Pith Number

pith:WKWMCJXC

pith:2026:WKWMCJXCD3UQHYPMJ45GKC4G5S

not attested not anchored not stored refs resolved

Crime hotspot dynamics in residential burglary models with police response

Annalisa Quaini, Baoli Hao, Kamrun Mily, Ming Zhong

Response delays in police deployment can destabilize stable crime equilibria through Hopf bifurcations, producing oscillating and moving hotspots.

arxiv:2605.17709 v1 · 2026-05-18 · math.DS · cs.NA · math.NA

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Claims

C1strongest claim

Linear stability analysis of homogeneous steady states reveals that response delays can destabilize otherwise stable equilibria through Hopf bifurcations. As a result, the model predicts sustained temporal oscillations and dynamically evolving crime hotspots. Timely access to crime data plays a more important role than police density in stabilizing crime levels.

C2weakest assumption

The mean-field limit of the agent-based model with the chosen form of delayed crime-signal feedback accurately represents real-world police deployment dynamics and neighborhood effects.

C3one line summary

A mean-field continuum model with delayed police feedback, derived from an agent-based burglary model, shows via linear stability analysis that information delays trigger Hopf bifurcations and produce dynamic, moving crime hotspots.

References

34 extracted · 34 resolved · 0 Pith anchors

[1] https://github.com/baolihao/UrbanCrime-Sim

[2] Chicago Data Portal, Boundaries - Police Beats.https://data.cityofchicago.org /Public-Safety/Boundaries-Police-Beats-current-/aerh-rz74

[3] Chicago Data Portal, Crimes - 2001 to Present.https://data.cityofchicago.org /Public-Safety/Crimes-2001-to-Present/ijzp-q8t2 2001

[4] Chicago Police Department Investigatory Stop Report data.https://www.chicagop olice.org/statistics-data/isr-data/. 30

[5] Sworn CPD Member Staffing Map.https://igchicago.org/information-portal/ data-dashboards/sworn-cpd-member-staffing-map-2/

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:54.074834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2acc126e21ee903e1ec4f3a650b86ec8817bc3c96995a6bc51e7eb57e9b57d4

Aliases

arxiv: 2605.17709 · arxiv_version: 2605.17709v1 · doi: 10.48550/arxiv.2605.17709 · pith_short_12: WKWMCJXCD3UQ · pith_short_16: WKWMCJXCD3UQHYPM · pith_short_8: WKWMCJXC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WKWMCJXCD3UQHYPMJ45GKC4G5S \
  | 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: b2acc126e21ee903e1ec4f3a650b86ec8817bc3c96995a6bc51e7eb57e9b57d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de9b8081b36721c4be65fbbb0bb2ef6ea629bf601b3b2ecb6d5409466b77fe07",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-18T00:09:04Z",
    "title_canon_sha256": "7393a84b7404ca4542d765e106383a80c1aff3f041353433adb56979d3a8ed63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17709",
    "kind": "arxiv",
    "version": 1
  }
}