{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PHMWAFTKDWV7C5LPONMZDXOEIY","short_pith_number":"pith:PHMWAFTK","schema_version":"1.0","canonical_sha256":"79d960166a1dabf1756f735991ddc446318c58b4bb397e2794df05f40fb997e4","source":{"kind":"arxiv","id":"1509.07142","version":2},"attestation_state":"computed","paper":{"title":"Black Hole Entropy and Viscosity Bound in Horndeski Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"C.N. Pope, Hai-Shan Liu, H. L\\\"u, Xing-Hui Feng","submitted_at":"2015-09-23T20:19:54Z","abstract_excerpt":"Horndeski gravities are theories of gravity coupled to a scalar field, in which the action contains an additional non-minimal quadratic coupling of the scalar, through its first derivative, to the Einstein tensor or the analogous higher-derivative tensors coming from the variation of Gauss-Bonnet or Lovelock terms. In this paper we study the thermodynamics of the static black hole solutions in $n$ dimensions, in the simplest case of a Horndeski coupling to the Einstein tensor. We apply the Wald formalism to calculate the entropy of the black holes, and show that there is an additional contribu"},"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":"1509.07142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-23T20:19:54Z","cross_cats_sorted":[],"title_canon_sha256":"0998a2c0faa63b73f7399ed18d2e17c02bbf9c4a1887bd54fac5b3e60602ef5d","abstract_canon_sha256":"a032179b3cb1d6053bf04af239fd69f527cf1497e299aaf8a813388a28b001c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:54.094197Z","signature_b64":"18LYMzIa03Igpe1hOscg85B1XwBfhBOLdzkvufBI4+c07Mel71ZP3r3DPFHKC7JsjLlk+1Nzqi3riQZkP4bFCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79d960166a1dabf1756f735991ddc446318c58b4bb397e2794df05f40fb997e4","last_reissued_at":"2026-05-18T01:21:54.093607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:54.093607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Black Hole Entropy and Viscosity Bound in Horndeski Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"C.N. Pope, Hai-Shan Liu, H. L\\\"u, Xing-Hui Feng","submitted_at":"2015-09-23T20:19:54Z","abstract_excerpt":"Horndeski gravities are theories of gravity coupled to a scalar field, in which the action contains an additional non-minimal quadratic coupling of the scalar, through its first derivative, to the Einstein tensor or the analogous higher-derivative tensors coming from the variation of Gauss-Bonnet or Lovelock terms. In this paper we study the thermodynamics of the static black hole solutions in $n$ dimensions, in the simplest case of a Horndeski coupling to the Einstein tensor. We apply the Wald formalism to calculate the entropy of the black holes, and show that there is an additional contribu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07142","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":""},"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":"1509.07142","created_at":"2026-05-18T01:21:54.093697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07142v2","created_at":"2026-05-18T01:21:54.093697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07142","created_at":"2026-05-18T01:21:54.093697+00:00"},{"alias_kind":"pith_short_12","alias_value":"PHMWAFTKDWV7","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PHMWAFTKDWV7C5LP","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PHMWAFTK","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2605.22429","citing_title":"Black Hole Entropy Beyond the Wald Term in Nonminimally Coupled Gravity: A Covariant Phase Space Decomposition","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2511.07209","citing_title":"Validity of the Background Subtraction Method for Black Hole Thermodynamics in Matter-Coupled Gravity Theories","ref_index":29,"is_internal_anchor":true},{"citing_arxiv_id":"2511.19926","citing_title":"Revisiting black holes and their thermodynamics in Einstein-Kalb-Ramond gravity","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2605.13963","citing_title":"When Bumblebee Meets NLED: Lorentz-Violating Black Holes and Regular Spacetimes","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY","json":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY.json","graph_json":"https://pith.science/api/pith-number/PHMWAFTKDWV7C5LPONMZDXOEIY/graph.json","events_json":"https://pith.science/api/pith-number/PHMWAFTKDWV7C5LPONMZDXOEIY/events.json","paper":"https://pith.science/paper/PHMWAFTK"},"agent_actions":{"view_html":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY","download_json":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY.json","view_paper":"https://pith.science/paper/PHMWAFTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07142&json=true","fetch_graph":"https://pith.science/api/pith-number/PHMWAFTKDWV7C5LPONMZDXOEIY/graph.json","fetch_events":"https://pith.science/api/pith-number/PHMWAFTKDWV7C5LPONMZDXOEIY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY/action/storage_attestation","attest_author":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY/action/author_attestation","sign_citation":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY/action/citation_signature","submit_replication":"https://pith.science/pith/PHMWAFTKDWV7C5LPONMZDXOEIY/action/replication_record"}},"created_at":"2026-05-18T01:21:54.093697+00:00","updated_at":"2026-05-18T01:21:54.093697+00:00"}