{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:E34CHCEYE77WVGD3XOECRWBEPM","short_pith_number":"pith:E34CHCEY","canonical_record":{"source":{"id":"1310.2664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-09T23:58:03Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"35058feb2859c40e1e60eb2640a195191a71bfd9f3ba63d239324121342bb5ff","abstract_canon_sha256":"b0b3592d5aa1f6a1cf1031184a97353a2439b9f975bf9bcd552130bb3869226b"},"schema_version":"1.0"},"canonical_sha256":"26f823889827ff6a987bbb8828d8247b1018faac05a629c164b3fae4ffb5786a","source":{"kind":"arxiv","id":"1310.2664","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2664","created_at":"2026-05-18T01:34:05Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2664v3","created_at":"2026-05-18T01:34:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2664","created_at":"2026-05-18T01:34:05Z"},{"alias_kind":"pith_short_12","alias_value":"E34CHCEYE77W","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E34CHCEYE77WVGD3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E34CHCEY","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:E34CHCEYE77WVGD3XOECRWBEPM","target":"record","payload":{"canonical_record":{"source":{"id":"1310.2664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-09T23:58:03Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"35058feb2859c40e1e60eb2640a195191a71bfd9f3ba63d239324121342bb5ff","abstract_canon_sha256":"b0b3592d5aa1f6a1cf1031184a97353a2439b9f975bf9bcd552130bb3869226b"},"schema_version":"1.0"},"canonical_sha256":"26f823889827ff6a987bbb8828d8247b1018faac05a629c164b3fae4ffb5786a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:05.729090Z","signature_b64":"Je8Y7QWozX14EIhcT/tDMGW6sdXR5DqtEH0zpL8YwUtJwoVjrk71dDSXkzCxp7B0lgUFdmQTDVRcIU0j79PLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26f823889827ff6a987bbb8828d8247b1018faac05a629c164b3fae4ffb5786a","last_reissued_at":"2026-05-18T01:34:05.728136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:05.728136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.2664","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":"2026-05-18T01:34:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D4RqA/eG962pkNHuNvYXchpxkax57uA4Wz9sihpfX/jV0lpe+ZAjCEJz2V+5d1pq7Nq6y4EtB/+vSQhZK7kECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:15:14.660534Z"},"content_sha256":"e7698ede2e497878a656a1eabee7afccda4210658d514b02f3e269b177eee8ff","schema_version":"1.0","event_id":"sha256:e7698ede2e497878a656a1eabee7afccda4210658d514b02f3e269b177eee8ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:E34CHCEYE77WVGD3XOECRWBEPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Lars Andersson, Pieter Blue","submitted_at":"2013-10-09T23:58:03Z","abstract_excerpt":"We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localised energy density is integrable in time. For the unchanged part, we study both the full "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2664","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":""},"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":"2026-05-18T01:34:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3Z3lidvDoD3mFJU/YB8Zw4VWt/XSPUB/K47nrNMbd5UUxG6TPJeY3Ecm2f9HIMy10xHFmaOpLnD+JSrPi5nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:15:14.660905Z"},"content_sha256":"491ba74a0658b5ca4533857d4800f4a0ce999f523fc79a816908521ee3e6dc74","schema_version":"1.0","event_id":"sha256:491ba74a0658b5ca4533857d4800f4a0ce999f523fc79a816908521ee3e6dc74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E34CHCEYE77WVGD3XOECRWBEPM/bundle.json","state_url":"https://pith.science/pith/E34CHCEYE77WVGD3XOECRWBEPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E34CHCEYE77WVGD3XOECRWBEPM/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":"2026-05-27T20:15:14Z","links":{"resolver":"https://pith.science/pith/E34CHCEYE77WVGD3XOECRWBEPM","bundle":"https://pith.science/pith/E34CHCEYE77WVGD3XOECRWBEPM/bundle.json","state":"https://pith.science/pith/E34CHCEYE77WVGD3XOECRWBEPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E34CHCEYE77WVGD3XOECRWBEPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E34CHCEYE77WVGD3XOECRWBEPM","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":"b0b3592d5aa1f6a1cf1031184a97353a2439b9f975bf9bcd552130bb3869226b","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-09T23:58:03Z","title_canon_sha256":"35058feb2859c40e1e60eb2640a195191a71bfd9f3ba63d239324121342bb5ff"},"schema_version":"1.0","source":{"id":"1310.2664","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2664","created_at":"2026-05-18T01:34:05Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2664v3","created_at":"2026-05-18T01:34:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2664","created_at":"2026-05-18T01:34:05Z"},{"alias_kind":"pith_short_12","alias_value":"E34CHCEYE77W","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E34CHCEYE77WVGD3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E34CHCEY","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:491ba74a0658b5ca4533857d4800f4a0ce999f523fc79a816908521ee3e6dc74","target":"graph","created_at":"2026-05-18T01:34:05Z","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 consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole. For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$. We also prove the convergence of each solution to a stationary Coulomb solution. We separate a general solution into the charged, Coulomb part and the uncharged part. Convergence to the Coulomb solutions follows from the fact that the uncharged part satisfies a Morawetz estimate, i.e. that a spatially localised energy density is integrable in time. For the unchanged part, we study both the full ","authors_text":"Lars Andersson, Pieter Blue","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-09T23:58:03Z","title":"Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2664","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:e7698ede2e497878a656a1eabee7afccda4210658d514b02f3e269b177eee8ff","target":"record","created_at":"2026-05-18T01:34:05Z","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":"b0b3592d5aa1f6a1cf1031184a97353a2439b9f975bf9bcd552130bb3869226b","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-09T23:58:03Z","title_canon_sha256":"35058feb2859c40e1e60eb2640a195191a71bfd9f3ba63d239324121342bb5ff"},"schema_version":"1.0","source":{"id":"1310.2664","kind":"arxiv","version":3}},"canonical_sha256":"26f823889827ff6a987bbb8828d8247b1018faac05a629c164b3fae4ffb5786a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26f823889827ff6a987bbb8828d8247b1018faac05a629c164b3fae4ffb5786a","first_computed_at":"2026-05-18T01:34:05.728136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:05.728136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Je8Y7QWozX14EIhcT/tDMGW6sdXR5DqtEH0zpL8YwUtJwoVjrk71dDSXkzCxp7B0lgUFdmQTDVRcIU0j79PLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:05.729090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2664","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7698ede2e497878a656a1eabee7afccda4210658d514b02f3e269b177eee8ff","sha256:491ba74a0658b5ca4533857d4800f4a0ce999f523fc79a816908521ee3e6dc74"],"state_sha256":"4a4dc24aca50b06b721a512f174cda8e9d2f524a81bb192ffad69c11f3fa3125"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ylKxX78YEAWJvye+FjAByOLDnjMRrsSYmDmA521C9lJ/dHHQYYVLHDmAxmGCy1SXeHsIb7JKTcnqbuRs4hdwCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:15:14.663887Z","bundle_sha256":"030350b355f4587aa06651381f531897c2c68646684758d572919e2abef982ed"}}