{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AFAGTKFSYPTT3I3EQAMVS6MLCA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b3dc80cf198accc3c005ea48dbcff109d12f30338734a3775fb3ceda1cce5be5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-29T00:05:56Z","title_canon_sha256":"5030a0a9024756ed88530ad455712f77f676a7027901a1f6511e77e3a7f669b4"},"schema_version":"1.0","source":{"id":"1601.07951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07951","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07951v2","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07951","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"AFAGTKFSYPTT","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AFAGTKFSYPTT3I3E","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AFAGTKFS","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:300fd0c22bd03efe6a828ba47d4911f83996587343c2dcb323d7b454dc9be412","target":"graph","created_at":"2026-05-18T01:15:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We analyze the distribution that extremizes a linear combination of the Boltzmann--Gibbs entropy and the nonadditive $q$-entropy. We show that this distribution can be expressed in terms of a Lambert function. Both the entropic functional and the extremizing distribution can be associated with a nonlinear Fokker--Planck equation obtained from a master equation with nonlinear transition rates. Also, we evaluate the entropy extremized by a linear combination of a Gaussian distribution (which extremizes the Boltzmann--Gibbs entropy) and a $q$-Gaussian distribution (which extremizes the $q$-entrop","authors_text":"Constantino Tsallis, Debarshee Bagchi, Gabriele Sicuro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-29T00:05:56Z","title":"On the connection between linear combination of entropies and linear combination of extremizing distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07951","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:619c31d5da40bf312051c77799ef2f475fb8704c8af935befb293833277ef22f","target":"record","created_at":"2026-05-18T01:15:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b3dc80cf198accc3c005ea48dbcff109d12f30338734a3775fb3ceda1cce5be5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-29T00:05:56Z","title_canon_sha256":"5030a0a9024756ed88530ad455712f77f676a7027901a1f6511e77e3a7f669b4"},"schema_version":"1.0","source":{"id":"1601.07951","kind":"arxiv","version":2}},"canonical_sha256":"014069a8b2c3e73da364801959798b103dd41c0bbbbfb91ae4af8b01d5cccfb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"014069a8b2c3e73da364801959798b103dd41c0bbbbfb91ae4af8b01d5cccfb4","first_computed_at":"2026-05-18T01:15:57.623045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:57.623045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"azMfqaH547vu7rTHPtLtc92cOoj9FlK+/06MESBAxP3rPHVO73QaQkJIO8RR7iDHvzL18wzRtirjjtSTZgTmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:57.623689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:619c31d5da40bf312051c77799ef2f475fb8704c8af935befb293833277ef22f","sha256:300fd0c22bd03efe6a828ba47d4911f83996587343c2dcb323d7b454dc9be412"],"state_sha256":"4b5d7bcdd69e5f3c8a3dd4a7c1242944eafd2f7a18109bc27f4c66f56263b209"}