Pith Number

pith:6YCVM5Z7

pith:2025:6YCVM5Z7WTI2O6GKYCUIINAVQ4

not attested not anchored not stored refs resolved

Emergence of power laws in hierarchical dynamics on multi-level graphs

Armando Bazzani, Gregorio Berselli, Mirko Degli Esposti, Tommaso Rondini

A hierarchical queue model with Laplacian fluctuations reproduces the power-law exponent of Italian local train delays.

arxiv:2509.18782 v2 · 2025-09-23 · physics.soc-ph · physics.app-ph

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The model accurately reproduces the empirically observed power-law exponent associated with the Italian local train delays.

C2weakest assumption

The stochastic fluctuations in scheduled travel times follow a Laplacian distribution derived from empirical data, which is used to drive the dynamics in the hierarchical network model.

C3one line summary

A queue-based model of hierarchical train priorities with stochastic delays generates power-law distributions in local train delays matching empirical Italian data.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Springer, New York (2013) 2013 · doi:10.1007/978-1-4757-5426-1

[2] Reviews of modern physics 74(1), 47 (2002) 2002

[3] science 286(5439), 509–512 (1999) 1999

[4] Phys ica A: Statistical 10 Mechanics and its Applications 369(1), 29–70 (2006) 2006

[5] Cont emporary physics 46(5), 323–351 (2005) 2005

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:04:13.542287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f60556773fb4d1a778cac0a8843415871ff1c3c0213ab117e7115f83b08661ea

Aliases

arxiv: 2509.18782 · arxiv_version: 2509.18782v2 · doi: 10.48550/arxiv.2509.18782 · pith_short_12: 6YCVM5Z7WTI2 · pith_short_16: 6YCVM5Z7WTI2O6GK · pith_short_8: 6YCVM5Z7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6YCVM5Z7WTI2O6GKYCUIINAVQ4 \
  | 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: f60556773fb4d1a778cac0a8843415871ff1c3c0213ab117e7115f83b08661ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e76719fbbd5c65015a6dbe554aea34bbb2b9a4941f8134aae48d246ac3e308a",
    "cross_cats_sorted": [
      "physics.app-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2025-09-23T08:21:20Z",
    "title_canon_sha256": "09eb2c155ad18699df0e4bdfa0c76a46b2e2f4b036e0bf69feead45ed83dae21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.18782",
    "kind": "arxiv",
    "version": 2
  }
}