trureturingGitHub MATHEMATICAL ATLAS

StatisticalMechanics / CONCEPT

Divisibility of the rectangular sandpile limit

The direct limit of the rectangular sandpile groups with Shkolnikov's signed reflected tiling maps is divisible: every element has a multiple-root at a later rectangular stage.

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THEOREM

Divisibility theorem

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The quarter-turn boundary recurrenceThe quarter-turn boundaryrecurrenceDivisibility of the rectangular sandpile limitDivisibility of the rectangularsandpile limit
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Lean sourceResearch workspace
Status
Closed
Depth
2
Layer
D5/S3
Domain
StatisticalMechanics
Node ID
D5/S3/StatisticalMechanics/Sandpiles/ShkolnikovSandpileLimitDivisible
Repository path
D5/S3/StatisticalMechanics/Sandpiles/ShkolnikovSandpileLimitDivisible.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.