{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:36:09Z","timestamp":1785404169133,"version":"3.56.0"},"reference-count":47,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T00:00:00Z","timestamp":1775088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"crossref","award":["200021-232060"],"award-info":[{"award-number":["200021-232060"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]},{"award":["200021-232060"],"award-info":[{"award-number":["200021-232060"]}],"id":[{"id":"https:\/\/ror.org\/00yjd3n13","id-type":"ROR","asserted-by":"publisher"}]},{"name":"German Academic Scholarship Foundation"},{"id":[{"id":"https:\/\/ror.org\/05xwwfy96","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We investigate majority-vote opinion dynamics on Geometric Inhomogeneous Random Graphs (GIRGs), a powerful model for spatial complex networks. In contrast to classic coarsening dynamics, where a single opinion typically achieves global consensus, our simulations reveal that sufficiently large, localized opinion domains do not disappear. Instead, they stabilize, leading to a persistent coexistence of competing opinions. To understand the mechanism behind this arrested coarsening, we develop and analyze a tractable mean-field model of the interface between two opinion domains. Our main theoretical result rigorously establishes the existence of a stable, non-trivial limiting distribution for the interface profile in a mean-field analysis. This demonstrates that the boundary between opinions is stationary, providing a mathematical explanation for how complex network geometry can support robust opinion diversity in social systems.<\/jats:p>","DOI":"10.3390\/e28040401","type":"journal-article","created":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T11:51:03Z","timestamp":1775130663000},"page":"401","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stable Boundaries of Opinion Dynamics in Heterogeneous Spatial Complex Networks"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-6470-4455","authenticated-orcid":false,"given":"Mats","family":"Bierwirth","sequence":"first","affiliation":[{"name":"Department of Computer Science, ETH Z\u00fcrich, 8092 Z\u00fcrich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0004-7629","authenticated-orcid":false,"given":"Johannes","family":"Lengler","sequence":"additional","affiliation":[{"name":"Department of Computer Science, ETH Z\u00fcrich, 8092 Z\u00fcrich, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1038\/ncomms1063","article-title":"Sustaining the internet with hyperbolic mapping","volume":"1","author":"Papadopoulos","year":"2010","journal-title":"Nat. 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