{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MGGXTMLGHPE5B7BDUIWY7XLESC","short_pith_number":"pith:MGGXTMLG","schema_version":"1.0","canonical_sha256":"618d79b1663bc9d0fc23a22d8fdd649083685bb9f4949e7d501157e1a06660f3","source":{"kind":"arxiv","id":"1308.4879","version":2},"attestation_state":"computed","paper":{"title":"Inverse problem for the wave equation with a white noise source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Lauri Oksanen, Matti Lassas, Tapio Helin","submitted_at":"2013-08-22T14:37:09Z","abstract_excerpt":"We consider a smooth Riemannian metric tensor $g$ on $\\R^n$ and study the stochastic wave equation for the Laplace-Beltrami operator $\\p_t^2 u - \\Delta_g u = F$. Here, $F=F(t,x,\\omega)$ is a random source that has white noise distribution supported on the boundary of some smooth compact domain $M \\subset \\R^n$. We study the following formally posed inverse problem with only one measurement. Suppose that $g$ is known only outside of a compact subset of $M^{int}$ and that a solution $u(t,x,\\omega_0)$ is produced by a single realization of the source $F(t,x,\\omega_0)$. We ask what information reg"},"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":"1308.4879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-22T14:37:09Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"11b9f14a47fcb4bd77a2a74db2ead4d77771ec61ac29d1de0f38ba70ab6335ee","abstract_canon_sha256":"b5163d7fe8ebf97e282de31d5bb962e8c8c93402a61c90f4dac39281e1569d0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:04.652895Z","signature_b64":"g62iDyBai+0pZ3VrR/UNjWpmCa/rruc3J+Q/medol73f0F30rhNRpWpARsj0x7r0U5VPfglzypolGS29AKMiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"618d79b1663bc9d0fc23a22d8fdd649083685bb9f4949e7d501157e1a06660f3","last_reissued_at":"2026-05-18T01:48:04.652336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:04.652336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inverse problem for the wave equation with a white noise source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Lauri Oksanen, Matti Lassas, Tapio Helin","submitted_at":"2013-08-22T14:37:09Z","abstract_excerpt":"We consider a smooth Riemannian metric tensor $g$ on $\\R^n$ and study the stochastic wave equation for the Laplace-Beltrami operator $\\p_t^2 u - \\Delta_g u = F$. Here, $F=F(t,x,\\omega)$ is a random source that has white noise distribution supported on the boundary of some smooth compact domain $M \\subset \\R^n$. We study the following formally posed inverse problem with only one measurement. Suppose that $g$ is known only outside of a compact subset of $M^{int}$ and that a solution $u(t,x,\\omega_0)$ is produced by a single realization of the source $F(t,x,\\omega_0)$. We ask what information reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4879","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":"1308.4879","created_at":"2026-05-18T01:48:04.652423+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.4879v2","created_at":"2026-05-18T01:48:04.652423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4879","created_at":"2026-05-18T01:48:04.652423+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGGXTMLGHPE5","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGGXTMLGHPE5B7BD","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGGXTMLG","created_at":"2026-05-18T12:27:52.871228+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/MGGXTMLGHPE5B7BDUIWY7XLESC","json":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC.json","graph_json":"https://pith.science/api/pith-number/MGGXTMLGHPE5B7BDUIWY7XLESC/graph.json","events_json":"https://pith.science/api/pith-number/MGGXTMLGHPE5B7BDUIWY7XLESC/events.json","paper":"https://pith.science/paper/MGGXTMLG"},"agent_actions":{"view_html":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC","download_json":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC.json","view_paper":"https://pith.science/paper/MGGXTMLG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.4879&json=true","fetch_graph":"https://pith.science/api/pith-number/MGGXTMLGHPE5B7BDUIWY7XLESC/graph.json","fetch_events":"https://pith.science/api/pith-number/MGGXTMLGHPE5B7BDUIWY7XLESC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC/action/storage_attestation","attest_author":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC/action/author_attestation","sign_citation":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC/action/citation_signature","submit_replication":"https://pith.science/pith/MGGXTMLGHPE5B7BDUIWY7XLESC/action/replication_record"}},"created_at":"2026-05-18T01:48:04.652423+00:00","updated_at":"2026-05-18T01:48:04.652423+00:00"}