{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VRX7LB2UC5SCDBZSAIZOYX4TAO","short_pith_number":"pith:VRX7LB2U","canonical_record":{"source":{"id":"1908.07403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-20T14:46:14Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b00ae2c1bff733e79778dc2187d257d5836b19a9a99d6f5f4e05c59f109d0035","abstract_canon_sha256":"cc9677ad4d770faa17534fbab3a85ef8d017fc2614938bc8e0e85a9058a308c2"},"schema_version":"1.0"},"canonical_sha256":"ac6ff5875417642187320232ec5f9303abf64b8002ce93b6bb45c3111c39eaf4","source":{"kind":"arxiv","id":"1908.07403","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07403","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07403v1","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07403","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"VRX7LB2UC5SC","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"VRX7LB2UC5SCDBZS","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"VRX7LB2U","created_at":"2026-07-05T02:21:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VRX7LB2UC5SCDBZSAIZOYX4TAO","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-20T14:46:14Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b00ae2c1bff733e79778dc2187d257d5836b19a9a99d6f5f4e05c59f109d0035","abstract_canon_sha256":"cc9677ad4d770faa17534fbab3a85ef8d017fc2614938bc8e0e85a9058a308c2"},"schema_version":"1.0"},"canonical_sha256":"ac6ff5875417642187320232ec5f9303abf64b8002ce93b6bb45c3111c39eaf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:21:49.803703Z","signature_b64":"Y0Iz4uHLSxlkkVM0vO8THtD8KZkflCMhguZUJUsBeK+hZ1KtgETs9UcGHxRmagvX0CCMsT8GvS3+D5h1Ib/1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac6ff5875417642187320232ec5f9303abf64b8002ce93b6bb45c3111c39eaf4","last_reissued_at":"2026-07-05T02:21:49.803306Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:21:49.803306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07403","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":"2026-07-05T02:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KM9QZ9eQrAfWZ4UmX9cA3RpSxpplbTtB4qs+A0A4KNoCBtNmPDcisMb78K4dPgaMeCKFikad5pnI4hhy+qLcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:08:30.348176Z"},"content_sha256":"7cb7a5c4e9eab520ba62cc9e2212085d14568f11fe0980ed44aff9dba609ff03","schema_version":"1.0","event_id":"sha256:7cb7a5c4e9eab520ba62cc9e2212085d14568f11fe0980ed44aff9dba609ff03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VRX7LB2UC5SCDBZSAIZOYX4TAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hatef Dastour, Wenyuan Liao","submitted_at":"2019-08-20T14:46:14Z","abstract_excerpt":"A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome when the perfectly matched layer (PML) boundary condition is implemented. In this paper, we present a general approach for constructing fourth-order finite difference schemes for the Helmholtz equation with PML in the two-dimensional domain based on point-weighting strategy. Particularly, we develop two optimal fourth-order finite difference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07403","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07403/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":"2026-07-05T02:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DB25dKdEL9hQ4QWMcS4/uCOE7vFQXPulYaC5Epbv7r+LKpFbtS2qeGoTzOwcGAdpxiaL9QrJ3+VItYnq+68cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:08:30.348755Z"},"content_sha256":"5f903fe18deff39e554582ab22052de7f1c51a2968687107b7e2920932e51bfb","schema_version":"1.0","event_id":"sha256:5f903fe18deff39e554582ab22052de7f1c51a2968687107b7e2920932e51bfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO/bundle.json","state_url":"https://pith.science/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO/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":"2026-08-16T10:08:30Z","links":{"resolver":"https://pith.science/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO","bundle":"https://pith.science/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO/bundle.json","state":"https://pith.science/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRX7LB2UC5SCDBZSAIZOYX4TAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VRX7LB2UC5SCDBZSAIZOYX4TAO","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":"cc9677ad4d770faa17534fbab3a85ef8d017fc2614938bc8e0e85a9058a308c2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-20T14:46:14Z","title_canon_sha256":"b00ae2c1bff733e79778dc2187d257d5836b19a9a99d6f5f4e05c59f109d0035"},"schema_version":"1.0","source":{"id":"1908.07403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07403","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07403v1","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07403","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"VRX7LB2UC5SC","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_16","alias_value":"VRX7LB2UC5SCDBZS","created_at":"2026-07-05T02:21:49Z"},{"alias_kind":"pith_short_8","alias_value":"VRX7LB2U","created_at":"2026-07-05T02:21:49Z"}],"graph_snapshots":[{"event_id":"sha256:5f903fe18deff39e554582ab22052de7f1c51a2968687107b7e2920932e51bfb","target":"graph","created_at":"2026-07-05T02:21:49Z","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/1908.07403/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can be troublesome when the perfectly matched layer (PML) boundary condition is implemented. In this paper, we present a general approach for constructing fourth-order finite difference schemes for the Helmholtz equation with PML in the two-dimensional domain based on point-weighting strategy. Particularly, we develop two optimal fourth-order finite difference ","authors_text":"Hatef Dastour, Wenyuan Liao","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-20T14:46:14Z","title":"A generalized optimal fourth-order finite difference scheme for a 2D Helmholtz equation with the perfectly matched layer boundary condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07403","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":"sha256:7cb7a5c4e9eab520ba62cc9e2212085d14568f11fe0980ed44aff9dba609ff03","target":"record","created_at":"2026-07-05T02:21:49Z","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":"cc9677ad4d770faa17534fbab3a85ef8d017fc2614938bc8e0e85a9058a308c2","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-20T14:46:14Z","title_canon_sha256":"b00ae2c1bff733e79778dc2187d257d5836b19a9a99d6f5f4e05c59f109d0035"},"schema_version":"1.0","source":{"id":"1908.07403","kind":"arxiv","version":1}},"canonical_sha256":"ac6ff5875417642187320232ec5f9303abf64b8002ce93b6bb45c3111c39eaf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac6ff5875417642187320232ec5f9303abf64b8002ce93b6bb45c3111c39eaf4","first_computed_at":"2026-07-05T02:21:49.803306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:49.803306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0Iz4uHLSxlkkVM0vO8THtD8KZkflCMhguZUJUsBeK+hZ1KtgETs9UcGHxRmagvX0CCMsT8GvS3+D5h1Ib/1BA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:49.803703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cb7a5c4e9eab520ba62cc9e2212085d14568f11fe0980ed44aff9dba609ff03","sha256:5f903fe18deff39e554582ab22052de7f1c51a2968687107b7e2920932e51bfb"],"state_sha256":"d233b96298975cf8811a34b921a216c002f1a44c6fcd51ed48c9f9fd3dae8547"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21Kb9ogLZ5EgtlkHhxj5Y7M2cqJsXnlrmNoyK/Krw5KNqovSY1gAih//dYLgan4jFJSzjBm8hztZF5g7FNCTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:08:30.354961Z","bundle_sha256":"5cca0f0b67108a7cd3a0000bb6fe344acdc53ce80252596b16a18e6717c740d2"}}