{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:V5F5GC6GAEA37HRXK3PCIJJ4MI","short_pith_number":"pith:V5F5GC6G","canonical_record":{"source":{"id":"2406.15138","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-06-21T13:34:54Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0707b8ba629e619381933e98150a892b4e6ea46c2b2b3918cebc5bb379618605","abstract_canon_sha256":"8bc206f45f4fff2bb3d00d3ff616c287b4866590bda757eecc465c827eb1b1e6"},"schema_version":"1.0"},"canonical_sha256":"af4bd30bc60101bf9e3756de24253c621dc8d6b05121817cbec44239247cbdc9","source":{"kind":"arxiv","id":"2406.15138","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.15138","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"arxiv_version","alias_value":"2406.15138v3","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.15138","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"pith_short_12","alias_value":"V5F5GC6GAEA3","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"pith_short_16","alias_value":"V5F5GC6GAEA37HRX","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"pith_short_8","alias_value":"V5F5GC6G","created_at":"2026-07-05T10:13:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:V5F5GC6GAEA37HRXK3PCIJJ4MI","target":"record","payload":{"canonical_record":{"source":{"id":"2406.15138","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-06-21T13:34:54Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"0707b8ba629e619381933e98150a892b4e6ea46c2b2b3918cebc5bb379618605","abstract_canon_sha256":"8bc206f45f4fff2bb3d00d3ff616c287b4866590bda757eecc465c827eb1b1e6"},"schema_version":"1.0"},"canonical_sha256":"af4bd30bc60101bf9e3756de24253c621dc8d6b05121817cbec44239247cbdc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:01.351206Z","signature_b64":"+xcQb4rOXvtfyc06QgXR9B+WnUePT6qUA9PzXPTye1bSH7PkiNbAuROiuHdxNBhsa8xnaf81d2mg/ad37ldDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af4bd30bc60101bf9e3756de24253c621dc8d6b05121817cbec44239247cbdc9","last_reissued_at":"2026-07-05T10:13:01.350727Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:01.350727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.15138","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:13:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qOJ6K31c6TjUXP5EUZ1K7vUB9SEDhLAQ0mwnJGednOCCaPGqr7ze+3wKll6Q2Dr57cZACstm64+25YoIoDnUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:17:35.244545Z"},"content_sha256":"71c70fc5831ce3512408f30e4fb8d9b19b0af8321e635da8711268048bf3b5bd","schema_version":"1.0","event_id":"sha256:71c70fc5831ce3512408f30e4fb8d9b19b0af8321e635da8711268048bf3b5bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:V5F5GC6GAEA37HRXK3PCIJJ4MI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in $F(R_{abcd})$ gravity theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Hongbao Zhang, Mingfeng Li, Wei Guo, Xiyao Guo, Zili Mou","submitted_at":"2024-06-21T13:34:54Z","abstract_excerpt":"By working with the covariant phase space formalism, we have shown that not only can the Hamiltonian conjugate to a Killing vector field $\\xi$ be expressed as the sum of the associated Noether charge and $\\xi$ contracted with the Hilbert action boundary term for $F(R_{abcd})$ gravity, but also be written as its contraction with another $\\xi$ independent tensor field. With this, we have proven the equivalence of Noether charge and Hilbert action boundary term formulae for the stationary black hole entropy in $F(R_{abcd})$ gravity, which is further substantiated by our explicit computation using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15138","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.15138/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:13:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twOY7tNN4MX557nM12lcNUtR6B7sQfUpaIMfxchA0pJ9nAGhr8zD4bw/ia5ovy4Fpnlk8hpTX+BTrIRBt11PCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:17:35.245398Z"},"content_sha256":"f51203a70fc3be1a04184f93eb64d7e4dacb318018fc81f1d37ff9d791036caf","schema_version":"1.0","event_id":"sha256:f51203a70fc3be1a04184f93eb64d7e4dacb318018fc81f1d37ff9d791036caf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI/bundle.json","state_url":"https://pith.science/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T16:17:35Z","links":{"resolver":"https://pith.science/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI","bundle":"https://pith.science/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI/bundle.json","state":"https://pith.science/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5F5GC6GAEA37HRXK3PCIJJ4MI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:V5F5GC6GAEA37HRXK3PCIJJ4MI","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":"8bc206f45f4fff2bb3d00d3ff616c287b4866590bda757eecc465c827eb1b1e6","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-06-21T13:34:54Z","title_canon_sha256":"0707b8ba629e619381933e98150a892b4e6ea46c2b2b3918cebc5bb379618605"},"schema_version":"1.0","source":{"id":"2406.15138","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.15138","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"arxiv_version","alias_value":"2406.15138v3","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.15138","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"pith_short_12","alias_value":"V5F5GC6GAEA3","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"pith_short_16","alias_value":"V5F5GC6GAEA37HRX","created_at":"2026-07-05T10:13:01Z"},{"alias_kind":"pith_short_8","alias_value":"V5F5GC6G","created_at":"2026-07-05T10:13:01Z"}],"graph_snapshots":[{"event_id":"sha256:f51203a70fc3be1a04184f93eb64d7e4dacb318018fc81f1d37ff9d791036caf","target":"graph","created_at":"2026-07-05T10:13:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.15138/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By working with the covariant phase space formalism, we have shown that not only can the Hamiltonian conjugate to a Killing vector field $\\xi$ be expressed as the sum of the associated Noether charge and $\\xi$ contracted with the Hilbert action boundary term for $F(R_{abcd})$ gravity, but also be written as its contraction with another $\\xi$ independent tensor field. With this, we have proven the equivalence of Noether charge and Hilbert action boundary term formulae for the stationary black hole entropy in $F(R_{abcd})$ gravity, which is further substantiated by our explicit computation using","authors_text":"Hongbao Zhang, Mingfeng Li, Wei Guo, Xiyao Guo, Zili Mou","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-06-21T13:34:54Z","title":"Equivalence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in $F(R_{abcd})$ gravity theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15138","kind":"arxiv","version":3},"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":"sha256:71c70fc5831ce3512408f30e4fb8d9b19b0af8321e635da8711268048bf3b5bd","target":"record","created_at":"2026-07-05T10:13:01Z","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":"8bc206f45f4fff2bb3d00d3ff616c287b4866590bda757eecc465c827eb1b1e6","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-06-21T13:34:54Z","title_canon_sha256":"0707b8ba629e619381933e98150a892b4e6ea46c2b2b3918cebc5bb379618605"},"schema_version":"1.0","source":{"id":"2406.15138","kind":"arxiv","version":3}},"canonical_sha256":"af4bd30bc60101bf9e3756de24253c621dc8d6b05121817cbec44239247cbdc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af4bd30bc60101bf9e3756de24253c621dc8d6b05121817cbec44239247cbdc9","first_computed_at":"2026-07-05T10:13:01.350727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:01.350727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xcQb4rOXvtfyc06QgXR9B+WnUePT6qUA9PzXPTye1bSH7PkiNbAuROiuHdxNBhsa8xnaf81d2mg/ad37ldDCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:01.351206Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.15138","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71c70fc5831ce3512408f30e4fb8d9b19b0af8321e635da8711268048bf3b5bd","sha256:f51203a70fc3be1a04184f93eb64d7e4dacb318018fc81f1d37ff9d791036caf"],"state_sha256":"e8fddcd66a3e5ce47f930c25d1df3db2cc990805be2125c0b3433b74f6ef6e10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qqLI/5nyizK4idI81Po4bABX5QwWdBKh5uyQfHS8cRKdqX2v9vhq1dKNOSDliccu9gND6Y0FJcT7imfbV0zFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:17:35.252688Z","bundle_sha256":"443de585ce44b1f50fc75bd85d560817368a3948494186f014d63d05fde038d2"}}