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pith:T6ZUQGUE

pith:2026:T6ZUQGUE6ISRA7YKG2UIOHTSQK

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Bak--Tang--Wiesenfeld model for various topologies and ranges of interaction

K. Malarz (AGH University of Krakow), P. Szczepaniak

The avalanche size exponent in the Bak-Tang-Wiesenfeld sandpile model equals 1.208(39) regardless of lattice topology or interaction range.

arxiv:2605.15930 v1 · 2026-05-15 · cond-mat.stat-mech

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Claims

C1strongest claim

independently of the substrate topology and the range of neighborhood, the exponent that governs the power law of the probability distribution of the size of avalanches is the same and approximately equal 1.208(39)

C2weakest assumption

That a 'smartly chosen' number of deposited grains relative to the linear size of the system can be selected in a way that does not introduce selection bias or post-hoc adjustment into the measured exponent and Z-score comparison.

C3one line summary

Simulations of the BTW model confirm the avalanche size power-law exponent is approximately 1.208 independent of topology and interaction range when the number of deposited grains is scaled appropriately with system size.

References

28 extracted · 28 resolved · 1 Pith anchors

[1] Bak--Tang--Wiesenfeld model for various topologies and ranges of interaction 1929 · arXiv:2605.15930

[2] In this case, the sites with high columnsh(i) = K − 1 are separated by too long distances, and avalanches involving a lot of grains are rather rare

[3] Bak,How Nature Works (Copernicus, New York, NY, 1996) 1996

[4] A. Dmitriev, A. Lebedev, V. Kornilov, and V. Dmitriev, Self-organization of the stock exchange to the edge of a phase transition: empirical and theoretical studies, Fron- tiers in Physics12, 1508465 ( 2025

[5] J. A. Laval, Self-organized criticality of traffic flow: Implications for congestion management technologies, Transportation Research Part C: Emerging Technologies 149, 104056 (2023) 2023

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Bak--Tang--Wiesenfeld model for various topologies and ranges of interaction

Receipt and verification

First computed	2026-05-20T00:01:45.538379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fb3481a84f225107f0a36a8871e72828bbf7e6212bb1fd2e9a2fd7f0b10d430

Aliases

arxiv: 2605.15930 · arxiv_version: 2605.15930v1 · doi: 10.48550/arxiv.2605.15930 · pith_short_12: T6ZUQGUE6ISR · pith_short_16: T6ZUQGUE6ISRA7YK · pith_short_8: T6ZUQGUE

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/T6ZUQGUE6ISRA7YKG2UIOHTSQK \
  | 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: 9fb3481a84f225107f0a36a8871e72828bbf7e6212bb1fd2e9a2fd7f0b10d430

Canonical record JSON

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    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-15T13:13:11Z",
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