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We define a deterministic source $f(t,x)$ called the pseudorandom noise as a sum of point sources, $f(t,x)=\\sum_{j=1}^\\infty a_j\\delta_{x_j}(x)\\delta(t)$, where the points $x_j,\\ j\\in\\Z_+$, form a dense set on $\\p M$. We show that when the weights $a_j$ are chosen appropriately, $u|_{\\R\\times \\p M}$ determines the scattering relation on $\\p M$, that is, it determines "},"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":"1011.2527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-10T23:18:02Z","cross_cats_sorted":[],"title_canon_sha256":"a69f64e00cd30a8ae48877418ad1a8e8b94aabfc58aeb8c9647a6881be090296","abstract_canon_sha256":"40850173dfc318bd7b329ae48396b15c94079595df588e70206f5aefb49e9745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:10.112870Z","signature_b64":"284u36TJ2GSuMd178uIz095OqIA+2cU+crdumH4PA6g5Pnqyl/TduYNDjbQqr70lgaJextC9CDRPF1rYIkUUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60f05387653826e7925c46a664fa0acbb67cad61b9ddf1c9e89f24b384121964","last_reissued_at":"2026-05-18T04:36:10.112420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:10.112420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An inverse problem for the wave equation with one measurement and the pseudorandom noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lauri Oksanen, Matti Lassas, Tapio Helin","submitted_at":"2010-11-10T23:18:02Z","abstract_excerpt":"We consider the wave equation $(\\p_t^2-\\Delta_g)u(t,x)=f(t,x)$, in $\\R^n$, $u|_{\\R_-\\times \\R^n}=0$, where the metric $g=(g_{jk}(x))_{j,k=1}^n$ is known outside an open and bounded set $M\\subset \\R^n$ with smooth boundary $\\p M$. 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