{"paper":{"title":"Mean-Field Theory for Heider Balance under Heterogeneous Social Temperatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A mean-field model shows that the full distribution of social temperatures across links determines the transition to polarized states in Heider balance.","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.soc-ph","authors_text":"Yuki Izumida, Zhen Li","submitted_at":"2026-02-06T03:13:08Z","abstract_excerpt":"Heider balance theory provides a fundamental framework for understanding the formation of friendly and hostile relations in social networks. Existing stochastic formulations typically assume a uniform social temperature, implying that all interpersonal relations fluctuate with the same intensity. However, studies show that social interactions are highly heterogeneous, with broad variability in stability, volatility, and susceptibility to change. In this work, we introduce a generalized Heider balance model on a complete graph in which each link is assigned its own social temperature. Within a "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A mean-field model shows that the full distribution of social temperatures across links determines the transition to polarized states in Heider balance.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f2b9256ba5f0c545564b35d5fd155e08a9ec3de54d7a1ca3c90a0355693ed5f8"},"source":{"id":"2602.06342","kind":"arxiv","version":2},"verdict":{"id":"0c8aa643-ff28-4d8b-804e-a12dd8892ea3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T06:57:46.402983Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"A mean-field model shows that the full distribution of social temperatures across links determines the transition to polarized states in Heider balance."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.06342/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":54,"sample":[{"doi":"","year":null,"title":"Friends of my friends are my friends","work_id":"5d5addb6-01c5-4fd6-afa5-eb010e0bd54d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Enemies of my friends are my enemies","work_id":"0582f6a8-e944-4d98-a1e7-3201024bdc5a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Friends of my enemies are my enemies","work_id":"678743d6-2ee9-40a3-93fb-17cca7c23aa8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"Mean-Field Theory for Heider Balance under Heterogeneous Social Temperatures","work_id":"ece1387f-a930-4980-9cb3-47b57e52f78a","ref_index":4,"cited_arxiv_id":"2602.06342","is_internal_anchor":true},{"doi":"","year":null,"title":"Here,C ∗ ≈1.716 is the critical value reached for a delta distribution [11]. 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