{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DJQFKHPDQ4B7JNX4CPFI6EPFEO","short_pith_number":"pith:DJQFKHPD","canonical_record":{"source":{"id":"1711.07944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-21T18:15:42Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"adff72d38dbfdb0104847f24169d1033247812a59ae7aa2f51b190db50eb92d6","abstract_canon_sha256":"fbab4e04e1d012a2617b7f8e86a9462a632456c05ea9a56bb434c76a0af03e8c"},"schema_version":"1.0"},"canonical_sha256":"1a60551de38703f4b6fc13ca8f11e5239d20f8496f371b157219c807ddb1c645","source":{"kind":"arxiv","id":"1711.07944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07944","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07944v1","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07944","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"pith_short_12","alias_value":"DJQFKHPDQ4B7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DJQFKHPDQ4B7JNX4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DJQFKHPD","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DJQFKHPDQ4B7JNX4CPFI6EPFEO","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-21T18:15:42Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"adff72d38dbfdb0104847f24169d1033247812a59ae7aa2f51b190db50eb92d6","abstract_canon_sha256":"fbab4e04e1d012a2617b7f8e86a9462a632456c05ea9a56bb434c76a0af03e8c"},"schema_version":"1.0"},"canonical_sha256":"1a60551de38703f4b6fc13ca8f11e5239d20f8496f371b157219c807ddb1c645","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:56.105495Z","signature_b64":"tYwW391eGZZjTOqempHa7eAc+ADXiNub3gRfJTkynrWBRUsYdToFKX9moTQmGxaDSdBevB7FaIeAyMKg61MZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a60551de38703f4b6fc13ca8f11e5239d20f8496f371b157219c807ddb1c645","last_reissued_at":"2026-05-18T00:29:56.104828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:56.104828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07944","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":"2026-05-18T00:29:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YWd722c3kPVT6GttKnANQhKrMAgW0VPbcPzpQB7bkE5eZSZm1WRoq+7ROc1lSaPOVa9Icnp2vHKzlxkErncgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:32:20.706687Z"},"content_sha256":"6dab5a64e87ca6c5c1442b4a996602844ee54681c8eb220f6afd478ab19dbf7f","schema_version":"1.0","event_id":"sha256:6dab5a64e87ca6c5c1442b4a996602844ee54681c8eb220f6afd478ab19dbf7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DJQFKHPDQ4B7JNX4CPFI6EPFEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case $|a|\\ll M$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Gustav Holzegel, Igor Rodnianski, Mihalis Dafermos","submitted_at":"2017-11-21T18:15:42Z","abstract_excerpt":"We prove boundedness and polynomial decay statements for solutions of the spin $\\pm2$ Teukolsky equation on a Kerr exterior background with parameters satisfying $|a|\\ll M$. The bounds are obtained by introducing generalisations of the higher order quantities $P$ and $\\underline{P}$ used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters $|a|<M$. As in the Schwarzschild "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07944","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":"2026-05-18T00:29:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7SG8oRFF+qnYwNfe3YtptnkJvGqZ4DayCrHZoKBjxE6XU5CmxPI+BY1wIksOmQ5ZUmOPUQjX9YxZPk1pisW4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:32:20.707035Z"},"content_sha256":"95377e813bac285edcb310244c1046e8ec36005e9d220bd5ba143748dd03e20d","schema_version":"1.0","event_id":"sha256:95377e813bac285edcb310244c1046e8ec36005e9d220bd5ba143748dd03e20d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO/bundle.json","state_url":"https://pith.science/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO/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":"2026-06-01T07:32:20Z","links":{"resolver":"https://pith.science/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO","bundle":"https://pith.science/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO/bundle.json","state":"https://pith.science/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJQFKHPDQ4B7JNX4CPFI6EPFEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DJQFKHPDQ4B7JNX4CPFI6EPFEO","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":"fbab4e04e1d012a2617b7f8e86a9462a632456c05ea9a56bb434c76a0af03e8c","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-21T18:15:42Z","title_canon_sha256":"adff72d38dbfdb0104847f24169d1033247812a59ae7aa2f51b190db50eb92d6"},"schema_version":"1.0","source":{"id":"1711.07944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07944","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07944v1","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07944","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"pith_short_12","alias_value":"DJQFKHPDQ4B7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DJQFKHPDQ4B7JNX4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DJQFKHPD","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:95377e813bac285edcb310244c1046e8ec36005e9d220bd5ba143748dd03e20d","target":"graph","created_at":"2026-05-18T00:29:56Z","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 prove boundedness and polynomial decay statements for solutions of the spin $\\pm2$ Teukolsky equation on a Kerr exterior background with parameters satisfying $|a|\\ll M$. The bounds are obtained by introducing generalisations of the higher order quantities $P$ and $\\underline{P}$ used in our previous work on the linear stability of Schwarzschild. The existence of these quantities in the Schwarzschild case is related to the transformation theory of Chandrasekhar. In a followup paper, we shall extend this result to the general sub-extremal range of parameters $|a|<M$. As in the Schwarzschild ","authors_text":"Gustav Holzegel, Igor Rodnianski, Mihalis Dafermos","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-21T18:15:42Z","title":"Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case $|a|\\ll M$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07944","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":"sha256:6dab5a64e87ca6c5c1442b4a996602844ee54681c8eb220f6afd478ab19dbf7f","target":"record","created_at":"2026-05-18T00:29:56Z","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":"fbab4e04e1d012a2617b7f8e86a9462a632456c05ea9a56bb434c76a0af03e8c","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-21T18:15:42Z","title_canon_sha256":"adff72d38dbfdb0104847f24169d1033247812a59ae7aa2f51b190db50eb92d6"},"schema_version":"1.0","source":{"id":"1711.07944","kind":"arxiv","version":1}},"canonical_sha256":"1a60551de38703f4b6fc13ca8f11e5239d20f8496f371b157219c807ddb1c645","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a60551de38703f4b6fc13ca8f11e5239d20f8496f371b157219c807ddb1c645","first_computed_at":"2026-05-18T00:29:56.104828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:56.104828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tYwW391eGZZjTOqempHa7eAc+ADXiNub3gRfJTkynrWBRUsYdToFKX9moTQmGxaDSdBevB7FaIeAyMKg61MZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:56.105495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dab5a64e87ca6c5c1442b4a996602844ee54681c8eb220f6afd478ab19dbf7f","sha256:95377e813bac285edcb310244c1046e8ec36005e9d220bd5ba143748dd03e20d"],"state_sha256":"ac5a9aff133700e8c242f9754aae8b603183efed496bb93bb7e6122b58ada199"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbwCyDJZ1/8AFxGak5eTBNUi63Pbh0x49VUPiDP+8ASjGLwprdKj2lb7BZWnpDDPzB3wkeheiuWJ9HD3atf/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:32:20.709072Z","bundle_sha256":"1cf2423e6177365b0cfcf09869f753f15184dd784777d2d62f6c7af84a20fbbb"}}