{"paper":{"title":"Hyperstatistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Hyperstatistics derives q-generalized Boltzmann factors that reduce to q-exponentials across multiple probability distributions while preserving q-entropy concavity.","cross_cats":["hep-ex","hep-th","nucl-th","physics.acc-ph","physics.data-an","physics.ins-det"],"primary_cat":"cond-mat.stat-mech","authors_text":"Constantino Tsallis, Lucas Squillante, Mariano de Souza, Samuel M. Soares","submitted_at":"2026-04-23T22:30:25Z","abstract_excerpt":"We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain analytical closed-form expressions for the here proposed $q$-generalized Boltzmann factor $B_q$ considering uniform, $\\gamma$, Log-normal, F, and the $q$-$\\gamma$ probability distribution functions. Remarkably, for all investigated distribution functions, $B_q$ reduces to a $q$-exponential-type function. To demonstrate the applicability of hyperstatistics, we "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We obtain analytical closed-form expressions for the here proposed q-generalized Boltzmann factor B_q considering uniform, γ, Log-normal, F, and the q-γ probability distribution functions. Remarkably, for all investigated distribution functions, B_q reduces to a q-exponential-type function.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the chosen probability distribution functions (uniform, gamma, etc.) accurately capture the domains where Boltzmann-Gibbs statistics breaks down and that the resulting B_q preserves concavity of the nonadditive q-entropy without additional constraints.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Hyperstatistics derives closed-form q-generalized Boltzmann factors for non-Boltzmann-Gibbs domains that reduce to q-exponentials across uniform, gamma, log-normal, F, and q-gamma distributions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hyperstatistics derives q-generalized Boltzmann factors that reduce to q-exponentials across multiple probability distributions while preserving q-entropy concavity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"780757f4fb1616772cd7075b8f762c07443685805733da31086ab6303f6a54dc"},"source":{"id":"2604.24783","kind":"arxiv","version":2},"verdict":{"id":"62a9db17-c84e-49c6-a5a0-077f2dbf61bb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T13:28:17.468928Z","strongest_claim":"We obtain analytical closed-form expressions for the here proposed q-generalized Boltzmann factor B_q considering uniform, γ, Log-normal, F, and the q-γ probability distribution functions. Remarkably, for all investigated distribution functions, B_q reduces to a q-exponential-type function.","one_line_summary":"Hyperstatistics derives closed-form q-generalized Boltzmann factors for non-Boltzmann-Gibbs domains that reduce to q-exponentials across uniform, gamma, log-normal, F, and q-gamma distributions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the chosen probability distribution functions (uniform, gamma, etc.) accurately capture the domains where Boltzmann-Gibbs statistics breaks down and that the resulting B_q preserves concavity of the nonadditive q-entropy without additional constraints.","pith_extraction_headline":"Hyperstatistics derives q-generalized Boltzmann factors that reduce to q-exponentials across multiple probability distributions while preserving q-entropy concavity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.24783/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T11:36:37.999850Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T00:15:22.262010Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"8129f6a0d99b085e8045eb8cdb7fed201090d38815fc9a098c081f0413e83e49"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}