{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MGGXTMLGHPE5B7BDUIWY7XLESC","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":"b5163d7fe8ebf97e282de31d5bb962e8c8c93402a61c90f4dac39281e1569d0b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-22T14:37:09Z","title_canon_sha256":"11b9f14a47fcb4bd77a2a74db2ead4d77771ec61ac29d1de0f38ba70ab6335ee"},"schema_version":"1.0","source":{"id":"1308.4879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4879","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4879v2","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4879","created_at":"2026-05-18T01:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"MGGXTMLGHPE5","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MGGXTMLGHPE5B7BD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MGGXTMLG","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:4f2fa2778baf0800461bb651950b09774bab034a31cccf1318294d849e159b4e","target":"graph","created_at":"2026-05-18T01:48:04Z","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":"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","authors_text":"Lauri Oksanen, Matti Lassas, Tapio Helin","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-22T14:37:09Z","title":"Inverse problem for the wave equation with a white noise source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4879","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:b3f5584752227ee1ea0d6e29180b25a9279b1c5e7a9449981b5a1b0c927ce1c1","target":"record","created_at":"2026-05-18T01:48:04Z","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":"b5163d7fe8ebf97e282de31d5bb962e8c8c93402a61c90f4dac39281e1569d0b","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-22T14:37:09Z","title_canon_sha256":"11b9f14a47fcb4bd77a2a74db2ead4d77771ec61ac29d1de0f38ba70ab6335ee"},"schema_version":"1.0","source":{"id":"1308.4879","kind":"arxiv","version":2}},"canonical_sha256":"618d79b1663bc9d0fc23a22d8fdd649083685bb9f4949e7d501157e1a06660f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"618d79b1663bc9d0fc23a22d8fdd649083685bb9f4949e7d501157e1a06660f3","first_computed_at":"2026-05-18T01:48:04.652336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:48:04.652336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g62iDyBai+0pZ3VrR/UNjWpmCa/rruc3J+Q/medol73f0F30rhNRpWpARsj0x7r0U5VPfglzypolGS29AKMiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:48:04.652895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f5584752227ee1ea0d6e29180b25a9279b1c5e7a9449981b5a1b0c927ce1c1","sha256:4f2fa2778baf0800461bb651950b09774bab034a31cccf1318294d849e159b4e"],"state_sha256":"b8adccb6ddac0b48c040b1be7721d64f2d0a6c40a6665557afb2a75dbf83bbab"}