{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SZYHU7ZOUED4DMXRHVTSSUG6IH","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":"c596fd1912ad0e6ebaf6ef1cf580fc3f517f20cb27b3ffd6f3f1c0713e82bf00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-21T20:52:05Z","title_canon_sha256":"c30a3c5a1b3873775bd8f56ccc04934f73a02f8fc53c9e7bc6caa8877aa5cfcd"},"schema_version":"1.0","source":{"id":"1402.5407","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5407","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5407v2","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5407","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"SZYHU7ZOUED4","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SZYHU7ZOUED4DMXR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SZYHU7ZO","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:266c3119b1027be79f1ccf9078a1fb3a4464fd894e3acc66f17f9d5a188448c0","target":"graph","created_at":"2026-05-18T02:55:12Z","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":"This paper is concerned with developing efficient numerical methods for acoustic wave scattering in random media which can be expressed as random perturbations of homogeneous media. We first analyze the random Helmholtz problem by deriving some wave-number-explicit solution estimates. We then establish a multi-modes representation of the solution as a power series of the perturbation parameter and analyze its finite modes approximations. Based on this multi-modes representation, we develop a Monte Carlo interior penalty discontinuous Galerkin (MCIP-DG) method for approximating the mode functio","authors_text":"Cody Lorton, Junshan Lin, Xiaobing Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-21T20:52:05Z","title":"An efficient numerical method for acoustic wave scattering in random media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5407","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":"sha256:872e616c67c55bdbbabfaf129f229bcbfca1b55fbc3ccc3bf28ae3e242e063d7","target":"record","created_at":"2026-05-18T02:55:12Z","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":"c596fd1912ad0e6ebaf6ef1cf580fc3f517f20cb27b3ffd6f3f1c0713e82bf00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-21T20:52:05Z","title_canon_sha256":"c30a3c5a1b3873775bd8f56ccc04934f73a02f8fc53c9e7bc6caa8877aa5cfcd"},"schema_version":"1.0","source":{"id":"1402.5407","kind":"arxiv","version":2}},"canonical_sha256":"96707a7f2ea107c1b2f13d672950de41e0834d2ecfe43b59aada5c63a3167a3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96707a7f2ea107c1b2f13d672950de41e0834d2ecfe43b59aada5c63a3167a3c","first_computed_at":"2026-05-18T02:55:12.957308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:12.957308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GU1yHWjGhU6olfHle0Da1dIaAQjJoMs3oBd07oFmx8sTdlIM3Oo4bSqKgSnsP3FSPGMCQSGwQ13FMdDz24CXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:12.957769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5407","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:872e616c67c55bdbbabfaf129f229bcbfca1b55fbc3ccc3bf28ae3e242e063d7","sha256:266c3119b1027be79f1ccf9078a1fb3a4464fd894e3acc66f17f9d5a188448c0"],"state_sha256":"3266603d4b7de865e41c87d03aa214a4fdc1b1abb9b84d61ff3917803426376b"}