{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FRQONZ6Z7QXW6UBDWDBVYBU4IM","short_pith_number":"pith:FRQONZ6Z","canonical_record":{"source":{"id":"1811.02252","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-06T09:33:52Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"65f4d73997e1e019587f62f51412ecabb01985959da3fb272efcf7f23ef7e584","abstract_canon_sha256":"d4850da3137be10987424caf0882106f6c7a6d2c619efc2f2917ebeb12453ebf"},"schema_version":"1.0"},"canonical_sha256":"2c60e6e7d9fc2f6f5023b0c35c069c433bab8d7642c6acd59889e93566cd4ba4","source":{"kind":"arxiv","id":"1811.02252","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02252","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02252v4","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02252","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"pith_short_12","alias_value":"FRQONZ6Z7QXW","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"pith_short_16","alias_value":"FRQONZ6Z7QXW6UBD","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"pith_short_8","alias_value":"FRQONZ6Z","created_at":"2026-07-04T23:59:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FRQONZ6Z7QXW6UBDWDBVYBU4IM","target":"record","payload":{"canonical_record":{"source":{"id":"1811.02252","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-06T09:33:52Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"65f4d73997e1e019587f62f51412ecabb01985959da3fb272efcf7f23ef7e584","abstract_canon_sha256":"d4850da3137be10987424caf0882106f6c7a6d2c619efc2f2917ebeb12453ebf"},"schema_version":"1.0"},"canonical_sha256":"2c60e6e7d9fc2f6f5023b0c35c069c433bab8d7642c6acd59889e93566cd4ba4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:29.464820Z","signature_b64":"essikhJH/2LR5F1P8uYsiIOyVQFJV+Brr+OuO3vmYBaZgP4IDDXFOM1loUCCB3EEaKSjT/fYemBqIhWacaCUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c60e6e7d9fc2f6f5023b0c35c069c433bab8d7642c6acd59889e93566cd4ba4","last_reissued_at":"2026-07-04T23:59:29.464451Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:29.464451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.02252","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:59:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NchjXN7NSjGrZPkf1mDMxaZ26QYJgaJC2do/GikGTBMNalPXgs/uR6HODjQal59aqXnY3bXMlcfPD0Dni4ShBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:15:25.771032Z"},"content_sha256":"65348fd3909ab6320a1aae766f6fef6a9a2e230d82293484b8ebac964c84f1b8","schema_version":"1.0","event_id":"sha256:65348fd3909ab6320a1aae766f6fef6a9a2e230d82293484b8ebac964c84f1b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FRQONZ6Z7QXW6UBDWDBVYBU4IM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bin Wang, Changying Liu, Yonglei Fang","submitted_at":"2018-11-06T09:33:52Z","abstract_excerpt":"In this paper, one-stage explicit trigonometric integrators for solving quasilinear wave equations are formulated and studied. For solving wave equations, we first introduce trigonometric integrators as the semidiscretization in time and then consider a spectral Galerkin method for the discretization in space. We show that one-stage explicit trigonometric integrators in time have second-order convergence and the result is also true for the fullydiscrete scheme without requiring any CFL-type coupling of the discretization parameters. The results are proved by using energy techniques, which are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02252","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.02252/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:59:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ga3kiN8QebRrULK6S713ahN5U1V+uoICDqgo4XT6dxGJ5pm3lfS4/ZCBbw80MQsFSPBhTTmgcDqvuSqg7gRGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T18:15:25.771983Z"},"content_sha256":"4efa8eceefb74bf4a3e187317c52a20d1fc38666a5abd30952000f59bc77db5d","schema_version":"1.0","event_id":"sha256:4efa8eceefb74bf4a3e187317c52a20d1fc38666a5abd30952000f59bc77db5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM/bundle.json","state_url":"https://pith.science/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM/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":"2026-08-21T18:15:25Z","links":{"resolver":"https://pith.science/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM","bundle":"https://pith.science/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM/bundle.json","state":"https://pith.science/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRQONZ6Z7QXW6UBDWDBVYBU4IM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FRQONZ6Z7QXW6UBDWDBVYBU4IM","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":"d4850da3137be10987424caf0882106f6c7a6d2c619efc2f2917ebeb12453ebf","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-06T09:33:52Z","title_canon_sha256":"65f4d73997e1e019587f62f51412ecabb01985959da3fb272efcf7f23ef7e584"},"schema_version":"1.0","source":{"id":"1811.02252","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02252","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02252v4","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02252","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"pith_short_12","alias_value":"FRQONZ6Z7QXW","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"pith_short_16","alias_value":"FRQONZ6Z7QXW6UBD","created_at":"2026-07-04T23:59:29Z"},{"alias_kind":"pith_short_8","alias_value":"FRQONZ6Z","created_at":"2026-07-04T23:59:29Z"}],"graph_snapshots":[{"event_id":"sha256:4efa8eceefb74bf4a3e187317c52a20d1fc38666a5abd30952000f59bc77db5d","target":"graph","created_at":"2026-07-04T23:59:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.02252/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, one-stage explicit trigonometric integrators for solving quasilinear wave equations are formulated and studied. For solving wave equations, we first introduce trigonometric integrators as the semidiscretization in time and then consider a spectral Galerkin method for the discretization in space. We show that one-stage explicit trigonometric integrators in time have second-order convergence and the result is also true for the fullydiscrete scheme without requiring any CFL-type coupling of the discretization parameters. The results are proved by using energy techniques, which are ","authors_text":"Bin Wang, Changying Liu, Yonglei Fang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-06T09:33:52Z","title":"One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02252","kind":"arxiv","version":4},"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":"sha256:65348fd3909ab6320a1aae766f6fef6a9a2e230d82293484b8ebac964c84f1b8","target":"record","created_at":"2026-07-04T23:59:29Z","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":"d4850da3137be10987424caf0882106f6c7a6d2c619efc2f2917ebeb12453ebf","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-06T09:33:52Z","title_canon_sha256":"65f4d73997e1e019587f62f51412ecabb01985959da3fb272efcf7f23ef7e584"},"schema_version":"1.0","source":{"id":"1811.02252","kind":"arxiv","version":4}},"canonical_sha256":"2c60e6e7d9fc2f6f5023b0c35c069c433bab8d7642c6acd59889e93566cd4ba4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c60e6e7d9fc2f6f5023b0c35c069c433bab8d7642c6acd59889e93566cd4ba4","first_computed_at":"2026-07-04T23:59:29.464451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:29.464451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"essikhJH/2LR5F1P8uYsiIOyVQFJV+Brr+OuO3vmYBaZgP4IDDXFOM1loUCCB3EEaKSjT/fYemBqIhWacaCUBw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:29.464820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02252","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65348fd3909ab6320a1aae766f6fef6a9a2e230d82293484b8ebac964c84f1b8","sha256:4efa8eceefb74bf4a3e187317c52a20d1fc38666a5abd30952000f59bc77db5d"],"state_sha256":"5cac407e177ef3434b4a7549e28378ba573650708604772bcc0ec7470c95fc64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c9kUH2CbtCC8VwqPadHBVehkLTDdy4/1xGlzYZe41QZ0KzshDBfzAaizP7Wt9hwLHClXlYbHAkLAFkCiSa1RAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T18:15:25.782002Z","bundle_sha256":"7c707e1f0a643bc3e2bcc366702e2fb20bbab13df93fa5503849a720cdbe24be"}}