{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6WSJBVJHCEYJPP5XRAWIGJQSQT","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":"be63be3dfcc90ccfa4198c53f670b4f97e75695da90cab9675a8747a5bcd568a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-14T02:45:46Z","title_canon_sha256":"f5e6a3d6569925d4dbea7c66c3b0b0c292aac89b4fc3435020b288782c571320"},"schema_version":"1.0","source":{"id":"1608.04052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04052","created_at":"2026-05-18T00:49:16Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04052v1","created_at":"2026-05-18T00:49:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04052","created_at":"2026-05-18T00:49:16Z"},{"alias_kind":"pith_short_12","alias_value":"6WSJBVJHCEYJ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6WSJBVJHCEYJPP5X","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6WSJBVJH","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:050ccaa346721b7bf59d58f533c6a5e87d9f06c4aaa3cb69f3ccce7d2abee755","target":"graph","created_at":"2026-05-18T00:49:16Z","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":"Curado \\textit{et al.} [Ann. Phys. \\textbf{366} (2016) 22] have recently studied the axiomatic structure and the universality of a three-parameter trace-form entropy inspired by the group-theoretical structure. In this work, we study the group-theoretical entropy $S_{a,b,r}$ in the context of the third law of thermodynamics where the parameters $\\left\\lbrace a,b,r \\right\\rbrace $ are all independent. We show that this three-parameter entropy expression can simultaneously satisfy the third law of thermodynamics and the three Khinchin axioms, namely continuity, concavity and expansibility only w","authors_text":"Bilal Canturk, G. Baris Bagci, Thomas Oikonomou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-14T02:45:46Z","title":"Group theory, entropy and the third law of thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04052","kind":"arxiv","version":1},"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:d9070c09ac948d3e67b0800f136e5d4494f0a9ca5e492cbce469fb39fe2629a3","target":"record","created_at":"2026-05-18T00:49:16Z","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":"be63be3dfcc90ccfa4198c53f670b4f97e75695da90cab9675a8747a5bcd568a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-14T02:45:46Z","title_canon_sha256":"f5e6a3d6569925d4dbea7c66c3b0b0c292aac89b4fc3435020b288782c571320"},"schema_version":"1.0","source":{"id":"1608.04052","kind":"arxiv","version":1}},"canonical_sha256":"f5a490d527113097bfb7882c83261284c710a1079ab9f6c941ae0a1b33989846","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5a490d527113097bfb7882c83261284c710a1079ab9f6c941ae0a1b33989846","first_computed_at":"2026-05-18T00:49:16.167948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:16.167948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IESrjCHkdUatwtKkWwtgEDPKRcAHqfDDeVap3ck4KSOwOO/eMbccHIve9VtUkB9rjjaEkewye+NFVz0IL88SDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:16.168399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9070c09ac948d3e67b0800f136e5d4494f0a9ca5e492cbce469fb39fe2629a3","sha256:050ccaa346721b7bf59d58f533c6a5e87d9f06c4aaa3cb69f3ccce7d2abee755"],"state_sha256":"6e2f6d42790d98d6395d83b50c9610d4cdc65c085da30b10588bbbd3a1658a0f"}