{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:A3OTWWMXCLEADY2PL5ICAH4H3G","short_pith_number":"pith:A3OTWWMX","canonical_record":{"source":{"id":"1209.3308","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-14T20:00:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d4297bf91b74779d1604c69daba9de4767ebc7236bd7c2e23b86d0cba3684e06","abstract_canon_sha256":"d12f50e12fe8cb945ccb0df4b3e83ee695d9bb9010a32fb4b41e6ed30f97b9d2"},"schema_version":"1.0"},"canonical_sha256":"06dd3b599712c801e34f5f50201f87d993d4add43f04e73a8fade82a4988a0a5","source":{"kind":"arxiv","id":"1209.3308","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3308","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3308v2","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3308","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"A3OTWWMXCLEA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A3OTWWMXCLEADY2P","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A3OTWWMX","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:A3OTWWMXCLEADY2PL5ICAH4H3G","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3308","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-14T20:00:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d4297bf91b74779d1604c69daba9de4767ebc7236bd7c2e23b86d0cba3684e06","abstract_canon_sha256":"d12f50e12fe8cb945ccb0df4b3e83ee695d9bb9010a32fb4b41e6ed30f97b9d2"},"schema_version":"1.0"},"canonical_sha256":"06dd3b599712c801e34f5f50201f87d993d4add43f04e73a8fade82a4988a0a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:31.525342Z","signature_b64":"7fZHWG8QKSJLhEqWAkOFgthFJA0Gd1zV1vjviaM6QJAYDH4WVOqNShDgbUBl4OZQABval93sycHGvRJnahNcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06dd3b599712c801e34f5f50201f87d993d4add43f04e73a8fade82a4988a0a5","last_reissued_at":"2026-05-18T02:46:31.524883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:31.524883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3308","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+3VPS9EnAdWtLP95D3v3YcDFeJtQ2uZThc1JchzEDKwql9XSsJQzq6Mak5rMljylr8uI7l7SK5PK+ekBYwHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:47:09.802418Z"},"content_sha256":"5e41d15d5f11bd025b21b25873ef4227f40c74b83c4bbc8be2141cbc95dc4e8c","schema_version":"1.0","event_id":"sha256:5e41d15d5f11bd025b21b25873ef4227f40c74b83c4bbc8be2141cbc95dc4e8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:A3OTWWMXCLEADY2PL5ICAH4H3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Claude M. Warnick, Gustav H. Holzegel","submitted_at":"2012-09-14T20:00:06Z","abstract_excerpt":"We study the global dynamics of free massive scalar fields on general, globally stationary, asymptotically AdS black hole backgrounds with Dirichlet-, Neumann- or Robin- boundary conditions imposed on $\\psi$ at infinity. This class includes the regular Kerr-AdS black holes satisfying the Hawking Reall bound $r_+^2 > |a|l$. We establish a suitable criterion for linear stability (in the sense of uniform boundedness) of $\\psi$ and demonstrate how the issue of stability can depend on the boundary condition prescribed. In particular, in the slowly rotating Kerr-AdS case, we obtain the existence of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3308","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tGud+IatqdBwIGQYNL2duWvQC1wGOkEPSiw8dbTNW66faB6BB+PhD66QdkfHELIZxogZ1kMluyQtyAshu3WDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:47:09.802880Z"},"content_sha256":"7ad34fa9ae45119032de98c1e6619c124897d5c67e59d6a9a428168c60226fb5","schema_version":"1.0","event_id":"sha256:7ad34fa9ae45119032de98c1e6619c124897d5c67e59d6a9a428168c60226fb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3OTWWMXCLEADY2PL5ICAH4H3G/bundle.json","state_url":"https://pith.science/pith/A3OTWWMXCLEADY2PL5ICAH4H3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3OTWWMXCLEADY2PL5ICAH4H3G/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":"2026-08-11T08:47:09Z","links":{"resolver":"https://pith.science/pith/A3OTWWMXCLEADY2PL5ICAH4H3G","bundle":"https://pith.science/pith/A3OTWWMXCLEADY2PL5ICAH4H3G/bundle.json","state":"https://pith.science/pith/A3OTWWMXCLEADY2PL5ICAH4H3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3OTWWMXCLEADY2PL5ICAH4H3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A3OTWWMXCLEADY2PL5ICAH4H3G","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":"d12f50e12fe8cb945ccb0df4b3e83ee695d9bb9010a32fb4b41e6ed30f97b9d2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-14T20:00:06Z","title_canon_sha256":"d4297bf91b74779d1604c69daba9de4767ebc7236bd7c2e23b86d0cba3684e06"},"schema_version":"1.0","source":{"id":"1209.3308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3308","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3308v2","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3308","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"A3OTWWMXCLEA","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A3OTWWMXCLEADY2P","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A3OTWWMX","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:7ad34fa9ae45119032de98c1e6619c124897d5c67e59d6a9a428168c60226fb5","target":"graph","created_at":"2026-05-18T02:46:31Z","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 study the global dynamics of free massive scalar fields on general, globally stationary, asymptotically AdS black hole backgrounds with Dirichlet-, Neumann- or Robin- boundary conditions imposed on $\\psi$ at infinity. This class includes the regular Kerr-AdS black holes satisfying the Hawking Reall bound $r_+^2 > |a|l$. We establish a suitable criterion for linear stability (in the sense of uniform boundedness) of $\\psi$ and demonstrate how the issue of stability can depend on the boundary condition prescribed. In particular, in the slowly rotating Kerr-AdS case, we obtain the existence of ","authors_text":"Claude M. Warnick, Gustav H. Holzegel","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-14T20:00:06Z","title":"Boundedness and growth for the massive wave equation on asymptotically anti-de Sitter black holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3308","kind":"arxiv","version":2},"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":"sha256:5e41d15d5f11bd025b21b25873ef4227f40c74b83c4bbc8be2141cbc95dc4e8c","target":"record","created_at":"2026-05-18T02:46:31Z","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":"d12f50e12fe8cb945ccb0df4b3e83ee695d9bb9010a32fb4b41e6ed30f97b9d2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-14T20:00:06Z","title_canon_sha256":"d4297bf91b74779d1604c69daba9de4767ebc7236bd7c2e23b86d0cba3684e06"},"schema_version":"1.0","source":{"id":"1209.3308","kind":"arxiv","version":2}},"canonical_sha256":"06dd3b599712c801e34f5f50201f87d993d4add43f04e73a8fade82a4988a0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06dd3b599712c801e34f5f50201f87d993d4add43f04e73a8fade82a4988a0a5","first_computed_at":"2026-05-18T02:46:31.524883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:31.524883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7fZHWG8QKSJLhEqWAkOFgthFJA0Gd1zV1vjviaM6QJAYDH4WVOqNShDgbUBl4OZQABval93sycHGvRJnahNcBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:31.525342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e41d15d5f11bd025b21b25873ef4227f40c74b83c4bbc8be2141cbc95dc4e8c","sha256:7ad34fa9ae45119032de98c1e6619c124897d5c67e59d6a9a428168c60226fb5"],"state_sha256":"ff6ddc7e26da466dd98a28a9e05443a7ae086bef36e4361628ea6f4c25632c71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ed1nMcx8r9DBUtb10MrFTbzIKb8wuvXnsoyhgXyHh6V5+rMDFBlSgM3Ep8Lqpr2F6QHD0Hr6Ii5PCJyufndvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T08:47:09.808120Z","bundle_sha256":"ef17b2a6c049a2240eb0553f169b1091d1fac3d54b62276ada3f4399e559b78d"}}