{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RCPQMUC5OPRLC3I7OTAT7EGK2O","short_pith_number":"pith:RCPQMUC5","canonical_record":{"source":{"id":"1703.08064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-23T13:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"61a7c044d9df41863efe5c75e0917e73d11a1a2d94519d43fa6729af01f1deb7","abstract_canon_sha256":"3d4b653f22f1dd8a500b47f8a0b4a116615ae5ea2b3e559d492e074d0eb5a7a7"},"schema_version":"1.0"},"canonical_sha256":"889f06505d73e2b16d1f74c13f90cad3b5fd9eb60321977c48c97c163a5cc780","source":{"kind":"arxiv","id":"1703.08064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08064","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08064v1","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08064","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"RCPQMUC5OPRL","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RCPQMUC5OPRLC3I7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RCPQMUC5","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RCPQMUC5OPRLC3I7OTAT7EGK2O","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-23T13:37:49Z","cross_cats_sorted":[],"title_canon_sha256":"61a7c044d9df41863efe5c75e0917e73d11a1a2d94519d43fa6729af01f1deb7","abstract_canon_sha256":"3d4b653f22f1dd8a500b47f8a0b4a116615ae5ea2b3e559d492e074d0eb5a7a7"},"schema_version":"1.0"},"canonical_sha256":"889f06505d73e2b16d1f74c13f90cad3b5fd9eb60321977c48c97c163a5cc780","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:03.994356Z","signature_b64":"mhn1Nb8ZXwPN6vbyfv0uhVDCpBLNWxanbdptlo01P6k7k7EfmItXJBLEVQoXUwwDbRXeBgAEiMbEX3Wz9QZlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"889f06505d73e2b16d1f74c13f90cad3b5fd9eb60321977c48c97c163a5cc780","last_reissued_at":"2026-05-18T00:48:03.993791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:03.993791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08064","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":"2026-05-18T00:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NR1O8v629N+Auh0SYdNN+fAp4aJzT2su0G6Nt0UVc8MXMtg1lX9ArXIxzt0Ksftj4n5gy/pL9QiZ20OYcobLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:32:00.971052Z"},"content_sha256":"1b81c8be84ad56e68430f3bbdebefb67c2f70774b34324974abe22847c520203","schema_version":"1.0","event_id":"sha256:1b81c8be84ad56e68430f3bbdebefb67c2f70774b34324974abe22847c520203"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RCPQMUC5OPRLC3I7OTAT7EGK2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local energy decay for scalar fields on time dependent non-trapping backgrounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Tataru, Jacob Sterbenz, Jason Metcalfe","submitted_at":"2017-03-23T13:37:49Z","abstract_excerpt":"We consider local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times. Our goals are two-fold. First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case. Then we consider the almost stationary, almost symmetric case. There we establish two main results: The first is a \"two point\" local energy decay estimate which is valid for a general class of (non-symmetric) almost stationary wave equations which satisfy a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08064","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":"2026-05-18T00:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kSp7u6F0f82/fhJe8GgH5jqy7wZAn6jq/LXHOjr/Gq2dnLGFel2+AMkfETMkHz7LYfXfizqU4jxWfkM0GnuzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:32:00.971482Z"},"content_sha256":"a8efb12062ab20d0fa2c2963f22600c6cf15845913930e5aa98e14bd925f9c88","schema_version":"1.0","event_id":"sha256:a8efb12062ab20d0fa2c2963f22600c6cf15845913930e5aa98e14bd925f9c88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O/bundle.json","state_url":"https://pith.science/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O/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":"2026-06-10T22:32:00Z","links":{"resolver":"https://pith.science/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O","bundle":"https://pith.science/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O/bundle.json","state":"https://pith.science/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCPQMUC5OPRLC3I7OTAT7EGK2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RCPQMUC5OPRLC3I7OTAT7EGK2O","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":"3d4b653f22f1dd8a500b47f8a0b4a116615ae5ea2b3e559d492e074d0eb5a7a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-23T13:37:49Z","title_canon_sha256":"61a7c044d9df41863efe5c75e0917e73d11a1a2d94519d43fa6729af01f1deb7"},"schema_version":"1.0","source":{"id":"1703.08064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08064","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08064v1","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08064","created_at":"2026-05-18T00:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"RCPQMUC5OPRL","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RCPQMUC5OPRLC3I7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RCPQMUC5","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:a8efb12062ab20d0fa2c2963f22600c6cf15845913930e5aa98e14bd925f9c88","target":"graph","created_at":"2026-05-18T00:48:03Z","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 local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times. Our goals are two-fold. First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case. Then we consider the almost stationary, almost symmetric case. There we establish two main results: The first is a \"two point\" local energy decay estimate which is valid for a general class of (non-symmetric) almost stationary wave equations which satisfy a ","authors_text":"Daniel Tataru, Jacob Sterbenz, Jason Metcalfe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-23T13:37:49Z","title":"Local energy decay for scalar fields on time dependent non-trapping backgrounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08064","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":"sha256:1b81c8be84ad56e68430f3bbdebefb67c2f70774b34324974abe22847c520203","target":"record","created_at":"2026-05-18T00:48:03Z","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":"3d4b653f22f1dd8a500b47f8a0b4a116615ae5ea2b3e559d492e074d0eb5a7a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-23T13:37:49Z","title_canon_sha256":"61a7c044d9df41863efe5c75e0917e73d11a1a2d94519d43fa6729af01f1deb7"},"schema_version":"1.0","source":{"id":"1703.08064","kind":"arxiv","version":1}},"canonical_sha256":"889f06505d73e2b16d1f74c13f90cad3b5fd9eb60321977c48c97c163a5cc780","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"889f06505d73e2b16d1f74c13f90cad3b5fd9eb60321977c48c97c163a5cc780","first_computed_at":"2026-05-18T00:48:03.993791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:03.993791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mhn1Nb8ZXwPN6vbyfv0uhVDCpBLNWxanbdptlo01P6k7k7EfmItXJBLEVQoXUwwDbRXeBgAEiMbEX3Wz9QZlDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:03.994356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b81c8be84ad56e68430f3bbdebefb67c2f70774b34324974abe22847c520203","sha256:a8efb12062ab20d0fa2c2963f22600c6cf15845913930e5aa98e14bd925f9c88"],"state_sha256":"33d5fc382eae384ce83fbb2049c54054078f01acaa83b4e93d0d283df5d1276a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKXkOr1WaMQ95Dk18HPCCj94jje8Dh/kiBk2cv/qx0s8HaeSSWAn++LMtgRr3PgRXd0lcnzBDlbyJa72KlCmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:32:00.973540Z","bundle_sha256":"dbc1db5e64cb92fd22acdf1969389767123727506712e93abeb27ec0869e2b6e"}}