{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PCRWWVR36BK65Q555X35CRKQR2","short_pith_number":"pith:PCRWWVR3","schema_version":"1.0","canonical_sha256":"78a36b563bf055eec3bdedf7d145508ea87779c7c189dd86916c1176d13c51b1","source":{"kind":"arxiv","id":"1507.05508","version":2},"attestation_state":"computed","paper":{"title":"A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gabriela Malenova, Mohammad Motamed, Olof Runborg, Raul Tempone","submitted_at":"2015-07-20T14:26:49Z","abstract_excerpt":"We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, $u^\\varepsilon$, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments and numerical evidence that quantities of interest based on local averages of $|u^\\varepsilon|^2$ are smooth, with derivatives in "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.05508","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-20T14:26:49Z","cross_cats_sorted":[],"title_canon_sha256":"a17277e2b39567d5004c9bef9d87b385efc5d1501a32cde474f0e0461fad47a5","abstract_canon_sha256":"3b284e6082e6334c74fd0dd44b4b777a1e757838c11595c3b42c02632aee16af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:26.346354Z","signature_b64":"Km/G+CN09YI1HvOl4SygSDdYN6iyQEbWwGjDtXtvQX2WQS2qQzF8anWryfTCMLJwUjOpMJp6nO6XKGIr8liHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a36b563bf055eec3bdedf7d145508ea87779c7c189dd86916c1176d13c51b1","last_reissued_at":"2026-05-18T01:33:26.345574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:26.345574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gabriela Malenova, Mohammad Motamed, Olof Runborg, Raul Tempone","submitted_at":"2015-07-20T14:26:49Z","abstract_excerpt":"We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, $u^\\varepsilon$, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments and numerical evidence that quantities of interest based on local averages of $|u^\\varepsilon|^2$ are smooth, with derivatives in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05508","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.05508","created_at":"2026-05-18T01:33:26.345682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05508v2","created_at":"2026-05-18T01:33:26.345682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05508","created_at":"2026-05-18T01:33:26.345682+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCRWWVR36BK6","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCRWWVR36BK65Q55","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCRWWVR3","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2","json":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2.json","graph_json":"https://pith.science/api/pith-number/PCRWWVR36BK65Q555X35CRKQR2/graph.json","events_json":"https://pith.science/api/pith-number/PCRWWVR36BK65Q555X35CRKQR2/events.json","paper":"https://pith.science/paper/PCRWWVR3"},"agent_actions":{"view_html":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2","download_json":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2.json","view_paper":"https://pith.science/paper/PCRWWVR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05508&json=true","fetch_graph":"https://pith.science/api/pith-number/PCRWWVR36BK65Q555X35CRKQR2/graph.json","fetch_events":"https://pith.science/api/pith-number/PCRWWVR36BK65Q555X35CRKQR2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2/action/storage_attestation","attest_author":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2/action/author_attestation","sign_citation":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2/action/citation_signature","submit_replication":"https://pith.science/pith/PCRWWVR36BK65Q555X35CRKQR2/action/replication_record"}},"created_at":"2026-05-18T01:33:26.345682+00:00","updated_at":"2026-05-18T01:33:26.345682+00:00"}