bibkey: shkolnikov2025sandpilelimits
authors: Mikhail Shkolnikov
year: 2025
title: "Algebraic Limits of Sandpiles"
doi: 10.48550/arXiv.2506.09912
url: https://arxiv.org/abs/2506.09912v3
claim: "Section 3 states that the direct limit of rectangular sandpile groups is expected to be a rational subtorus or a divisible group."
strata_touched:
  - D5/S3/StatisticalMechanics/Sandpiles/ShkolnikovSandpileLimitDivisible
license: citation-only
triage: anchor

Shkolnikov, Algebraic Limits of Sandpiles

Mikhail Shkolnikov’s paper studies sandpile groups of rectangular domains in the square lattice. In Section 3 it defines the signed reflected tiling monomorphisms between rectangles and states:

“one may expect that it is a rational subtorus or a divisible group”

The formalized settlement proves the divisible-group alternative for the direct limit by lifting the first harmonic row to a finite-denominator subgroup and using periodicity of the reversible row recurrence. The full image question and the rational-subtorus alternative remain open.

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DOI: https://doi.org/10.48550/arXiv.2506.09912

Source: https://arxiv.org/abs/2506.09912v3