Function[n,

NestGraph[n{2n,n+1},0,11]

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NestGraph[n{2n,n+1,n/2,n-1},1,3,VertexLabelsAutomatic]

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NestGraph[n{n+1,n-1},1,3,VertexLabelsAutomatic]

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NestGraph[n{n+1,n-1,n+5,n-5},1,3,VertexLabelsAutomatic]

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NestGraph[n{n+1,n-1,n+5,n-5},1,6]

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Graph3D[%]

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NestGraph[n{n+4,n-4,n+7,n-7},1,10]

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Graph3D[%]

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NestGraph[n{n+4,n+7},0,5,VertexLabelsAutomatic]

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The grid is just commutativity

FrobeniusNumber[{4,7}]

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17

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NestGraph[n{n+4,n+7},18,7,VertexLabelsAutomatic]

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Graph[MultiwayFunctionSystem[n{n+4,n+7},0,10,"StatesGraphStructure"],VertexLabelsAutomatic]

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Graph[MultiwayFunctionSystem[n{n+2,n+3},0,10,"StatesGraphStructure","IncludeEventInstances"True,"IncludeStatePathWeights"True],VertexLabels#,ImageSize70]&/@{Automatic,"VertexWeight"}

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,

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How is the distribution of path weights determined by a and b?

Graph[MultiwayFunctionSystem[n{n+2,n+3},0,5,"StatesGraphStructure","IncludeEventInstances"True,"IncludeStatePathWeights"True],VertexLabelsPlaced[{"Name","VertexWeight"},{Top,Bottom}],ImageSize70]

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After a certain transient, every value can be reached by the iteration.

## Branch pair convergence

Branch pair convergence

#### a n+b, c n+d

a n+b, c n+d

The symbolic case will not crosslink:

#### Look at all numbers mod k

Look at all numbers mod k

A necessary condition for merging is the last step not go astray by having numbers that don’t match mod k

n = 1 mod 3 and n = 0 mod 2

### Chinese remainder estimation

Chinese remainder estimation

## Tilga’s claim

Tilga’s claim