{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BXT3CG3NYTGGQQXKAJVANJI7QS","short_pith_number":"pith:BXT3CG3N","canonical_record":{"source":{"id":"2506.04469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-06-04T21:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"2d370c615a6507a341511d6cda132556ae9194721b715e34f5958eff96476ad8","abstract_canon_sha256":"ba2e4b23125c9d174a8394186038162fbc0a469dfdc1f018c0e2aedfa660faa1"},"schema_version":"1.0"},"canonical_sha256":"0de7b11b6dc4cc6842ea026a06a51f84a1df03df6d314669f6ba7476ac6aaf69","source":{"kind":"arxiv","id":"2506.04469","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04469","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04469v1","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04469","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"pith_short_12","alias_value":"BXT3CG3NYTGG","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"pith_short_16","alias_value":"BXT3CG3NYTGGQQXK","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"pith_short_8","alias_value":"BXT3CG3N","created_at":"2026-07-05T11:16:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BXT3CG3NYTGGQQXKAJVANJI7QS","target":"record","payload":{"canonical_record":{"source":{"id":"2506.04469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-06-04T21:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"2d370c615a6507a341511d6cda132556ae9194721b715e34f5958eff96476ad8","abstract_canon_sha256":"ba2e4b23125c9d174a8394186038162fbc0a469dfdc1f018c0e2aedfa660faa1"},"schema_version":"1.0"},"canonical_sha256":"0de7b11b6dc4cc6842ea026a06a51f84a1df03df6d314669f6ba7476ac6aaf69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:15.004023Z","signature_b64":"vitFZBt77wKel6i/L7UgJRM++gx9M733rKf5FYqcvxT1SpU+IPl/9N4GNjY9i6zQ53NtMrPVmHrNnCAG4JJYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0de7b11b6dc4cc6842ea026a06a51f84a1df03df6d314669f6ba7476ac6aaf69","last_reissued_at":"2026-07-05T11:16:15.003589Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:15.003589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.04469","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6nqFalTVRnxCEAXn1SJsTWkY4/RXyYxLMpV8jqrQZB82vBHDZXU/WCvdGW2BxTFPb6JwSE1wsMeYoBi+i9g6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:57:20.907312Z"},"content_sha256":"f3f98ca91d69af49825856d5b2101d620433ff8d5a6e03d73e662608743dc2fe","schema_version":"1.0","event_id":"sha256:f3f98ca91d69af49825856d5b2101d620433ff8d5a6e03d73e662608743dc2fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BXT3CG3NYTGGQQXKAJVANJI7QS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Misner-Sharp energy in $f(R,\\mathcal{G})$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Amin Rezaei Akbarieh, Navid Safarzadeh Ilkhchi, Yaghoub Heydarzade","submitted_at":"2025-06-04T21:39:08Z","abstract_excerpt":"In this work, we explore the formulation of the Misner-Sharp energy within the framework of $f(R, \\mathcal{G})$ gravity, a modified theory incorporating the Ricci scalar $R$ and the Gauss-Bonnet scalar $\\mathcal{G}$. By extending the quasilocal energy definition to both static spherically symmetric spacetime and the dynamic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive explicit expressions for the generalized Misner-Sharp energy using two complementary approaches: the integration method and the conserved charge method based on the Kodama vector. Our analysis shows that the Mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04469","kind":"arxiv","version":1},"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/2506.04469/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":"2026-07-05T11:16:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C0Z9Hu1Su7c6vMt81ZCZdQ/hedEZIU/fzxTpDxJClR3f6Or8KYOEtFFNsUOb7/x0cssxeyPzUovUcVevjlNhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:57:20.907820Z"},"content_sha256":"02c0757e6848edcfec1710527e2a2f35b7a5e733e7fe8815c5564ff258d77b60","schema_version":"1.0","event_id":"sha256:02c0757e6848edcfec1710527e2a2f35b7a5e733e7fe8815c5564ff258d77b60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXT3CG3NYTGGQQXKAJVANJI7QS/bundle.json","state_url":"https://pith.science/pith/BXT3CG3NYTGGQQXKAJVANJI7QS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXT3CG3NYTGGQQXKAJVANJI7QS/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":"2026-08-21T18:57:20Z","links":{"resolver":"https://pith.science/pith/BXT3CG3NYTGGQQXKAJVANJI7QS","bundle":"https://pith.science/pith/BXT3CG3NYTGGQQXKAJVANJI7QS/bundle.json","state":"https://pith.science/pith/BXT3CG3NYTGGQQXKAJVANJI7QS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXT3CG3NYTGGQQXKAJVANJI7QS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BXT3CG3NYTGGQQXKAJVANJI7QS","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":"ba2e4b23125c9d174a8394186038162fbc0a469dfdc1f018c0e2aedfa660faa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-06-04T21:39:08Z","title_canon_sha256":"2d370c615a6507a341511d6cda132556ae9194721b715e34f5958eff96476ad8"},"schema_version":"1.0","source":{"id":"2506.04469","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04469","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04469v1","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04469","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"pith_short_12","alias_value":"BXT3CG3NYTGG","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"pith_short_16","alias_value":"BXT3CG3NYTGGQQXK","created_at":"2026-07-05T11:16:15Z"},{"alias_kind":"pith_short_8","alias_value":"BXT3CG3N","created_at":"2026-07-05T11:16:15Z"}],"graph_snapshots":[{"event_id":"sha256:02c0757e6848edcfec1710527e2a2f35b7a5e733e7fe8815c5564ff258d77b60","target":"graph","created_at":"2026-07-05T11:16:15Z","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/2506.04469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we explore the formulation of the Misner-Sharp energy within the framework of $f(R, \\mathcal{G})$ gravity, a modified theory incorporating the Ricci scalar $R$ and the Gauss-Bonnet scalar $\\mathcal{G}$. By extending the quasilocal energy definition to both static spherically symmetric spacetime and the dynamic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive explicit expressions for the generalized Misner-Sharp energy using two complementary approaches: the integration method and the conserved charge method based on the Kodama vector. Our analysis shows that the Mi","authors_text":"Amin Rezaei Akbarieh, Navid Safarzadeh Ilkhchi, Yaghoub Heydarzade","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-06-04T21:39:08Z","title":"Generalized Misner-Sharp energy in $f(R,\\mathcal{G})$ gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04469","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:f3f98ca91d69af49825856d5b2101d620433ff8d5a6e03d73e662608743dc2fe","target":"record","created_at":"2026-07-05T11:16:15Z","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":"ba2e4b23125c9d174a8394186038162fbc0a469dfdc1f018c0e2aedfa660faa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-06-04T21:39:08Z","title_canon_sha256":"2d370c615a6507a341511d6cda132556ae9194721b715e34f5958eff96476ad8"},"schema_version":"1.0","source":{"id":"2506.04469","kind":"arxiv","version":1}},"canonical_sha256":"0de7b11b6dc4cc6842ea026a06a51f84a1df03df6d314669f6ba7476ac6aaf69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0de7b11b6dc4cc6842ea026a06a51f84a1df03df6d314669f6ba7476ac6aaf69","first_computed_at":"2026-07-05T11:16:15.003589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:15.003589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vitFZBt77wKel6i/L7UgJRM++gx9M733rKf5FYqcvxT1SpU+IPl/9N4GNjY9i6zQ53NtMrPVmHrNnCAG4JJYDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:15.004023Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04469","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3f98ca91d69af49825856d5b2101d620433ff8d5a6e03d73e662608743dc2fe","sha256:02c0757e6848edcfec1710527e2a2f35b7a5e733e7fe8815c5564ff258d77b60"],"state_sha256":"6a74512b15e9d354f366e4e366ac06a37c589a4d385c995f2924931909f2a866"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cSzSnBCj/v69+zwrPXlhlJYny210tdZ2yfNqHAJRtCJ6Z2bZbVqm7yuZx9i7xxaBOETnV8TKijqsNtCcnl3RAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T18:57:20.911456Z","bundle_sha256":"60b0c09e55544b05a21f1d9d937ee5f0917628ca57c100a93f14d9413c539a85"}}