{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7FXBDWGZQV4F3DUSNKXXV5UT7D","short_pith_number":"pith:7FXBDWGZ","canonical_record":{"source":{"id":"1409.2369","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2014-09-08T14:38:33Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"b17e12771bf9e89edb2d2c7752582c42b95d2110437dbf79e7b31cbecfc8c7e5","abstract_canon_sha256":"cd906e24c52e28299a1112fb5b992acf717cd4e6610f823e12c0b27b03cc0784"},"schema_version":"1.0"},"canonical_sha256":"f96e11d8d985785d8e926aaf7af693f8c50738308bebdd2bc4736a1d15655790","source":{"kind":"arxiv","id":"1409.2369","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2369","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2369v1","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2369","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"7FXBDWGZQV4F","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7FXBDWGZQV4F3DUS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7FXBDWGZ","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7FXBDWGZQV4F3DUSNKXXV5UT7D","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2369","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2014-09-08T14:38:33Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"b17e12771bf9e89edb2d2c7752582c42b95d2110437dbf79e7b31cbecfc8c7e5","abstract_canon_sha256":"cd906e24c52e28299a1112fb5b992acf717cd4e6610f823e12c0b27b03cc0784"},"schema_version":"1.0"},"canonical_sha256":"f96e11d8d985785d8e926aaf7af693f8c50738308bebdd2bc4736a1d15655790","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:47.597792Z","signature_b64":"m0morobYx/3AJYLH1BEKOsGkgdW4BxNMwshwdPFEa2GVP4+G4kfvHso9rVMdlO66vq/b960e+xJAxEqea5QBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f96e11d8d985785d8e926aaf7af693f8c50738308bebdd2bc4736a1d15655790","last_reissued_at":"2026-05-18T02:28:47.597299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:47.597299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2369","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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bU/OadapbvQmxeZ6i1lkAFPrVoBdS/T0uqAmzxToY4MRzm7x0QuoLKrjNoOUj3ngzDQFxQklzx9qXl/H1Jr9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:32:02.858507Z"},"content_sha256":"116c89d3dab2e3c407abb9d3ae1880aa2ac8ca3a3d547bb573c9066632fa635d","schema_version":"1.0","event_id":"sha256:116c89d3dab2e3c407abb9d3ae1880aa2ac8ca3a3d547bb573c9066632fa635d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7FXBDWGZQV4F3DUSNKXXV5UT7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Thermodynamics of Black Holes in Massive Gravity","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Qi-Yuan Pan, Rong-Gen Cai, Ya-Peng Hu, Yun-Long Zhang","submitted_at":"2014-09-08T14:38:33Z","abstract_excerpt":"We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2369","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":""},"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":"2026-05-18T02:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQ18Ce462n9EeyE+GJac8CCa972jq6wU4gPgHieMLNP0NoeKNpbiDQqNO+MOx+rfPFiLYNTFOxtcduOGh0B8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:32:02.859150Z"},"content_sha256":"92e9d6a1986a96d2518d8a16631216bebb0d4b4f4fc8398864f7237dede16fbb","schema_version":"1.0","event_id":"sha256:92e9d6a1986a96d2518d8a16631216bebb0d4b4f4fc8398864f7237dede16fbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D/bundle.json","state_url":"https://pith.science/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D/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":"2026-05-28T22:32:02Z","links":{"resolver":"https://pith.science/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D","bundle":"https://pith.science/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D/bundle.json","state":"https://pith.science/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FXBDWGZQV4F3DUSNKXXV5UT7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7FXBDWGZQV4F3DUSNKXXV5UT7D","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":"cd906e24c52e28299a1112fb5b992acf717cd4e6610f823e12c0b27b03cc0784","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2014-09-08T14:38:33Z","title_canon_sha256":"b17e12771bf9e89edb2d2c7752582c42b95d2110437dbf79e7b31cbecfc8c7e5"},"schema_version":"1.0","source":{"id":"1409.2369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2369","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2369v1","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2369","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"7FXBDWGZQV4F","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7FXBDWGZQV4F3DUS","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7FXBDWGZ","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:92e9d6a1986a96d2518d8a16631216bebb0d4b4f4fc8398864f7237dede16fbb","target":"graph","created_at":"2026-05-18T02:28:47Z","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"},"paper":{"abstract_excerpt":"We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law ","authors_text":"Qi-Yuan Pan, Rong-Gen Cai, Ya-Peng Hu, Yun-Long Zhang","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2014-09-08T14:38:33Z","title":"Thermodynamics of Black Holes in Massive Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2369","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":"sha256:116c89d3dab2e3c407abb9d3ae1880aa2ac8ca3a3d547bb573c9066632fa635d","target":"record","created_at":"2026-05-18T02:28:47Z","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":"cd906e24c52e28299a1112fb5b992acf717cd4e6610f823e12c0b27b03cc0784","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"hep-th","submitted_at":"2014-09-08T14:38:33Z","title_canon_sha256":"b17e12771bf9e89edb2d2c7752582c42b95d2110437dbf79e7b31cbecfc8c7e5"},"schema_version":"1.0","source":{"id":"1409.2369","kind":"arxiv","version":1}},"canonical_sha256":"f96e11d8d985785d8e926aaf7af693f8c50738308bebdd2bc4736a1d15655790","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f96e11d8d985785d8e926aaf7af693f8c50738308bebdd2bc4736a1d15655790","first_computed_at":"2026-05-18T02:28:47.597299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:47.597299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m0morobYx/3AJYLH1BEKOsGkgdW4BxNMwshwdPFEa2GVP4+G4kfvHso9rVMdlO66vq/b960e+xJAxEqea5QBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:47.597792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:116c89d3dab2e3c407abb9d3ae1880aa2ac8ca3a3d547bb573c9066632fa635d","sha256:92e9d6a1986a96d2518d8a16631216bebb0d4b4f4fc8398864f7237dede16fbb"],"state_sha256":"121f717ca988d217eda5d121ea4a42ba9bb2bdfb47490252a2cdd19d796bdd73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DPEIVlg1d0SfpslUICNri36SexvbvpaI47aTYyBzC/Ncz0NVsPvwW2je9W0Cnc4ljhOOLVJWvvV0kiUnfP8nBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:32:02.862908Z","bundle_sha256":"3d217d18665e2ca832d3b9cb0ac2ed4a98be566228ac1ada07429daf44adfc7c"}}