{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VLGFHUJXD5VARQJUT637Y6N7LB","short_pith_number":"pith:VLGFHUJX","schema_version":"1.0","canonical_sha256":"aacc53d1371f6a08c1349fb7fc79bf5877dd29fd1528aa854987a7b11c242f34","source":{"kind":"arxiv","id":"1806.03996","version":3},"attestation_state":"computed","paper":{"title":"Modified Friedmann Equations from Tsallis Entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Ahmad Sheykhi","submitted_at":"2018-06-07T23:30:49Z","abstract_excerpt":"It was shown by Tsallis and Cirto that thermodynamical entropy of a gravitational system such as black hole must be generalized to the non-additive entropy, which is given by $S_h=\\gamma A^{\\beta}$, where $A$ is the horizon area and $\\beta$ is the nonextensive parameter \\cite{Tsa}. In this paper, by taking the entropy associated with the apparent horizon of the Friedmann-Robertson-Walker (FRW) Universe in the form of Tsallis entropy, and assuming the first law of thermodynamics, $dE=T_hdS_h+WdV$, holds on the apparent horizon, we are able to derive the corresponding Friedmann equations describ"},"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":"1806.03996","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2018-06-07T23:30:49Z","cross_cats_sorted":[],"title_canon_sha256":"1a4a87c024bde667b55b13a3244172a02311e92bffe099912e540313999348a4","abstract_canon_sha256":"c53750577a1dc087ea61b6b193fcdfd4dcf7e5fbe6cde876200431ce9bfa78bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:48.725842Z","signature_b64":"ZiwyR9GQz5O4hLIccFSqLRzhbp4N8U/JnieoAtZ8Luiy2B6D28vla9EdMoh3WmIBkJxlfA69B7CMsIwOI/39Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aacc53d1371f6a08c1349fb7fc79bf5877dd29fd1528aa854987a7b11c242f34","last_reissued_at":"2026-05-18T00:04:48.725209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:48.725209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modified Friedmann Equations from Tsallis Entropy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Ahmad Sheykhi","submitted_at":"2018-06-07T23:30:49Z","abstract_excerpt":"It was shown by Tsallis and Cirto that thermodynamical entropy of a gravitational system such as black hole must be generalized to the non-additive entropy, which is given by $S_h=\\gamma A^{\\beta}$, where $A$ is the horizon area and $\\beta$ is the nonextensive parameter \\cite{Tsa}. In this paper, by taking the entropy associated with the apparent horizon of the Friedmann-Robertson-Walker (FRW) Universe in the form of Tsallis entropy, and assuming the first law of thermodynamics, $dE=T_hdS_h+WdV$, holds on the apparent horizon, we are able to derive the corresponding Friedmann equations describ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03996","kind":"arxiv","version":3},"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":"1806.03996","created_at":"2026-05-18T00:04:48.725324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.03996v3","created_at":"2026-05-18T00:04:48.725324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03996","created_at":"2026-05-18T00:04:48.725324+00:00"},{"alias_kind":"pith_short_12","alias_value":"VLGFHUJXD5VA","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VLGFHUJXD5VARQJU","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VLGFHUJX","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.03568","citing_title":"Observational constraints on Luciano-Saridakis entropic cosmology","ref_index":111,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB","json":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB.json","graph_json":"https://pith.science/api/pith-number/VLGFHUJXD5VARQJUT637Y6N7LB/graph.json","events_json":"https://pith.science/api/pith-number/VLGFHUJXD5VARQJUT637Y6N7LB/events.json","paper":"https://pith.science/paper/VLGFHUJX"},"agent_actions":{"view_html":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB","download_json":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB.json","view_paper":"https://pith.science/paper/VLGFHUJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.03996&json=true","fetch_graph":"https://pith.science/api/pith-number/VLGFHUJXD5VARQJUT637Y6N7LB/graph.json","fetch_events":"https://pith.science/api/pith-number/VLGFHUJXD5VARQJUT637Y6N7LB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB/action/storage_attestation","attest_author":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB/action/author_attestation","sign_citation":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB/action/citation_signature","submit_replication":"https://pith.science/pith/VLGFHUJXD5VARQJUT637Y6N7LB/action/replication_record"}},"created_at":"2026-05-18T00:04:48.725324+00:00","updated_at":"2026-05-18T00:04:48.725324+00:00"}