{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VKBUG5RCIILBCPBSICQLEWPD66","short_pith_number":"pith:VKBUG5RC","canonical_record":{"source":{"id":"0901.4125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-01-26T21:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"9319d15380afbd54eacb4fb029c97cb88602f93edbf0a278680305087b5f2b88","abstract_canon_sha256":"00cc998fc21b25b03c8197ebd4af7ea38d2e77a5c635389f37f69632191e31b9"},"schema_version":"1.0"},"canonical_sha256":"aa834376224216113c3240a0b259e3f7a7d2a1aec85c895b79f1bbf982d2bb7e","source":{"kind":"arxiv","id":"0901.4125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4125","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4125v1","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4125","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"VKBUG5RCIILB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VKBUG5RCIILBCPBS","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VKBUG5RC","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VKBUG5RCIILBCPBSICQLEWPD66","target":"record","payload":{"canonical_record":{"source":{"id":"0901.4125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-01-26T21:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"9319d15380afbd54eacb4fb029c97cb88602f93edbf0a278680305087b5f2b88","abstract_canon_sha256":"00cc998fc21b25b03c8197ebd4af7ea38d2e77a5c635389f37f69632191e31b9"},"schema_version":"1.0"},"canonical_sha256":"aa834376224216113c3240a0b259e3f7a7d2a1aec85c895b79f1bbf982d2bb7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:55.768247Z","signature_b64":"79UPjbigXeu0o/GTFwjRN/sXhX5yEnSSkTC/XuLTFaBuQsX8I7bPiOYTUMyk6NNKIcZFcjrmX12QZhGjIU3xDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa834376224216113c3240a0b259e3f7a7d2a1aec85c895b79f1bbf982d2bb7e","last_reissued_at":"2026-05-18T02:14:55.767639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:55.767639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.4125","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":"2026-05-18T02:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+qNkj4Hd90Ol0m6Rk27088i88TF0SAsAkVrW9eShIrR8M7Rfo2yPTIgqqVfRAP44J89P26c7dLN3xrzRMtyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:11:14.561489Z"},"content_sha256":"beb421a4bdc05ead216fa45578bd08968baae56762a270b9c4872c234e8f58ae","schema_version":"1.0","event_id":"sha256:beb421a4bdc05ead216fa45578bd08968baae56762a270b9c4872c234e8f58ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VKBUG5RCIILBCPBSICQLEWPD66","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The wave equation on axisymmetric stationary black hole backgrounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Mihalis Dafermos","submitted_at":"2009-01-26T21:38:07Z","abstract_excerpt":"Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations--a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4125","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":"2026-05-18T02:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+iPZkEEsokUhZWqtXzkE6z80wmt1Q4ZaRBCNbC2684vq24aLIk0C3noLof73KoRF7pXGqnkEPM1eoaV6ubJYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:11:14.561839Z"},"content_sha256":"80db539a649194460deb46b45f11ef030e5f3fb004898e952473d0104f635b4c","schema_version":"1.0","event_id":"sha256:80db539a649194460deb46b45f11ef030e5f3fb004898e952473d0104f635b4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKBUG5RCIILBCPBSICQLEWPD66/bundle.json","state_url":"https://pith.science/pith/VKBUG5RCIILBCPBSICQLEWPD66/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKBUG5RCIILBCPBSICQLEWPD66/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":"2026-06-01T09:11:14Z","links":{"resolver":"https://pith.science/pith/VKBUG5RCIILBCPBSICQLEWPD66","bundle":"https://pith.science/pith/VKBUG5RCIILBCPBSICQLEWPD66/bundle.json","state":"https://pith.science/pith/VKBUG5RCIILBCPBSICQLEWPD66/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKBUG5RCIILBCPBSICQLEWPD66/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VKBUG5RCIILBCPBSICQLEWPD66","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":"00cc998fc21b25b03c8197ebd4af7ea38d2e77a5c635389f37f69632191e31b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-01-26T21:38:07Z","title_canon_sha256":"9319d15380afbd54eacb4fb029c97cb88602f93edbf0a278680305087b5f2b88"},"schema_version":"1.0","source":{"id":"0901.4125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4125","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4125v1","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4125","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"VKBUG5RCIILB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VKBUG5RCIILBCPBS","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VKBUG5RC","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:80db539a649194460deb46b45f11ef030e5f3fb004898e952473d0104f635b4c","target":"graph","created_at":"2026-05-18T02:14:55Z","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":"Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations--a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with t","authors_text":"Mihalis Dafermos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-01-26T21:38:07Z","title":"The wave equation on axisymmetric stationary black hole backgrounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4125","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:beb421a4bdc05ead216fa45578bd08968baae56762a270b9c4872c234e8f58ae","target":"record","created_at":"2026-05-18T02:14:55Z","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":"00cc998fc21b25b03c8197ebd4af7ea38d2e77a5c635389f37f69632191e31b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-01-26T21:38:07Z","title_canon_sha256":"9319d15380afbd54eacb4fb029c97cb88602f93edbf0a278680305087b5f2b88"},"schema_version":"1.0","source":{"id":"0901.4125","kind":"arxiv","version":1}},"canonical_sha256":"aa834376224216113c3240a0b259e3f7a7d2a1aec85c895b79f1bbf982d2bb7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa834376224216113c3240a0b259e3f7a7d2a1aec85c895b79f1bbf982d2bb7e","first_computed_at":"2026-05-18T02:14:55.767639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:55.767639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"79UPjbigXeu0o/GTFwjRN/sXhX5yEnSSkTC/XuLTFaBuQsX8I7bPiOYTUMyk6NNKIcZFcjrmX12QZhGjIU3xDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:55.768247Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:beb421a4bdc05ead216fa45578bd08968baae56762a270b9c4872c234e8f58ae","sha256:80db539a649194460deb46b45f11ef030e5f3fb004898e952473d0104f635b4c"],"state_sha256":"d84c2a01e74c3496e1a8d829fe26acf3efd55e31a7afa57861cf42915594f54f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HwSmXK5uw/+XIYqsSssAib+hSI4WC5hMAONB03ZCO0ieZVq0qPHzAZmmkXxwgZsqZ9afa1AZakj8HtduvV1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:11:14.563837Z","bundle_sha256":"91e0f1faa2fde1c7c78d2af9082e1c193ee3ae0360e08a3b77670331f55a8897"}}