{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JN5CCSU26SFV43F3GMT5WPB3I5","short_pith_number":"pith:JN5CCSU2","canonical_record":{"source":{"id":"1401.0984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-06T04:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"8af030070c5cb81c5278b6197d8e493ef87a9df8e9eba478212394c263e32cf7","abstract_canon_sha256":"3c265360ac95f4fd1d9599b51636ab04b41fc76b38f74d96b9e40585da9d866c"},"schema_version":"1.0"},"canonical_sha256":"4b7a214a9af48b5e6cbb3327db3c3b476e84fd0438ee535f880ec858b7ecfc83","source":{"kind":"arxiv","id":"1401.0984","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0984","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0984v2","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0984","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"JN5CCSU26SFV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JN5CCSU26SFV43F3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JN5CCSU2","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JN5CCSU26SFV43F3GMT5WPB3I5","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-06T04:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"8af030070c5cb81c5278b6197d8e493ef87a9df8e9eba478212394c263e32cf7","abstract_canon_sha256":"3c265360ac95f4fd1d9599b51636ab04b41fc76b38f74d96b9e40585da9d866c"},"schema_version":"1.0"},"canonical_sha256":"4b7a214a9af48b5e6cbb3327db3c3b476e84fd0438ee535f880ec858b7ecfc83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:06.174369Z","signature_b64":"mJPa091SkaIliU5ywZsmVof02WJKt//ydKsrmi+ExfUuDsHfk/6KJ3uyisk6S/07UH4rdLJgrBV3LKAIgVjJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7a214a9af48b5e6cbb3327db3c3b476e84fd0438ee535f880ec858b7ecfc83","last_reissued_at":"2026-05-18T02:19:06.173772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:06.173772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0984","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+S4CyChASAiZ9C9ebtVwdEZLf7XP3TPaFsrnC06EkqAiZTE7Mx8Y7HAJ/7HepO5iABSbEhXXBv7sdJRujQVvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:15:21.002197Z"},"content_sha256":"821f4ae0b0edb65f339313974af4f27a544b0939731e8e66b02e5b16a9740069","schema_version":"1.0","event_id":"sha256:821f4ae0b0edb65f339313974af4f27a544b0939731e8e66b02e5b16a9740069"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JN5CCSU26SFV43F3GMT5WPB3I5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Weizhu Bao, Xiaofei Zhao, Yongyong Cai","submitted_at":"2014-01-06T04:47:00Z","abstract_excerpt":"We propose and analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for solving the Klein-Gordon (KG) equation with a dimensionless parameter $0<\\varepsilon\\leq1$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e. $0<\\varepsilon\\ll1$, the solution to the KG equation propagates waves with amplitude at $O(1)$ and wavelength at $O(\\varepsilon^2)$ in time and $O(1)$ in space, which causes significantly numerical burdens due to the high oscillation in time. The MTI-FP method is designed by adapting a multiscale decomposition by fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0984","kind":"arxiv","version":2},"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":"2026-05-18T02:19:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOfcQWA3Ey3Kbwx/ZKWxDZUMo/6/HX40oGVZmyUzP3EZMUI7ctiJn4iqR9wsnXEM8W0vxhC5i90AjTTNajBlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:15:21.002565Z"},"content_sha256":"bd92779e2a00c3bb3a42013432f90561c49fe223947f771f860d2e219b4c6d2d","schema_version":"1.0","event_id":"sha256:bd92779e2a00c3bb3a42013432f90561c49fe223947f771f860d2e219b4c6d2d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JN5CCSU26SFV43F3GMT5WPB3I5/bundle.json","state_url":"https://pith.science/pith/JN5CCSU26SFV43F3GMT5WPB3I5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JN5CCSU26SFV43F3GMT5WPB3I5/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":"2026-06-03T08:15:21Z","links":{"resolver":"https://pith.science/pith/JN5CCSU26SFV43F3GMT5WPB3I5","bundle":"https://pith.science/pith/JN5CCSU26SFV43F3GMT5WPB3I5/bundle.json","state":"https://pith.science/pith/JN5CCSU26SFV43F3GMT5WPB3I5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JN5CCSU26SFV43F3GMT5WPB3I5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JN5CCSU26SFV43F3GMT5WPB3I5","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":"3c265360ac95f4fd1d9599b51636ab04b41fc76b38f74d96b9e40585da9d866c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-06T04:47:00Z","title_canon_sha256":"8af030070c5cb81c5278b6197d8e493ef87a9df8e9eba478212394c263e32cf7"},"schema_version":"1.0","source":{"id":"1401.0984","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0984","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0984v2","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0984","created_at":"2026-05-18T02:19:06Z"},{"alias_kind":"pith_short_12","alias_value":"JN5CCSU26SFV","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JN5CCSU26SFV43F3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JN5CCSU2","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:bd92779e2a00c3bb3a42013432f90561c49fe223947f771f860d2e219b4c6d2d","target":"graph","created_at":"2026-05-18T02:19:06Z","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 propose and analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for solving the Klein-Gordon (KG) equation with a dimensionless parameter $0<\\varepsilon\\leq1$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e. $0<\\varepsilon\\ll1$, the solution to the KG equation propagates waves with amplitude at $O(1)$ and wavelength at $O(\\varepsilon^2)$ in time and $O(1)$ in space, which causes significantly numerical burdens due to the high oscillation in time. The MTI-FP method is designed by adapting a multiscale decomposition by fr","authors_text":"Weizhu Bao, Xiaofei Zhao, Yongyong Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-06T04:47:00Z","title":"A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0984","kind":"arxiv","version":2},"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":"sha256:821f4ae0b0edb65f339313974af4f27a544b0939731e8e66b02e5b16a9740069","target":"record","created_at":"2026-05-18T02:19:06Z","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":"3c265360ac95f4fd1d9599b51636ab04b41fc76b38f74d96b9e40585da9d866c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-06T04:47:00Z","title_canon_sha256":"8af030070c5cb81c5278b6197d8e493ef87a9df8e9eba478212394c263e32cf7"},"schema_version":"1.0","source":{"id":"1401.0984","kind":"arxiv","version":2}},"canonical_sha256":"4b7a214a9af48b5e6cbb3327db3c3b476e84fd0438ee535f880ec858b7ecfc83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7a214a9af48b5e6cbb3327db3c3b476e84fd0438ee535f880ec858b7ecfc83","first_computed_at":"2026-05-18T02:19:06.173772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:06.173772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJPa091SkaIliU5ywZsmVof02WJKt//ydKsrmi+ExfUuDsHfk/6KJ3uyisk6S/07UH4rdLJgrBV3LKAIgVjJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:06.174369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:821f4ae0b0edb65f339313974af4f27a544b0939731e8e66b02e5b16a9740069","sha256:bd92779e2a00c3bb3a42013432f90561c49fe223947f771f860d2e219b4c6d2d"],"state_sha256":"28612413891af74ad1a0a73213584e0aa7c98755ed73b78a9579e783fc17c17b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdxzQrg0Bvrr0Hu1Kg0jmKK7C75BGYHdSLyKNZoh4SlxbZ9XAiv+VtiX1xvsKmbXUB8j+ischbvwS1Re3lQhBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:15:21.004686Z","bundle_sha256":"5a4fc96abbe7a8e860a5c9f2b872c5567d510e115b3d8cbdb0dd01e3f0df1003"}}