{"paper":{"title":"The unique, universal entropy for complex systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Coupled entropy is the unique universal entropy for complex systems because it measures uncertainty at the maximizing distribution's scale and is extensive across all scaling classes.","cross_cats":["cs.IT","math.IT"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kenric P. Nelson","submitted_at":"2026-05-06T04:47:03Z","abstract_excerpt":"An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution, where the log-log slope equals $-1$. Additionally, entropy must be extensive across the full universality scaling classes defined by Hanel-Thurner. The coupled entropy, maximized by the coupled stretched exponential distributions, is proven to be the unique, universal entropy that satisfies these requirements. The non-additivity of the entropy is equal to the lo"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The coupled entropy, maximized by the coupled stretched exponential distributions, is proven to be the unique, universal entropy that satisfies these requirements.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution where the log-log slope equals -1, plus the requirement of extensivity across the full Hanel-Thurner universality scaling classes; these are asserted as previously missing from decades of research.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The coupled entropy maximized by coupled stretched exponential distributions is the unique universal entropy satisfying the requirements to measure uncertainty at the informational scale with log-log slope -1 and extensivity across Hanel-Thurner universality classes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Coupled entropy is the unique universal entropy for complex systems because it measures uncertainty at the maximizing distribution's scale and is extensive across all scaling classes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d7c05247ee0d7d9af38067a2b6d04c2ac48eeb74df69940ac2ea8203e46a96f7"},"source":{"id":"2605.04493","kind":"arxiv","version":4},"verdict":{"id":"e111a8f7-00b0-4a63-afcf-2023149d954f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T02:28:38.875469Z","strongest_claim":"The coupled entropy, maximized by the coupled stretched exponential distributions, is proven to be the unique, universal entropy that satisfies these requirements.","one_line_summary":"The coupled entropy maximized by coupled stretched exponential distributions is the unique universal entropy satisfying the requirements to measure uncertainty at the informational scale with log-log slope -1 and extensivity across Hanel-Thurner universality classes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution where the log-log slope equals -1, plus the requirement of extensivity across the full Hanel-Thurner universality scaling classes; these are asserted as previously missing from decades of research.","pith_extraction_headline":"Coupled entropy is the unique universal entropy for complex systems because it measures uncertainty at the maximizing distribution's scale and is extensive across all scaling classes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04493/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T11:41:10.368050Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.821978Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:22:25.961237Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"91481bdc48ed6bdecf98ddd0a2b6c2f99281f5a1718613f25aad348e457089b9"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8f84b89c33754fc1b7ebc2dec8289351d38edaad2cbac37e416afe1e408ad974"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}