{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4IRWTOZWTB66YEMJSSVPAHVHI7","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":"05da3a2d00933c58c67bd3c83e72444f33b34f728e22376e677ca0ec3ee4f9d2","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-25T14:16:11Z","title_canon_sha256":"d9fb752e299dca76c47a156bdceceb10d3e7e00528c3982f48dddba06ac7a254"},"schema_version":"1.0","source":{"id":"1010.5137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5137","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5137v1","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5137","created_at":"2026-05-18T00:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"4IRWTOZWTB66","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4IRWTOZWTB66YEMJ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4IRWTOZW","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:381c0f388e2082bb0deb31437691f27e55d58f69b5f9d8b969fe7a9e8935ee0d","target":"graph","created_at":"2026-05-18T00:37:22Z","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 review our recent work on linear stability for scalar perturbations of Kerr spacetimes, that is to say, boundedness and decay properties for solutions of the scalar wave equation \\Box_g{\\psi} = 0 on Kerr exterior backgrounds. We begin with the very slowly rotating case |a| \\ll M, where first boundedness and then decay has been shown in rapid developments over the last two years, following earlier progress in the Schwarzschild case a = 0. We then turn to the general subextremal range |a| < M, where we give here for the first time the essential elements of a proof of definitive decay bounds f","authors_text":"Igor Rodnianski, Mihalis Dafermos","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-25T14:16:11Z","title":"The black hole stability problem for linear scalar perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5137","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":"sha256:6fe490d12bad1783ef50736c175fe0758fcedc3023d780190b49823786f8340f","target":"record","created_at":"2026-05-18T00:37:22Z","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":"05da3a2d00933c58c67bd3c83e72444f33b34f728e22376e677ca0ec3ee4f9d2","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-25T14:16:11Z","title_canon_sha256":"d9fb752e299dca76c47a156bdceceb10d3e7e00528c3982f48dddba06ac7a254"},"schema_version":"1.0","source":{"id":"1010.5137","kind":"arxiv","version":1}},"canonical_sha256":"e22369bb36987dec118994aaf01ea747ed36826f952254007814002955e82d6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e22369bb36987dec118994aaf01ea747ed36826f952254007814002955e82d6f","first_computed_at":"2026-05-18T00:37:22.771961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:22.771961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kfq9Yps1wgtFHTeBPyX/cMjk4Rn+lWVOf25h24X44e0FoGo4jaii8Hb+hTeqNaxeLL8Mfx3MBjODKjP1belSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:22.772536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe490d12bad1783ef50736c175fe0758fcedc3023d780190b49823786f8340f","sha256:381c0f388e2082bb0deb31437691f27e55d58f69b5f9d8b969fe7a9e8935ee0d"],"state_sha256":"32875ee2df0b01e781988fbcb43812fc73a60088b6f54d27557717788eaf2ac8"}