448,448,448,448,448},{1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}}
What is the dimension of the entailment cone for given theorems (or axioms)?
What is the dimension of the entailment cone for given theorems (or axioms)?
Growth rate of the entailment cone for each axiom
Growth rate of the entailment cone for each axiom