{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ADXHCWXHWFVQ646TUGO2PA46WZ","short_pith_number":"pith:ADXHCWXH","schema_version":"1.0","canonical_sha256":"00ee715ae7b16b0f73d3a19da7839eb65b8202060130a69c6e85f8e4184b896b","source":{"kind":"arxiv","id":"1105.1935","version":1},"attestation_state":"computed","paper":{"title":"Group entropies, correlation laws and zeta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Piergiulio Tempesta","submitted_at":"2011-05-10T12:47:37Z","abstract_excerpt":"The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dic"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.1935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-05-10T12:47:37Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"5810cadc24ea5491c3e02cf564e4d630fc6aef1a51a9eb1d56f63a248f85a233","abstract_canon_sha256":"4339e2d983fe19a9f08cc31596280840c6cd27b17c7271e76140ce6a7c34d2db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:02.004257Z","signature_b64":"ABaDohjPI9J4LB2gj8SMsMkSGuRlaT8ocQonxKXpYhb5Rdt4fWFt+GMXvuUVLxbi0tjW6etv8pHAhhBSfHewDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00ee715ae7b16b0f73d3a19da7839eb65b8202060130a69c6e85f8e4184b896b","last_reissued_at":"2026-05-18T02:02:02.003697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:02.003697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group entropies, correlation laws and zeta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Piergiulio Tempesta","submitted_at":"2011-05-10T12:47:37Z","abstract_excerpt":"The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1935","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.1935","created_at":"2026-05-18T02:02:02.003794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1935v1","created_at":"2026-05-18T02:02:02.003794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1935","created_at":"2026-05-18T02:02:02.003794+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADXHCWXHWFVQ","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADXHCWXHWFVQ646T","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADXHCWXH","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ","json":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ.json","graph_json":"https://pith.science/api/pith-number/ADXHCWXHWFVQ646TUGO2PA46WZ/graph.json","events_json":"https://pith.science/api/pith-number/ADXHCWXHWFVQ646TUGO2PA46WZ/events.json","paper":"https://pith.science/paper/ADXHCWXH"},"agent_actions":{"view_html":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ","download_json":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ.json","view_paper":"https://pith.science/paper/ADXHCWXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1935&json=true","fetch_graph":"https://pith.science/api/pith-number/ADXHCWXHWFVQ646TUGO2PA46WZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ADXHCWXHWFVQ646TUGO2PA46WZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ/action/storage_attestation","attest_author":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ/action/author_attestation","sign_citation":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ/action/citation_signature","submit_replication":"https://pith.science/pith/ADXHCWXHWFVQ646TUGO2PA46WZ/action/replication_record"}},"created_at":"2026-05-18T02:02:02.003794+00:00","updated_at":"2026-05-18T02:02:02.003794+00:00"}