{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MPNKIU3ABSCC643GTUOAMCRBJI","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":"d487762e05d9c66e870fc43c3bdf67791ceec38c0f4650617ace556a51a1684f","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-25T14:07:37Z","title_canon_sha256":"7a0184eea5e438a192364c0c814d7a9f63ead32ec9ea65d130a36c3352c3be43"},"schema_version":"1.0","source":{"id":"1010.5132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5132","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5132v1","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5132","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"pith_short_12","alias_value":"MPNKIU3ABSCC","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MPNKIU3ABSCC643G","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MPNKIU3A","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:83ce75cfa5f72eb6f8b8e0536d4ccb14fb7aebfeda3e9dc5e69c1a5bab1f4561","target":"graph","created_at":"2026-05-18T04:38:49Z","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":"This paper contains the first two parts (I-II) of a three-part series concerning the scalar wave equation \\Box_g{\\psi} = 0 on a fixed Kerr background. We here restrict to two cases: (II1) |a| \\ll M, general {\\psi} or (II2) |a| < M, {\\psi} axisymmetric. In either case, we prove a version of 'integrated local energy decay', specifically, that the 4-integral of an energy-type density (degenerating in a neighborhood of the Schwarzschild photon sphere and at infinity), integrated over the domain of dependence of a spacelike hypersurface {\\Sigma} connecting the future event horizon with spacelike in","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":"2010-10-25T14:07:37Z","title":"Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The cases |a| << M or axisymmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5132","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":"sha256:73938f829af2748139e49cf7748e2bdc5ba1fc83d01f9870aa0b5a4782e82d97","target":"record","created_at":"2026-05-18T04:38:49Z","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":"d487762e05d9c66e870fc43c3bdf67791ceec38c0f4650617ace556a51a1684f","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-25T14:07:37Z","title_canon_sha256":"7a0184eea5e438a192364c0c814d7a9f63ead32ec9ea65d130a36c3352c3be43"},"schema_version":"1.0","source":{"id":"1010.5132","kind":"arxiv","version":1}},"canonical_sha256":"63daa453600c842f73669d1c060a214a23a30e87e2e5424bd2bf6d4742f5abf3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63daa453600c842f73669d1c060a214a23a30e87e2e5424bd2bf6d4742f5abf3","first_computed_at":"2026-05-18T04:38:49.332217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:49.332217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UwaswN0pQHZzCRt1D9cb3kiDR+x0/y9R2UI+FS0PsvHqDnq7PGfdrxT//NsMy0MUP1J94/lhlAKoFPk4jUJ/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:49.332699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73938f829af2748139e49cf7748e2bdc5ba1fc83d01f9870aa0b5a4782e82d97","sha256:83ce75cfa5f72eb6f8b8e0536d4ccb14fb7aebfeda3e9dc5e69c1a5bab1f4561"],"state_sha256":"a9aac54ea18d6b6771a68118f4987a01a3e57a24cdc5277ba130acc4bec5b82f"}