{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PWFT7WLCKJ23DWNRTEPXFMWSR3","short_pith_number":"pith:PWFT7WLC","schema_version":"1.0","canonical_sha256":"7d8b3fd9625275b1d9b1991f72b2d28ed5f9177ca8fc212d62fc81bb2b0f9037","source":{"kind":"arxiv","id":"1001.2597","version":2},"attestation_state":"computed","paper":{"title":"Clausius relation and Friedmann equation in FRW universe model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Kai-Nan Shao, Qiao-Jun Cao, Yi-Xin Chen","submitted_at":"2010-01-15T01:50:20Z","abstract_excerpt":"It has been shown that Friedmann equation of FRW universe can be derived from the first law of thermodynamics in Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, scalar-tensor gravity and $f(R)$ gravity. Moreover, it was pointed out that the temperature of the apparent horizon can be obtained using the tunneling formalism for the corresponding observers defined by Kodama vector. In this article, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics ass"},"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":"1001.2597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-01-15T01:50:20Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"7f115218ac1aa76f1f3a795dff06091acbd6bbc217990d0c6eac1c3163887c62","abstract_canon_sha256":"22658a0dfc11b0b6085b9b86c03a6e5b93e0fe8ac2e425cf6bac79650ec51a01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:29:18.459013Z","signature_b64":"y5THb758831m4/yf3wcSB9vQ2KTNeAlxMrad1sa/gwa/vB1gXreAyYUge700hgDvl7NvLoOpk4HhFQRUMfauBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d8b3fd9625275b1d9b1991f72b2d28ed5f9177ca8fc212d62fc81bb2b0f9037","last_reissued_at":"2026-07-04T17:29:18.458572Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:29:18.458572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Clausius relation and Friedmann equation in FRW universe model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Kai-Nan Shao, Qiao-Jun Cao, Yi-Xin Chen","submitted_at":"2010-01-15T01:50:20Z","abstract_excerpt":"It has been shown that Friedmann equation of FRW universe can be derived from the first law of thermodynamics in Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, scalar-tensor gravity and $f(R)$ gravity. Moreover, it was pointed out that the temperature of the apparent horizon can be obtained using the tunneling formalism for the corresponding observers defined by Kodama vector. In this article, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics ass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2597","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1001.2597/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1001.2597","created_at":"2026-07-04T17:29:18.458648+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.2597v2","created_at":"2026-07-04T17:29:18.458648+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2597","created_at":"2026-07-04T17:29:18.458648+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWFT7WLCKJ23","created_at":"2026-07-04T17:29:18.458648+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWFT7WLCKJ23DWNR","created_at":"2026-07-04T17:29:18.458648+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWFT7WLC","created_at":"2026-07-04T17:29:18.458648+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/PWFT7WLCKJ23DWNRTEPXFMWSR3","json":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3.json","graph_json":"https://pith.science/api/pith-number/PWFT7WLCKJ23DWNRTEPXFMWSR3/graph.json","events_json":"https://pith.science/api/pith-number/PWFT7WLCKJ23DWNRTEPXFMWSR3/events.json","paper":"https://pith.science/paper/PWFT7WLC"},"agent_actions":{"view_html":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3","download_json":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3.json","view_paper":"https://pith.science/paper/PWFT7WLC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.2597&json=true","fetch_graph":"https://pith.science/api/pith-number/PWFT7WLCKJ23DWNRTEPXFMWSR3/graph.json","fetch_events":"https://pith.science/api/pith-number/PWFT7WLCKJ23DWNRTEPXFMWSR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3/action/storage_attestation","attest_author":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3/action/author_attestation","sign_citation":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3/action/citation_signature","submit_replication":"https://pith.science/pith/PWFT7WLCKJ23DWNRTEPXFMWSR3/action/replication_record"}},"created_at":"2026-07-04T17:29:18.458648+00:00","updated_at":"2026-07-04T17:29:18.458648+00:00"}