Pith Number

pith:LSOGR5KF

pith:2026:LSOGR5KF7VSEAGFX43I7V5PQJH

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The Directed Abelian Sandpile Model on Cylinders

Abdul Quadir, Nikita Kalinin, Ram Ramaswamy

The sandpile group on a directed cylindrical lattice reduces exactly to a transverse problem.

arxiv:2605.15914 v1 · 2026-05-15 · cond-mat.stat-mech

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Claims

C1strongest claim

We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition.

C2weakest assumption

The directed cylindrical lattice with periodic transverse boundary conditions and dissipation at one boundary permits an exact reduction of the sandpile group to a purely transverse problem without residual longitudinal contributions (as invoked when applying Dhar's formulation to identify the group with the co-kernel of the reduced directed Laplacian).

C3one line summary

The sandpile group on directed cylinders reduces exactly to a transverse problem, fully determining its cyclic decomposition and linking it to the periodicity of driven dynamics.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] In particu- lar, odd and even transverse widths lead to qualitatively different algebraic structures

[2] The directed ladder [8, 9] is a special limit of the cylin- drical construction

[3] P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A38, 364 (1988) 1987

[4] C. Tang and P. Bak, Phys. Rev. Lett.60, 2347 (1988); J. Stat. Phys.51, 797 (1988) 1988

[5] D. Dhar and R. Ramaswamy, Phys. Rev. Lett.63, 1659 (1989) 1989

Receipt and verification

First computed	2026-05-20T00:01:45.048463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c9c68f545fd644018b7e6d1faf5f049c8f3c919b8283254e4ea59a3c82fd0ef

Aliases

arxiv: 2605.15914 · arxiv_version: 2605.15914v1 · doi: 10.48550/arxiv.2605.15914 · pith_short_12: LSOGR5KF7VSE · pith_short_16: LSOGR5KF7VSEAGFX · pith_short_8: LSOGR5KF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LSOGR5KF7VSEAGFX43I7V5PQJH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5c9c68f545fd644018b7e6d1faf5f049c8f3c919b8283254e4ea59a3c82fd0ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "132f81fedb17987a61a978d2d2c15e977a25ba43092149f2fadb8a8abf343d29",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-15T12:52:20Z",
    "title_canon_sha256": "177d4a162cc17f3d0550ebf23c40b7bf106fa76d49218f3dfece2226f959711d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15914",
    "kind": "arxiv",
    "version": 1
  }
}