Pith Number

pith:WHKF6KUC

pith:2026:WHKF6KUCOLOPXY4K7KZBB3KOOJ

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Mean-Field Theory for Heider Balance under Heterogeneous Social Temperatures

Yuki Izumida, Zhen Li

A mean-field model shows that the full distribution of social temperatures across links determines the transition to polarized states in Heider balance.

arxiv:2602.06342 v2 · 2026-02-06 · physics.soc-ph · cond-mat.stat-mech

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Claims

C1strongest claim

Within a mean-field formulation, we derive a distribution-dependent self-consistency condition for the collective opinion state and identify the criteria governing the transition between polarized and non-polarized configurations. This framework reveals how the entire distribution of interaction heterogeneity shapes the macroscopic behavior of the system.

C2weakest assumption

The mean-field approximation remains accurate on the complete graph even when temperatures are drawn from an arbitrary distribution; the derivation assumes the temperatures are fixed, independent, and drawn once from a stationary distribution whose functional form is chosen by the modeler.

C3one line summary

A mean-field model of Heider balance with heterogeneous link temperatures shows that the inverse-temperature distribution's tail behavior governs the transition between polarized and non-polarized states, with universal bounds.

References

54 extracted · 54 resolved · 2 Pith anchors

[1] Friends of my friends are my friends

[2] Enemies of my friends are my enemies

[3] Friends of my enemies are my enemies

[4] Mean-Field Theory for Heider Balance under Heterogeneous Social Temperatures 2026 · arXiv:2602.06342

[5] Here,C ∗ ≈1.716 is the critical value reached for a delta distribution [11]. The derivation of the bounds (11) is provided in Ap- pendix B The lower bound indicates that the homogeneous tem- perature

Formal links

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Cited by

1 paper in Pith

Mean-Field Theory for Heider Balance under Heterogeneous Social Temperatures

Receipt and verification

First computed	2026-05-20T00:02:09.423245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1d45f2a8272dcfbe38afab210ed4e724f529da41b71a73c4573d37883b5ab71

Aliases

arxiv: 2602.06342 · arxiv_version: 2602.06342v2 · doi: 10.48550/arxiv.2602.06342 · pith_short_12: WHKF6KUCOLOP · pith_short_16: WHKF6KUCOLOPXY4K · pith_short_8: WHKF6KUC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WHKF6KUCOLOPXY4K7KZBB3KOOJ \
  | 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: b1d45f2a8272dcfbe38afab210ed4e724f529da41b71a73c4573d37883b5ab71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33ad2209c32f340d48b01567cf3a5591f6c429fed768e8e957d9f387066b79f9",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2026-02-06T03:13:08Z",
    "title_canon_sha256": "37cfc52f88806364d7646ea9d5b8b50515049159ad3358344a2f68c4ce63fd40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.06342",
    "kind": "arxiv",
    "version": 2
  }
}