{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FMBMJJDMHOJSFVJ4Q2KM5HIPBG","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":"47808c8a1b6e2d9960c7258016eb8f906437b376cceb02ed825b310804c39ed0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-10T07:39:11Z","title_canon_sha256":"6d80b26f7df4bb36e648aac2d5991142280817f5f5b7b825589c112d8995a215"},"schema_version":"1.0","source":{"id":"1208.2105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2105","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2105v1","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2105","created_at":"2026-05-18T02:29:32Z"},{"alias_kind":"pith_short_12","alias_value":"FMBMJJDMHOJS","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FMBMJJDMHOJSFVJ4","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FMBMJJDM","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:7bddfe756a502dc6e5e4b040be6eb035f8f9fee9647b737eea9afe8fadf89538","target":"graph","created_at":"2026-05-18T02:29:32Z","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 the inverse problem to determine a smooth compact Riemannian manifold with boundary $(M, g)$ from a restriction $\\Lambda_{\\Src, \\Rec}$ of the Dirichlet-to-Neumann operator for the wave equation on the manifold. Here $\\Src$ and $\\Rec$ are open sets in $\\p M$ and the restriction $\\Lambda_{\\Src, \\Rec}$ corresponds to the case where the Dirichlet data is supported on $\\R_+\\times \\Src$ and the Neumann data is measured on $\\R_+\\times \\Rec$. In the novel case where $\\bar \\Src \\cap \\bar \\Rec = \\emptyset$, we show that $\\Lambda_{\\Src, \\Rec}$ determines the manifold $(M,g)$ uniquely, assumin","authors_text":"Lauri Oksanen, Matti Lassas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-10T07:39:11Z","title":"Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2105","kind":"arxiv","version":1},"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:b434ab11c5351db76e85b3c2818c41471491a4125aec1d88759a64a264603991","target":"record","created_at":"2026-05-18T02:29:32Z","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":"47808c8a1b6e2d9960c7258016eb8f906437b376cceb02ed825b310804c39ed0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-10T07:39:11Z","title_canon_sha256":"6d80b26f7df4bb36e648aac2d5991142280817f5f5b7b825589c112d8995a215"},"schema_version":"1.0","source":{"id":"1208.2105","kind":"arxiv","version":1}},"canonical_sha256":"2b02c4a46c3b9322d53c8694ce9d0f09ba5944eec8ed790a441fe3ee6a2cadd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b02c4a46c3b9322d53c8694ce9d0f09ba5944eec8ed790a441fe3ee6a2cadd0","first_computed_at":"2026-05-18T02:29:32.582256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:32.582256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5VFOeDtawXsGVvo6YWE8RwHC/H2smXlCRffNfHj/8NprI8TXnACoapAVaRt//Q6eRQKEHyRsgT92geZJ6QMoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:32.582768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b434ab11c5351db76e85b3c2818c41471491a4125aec1d88759a64a264603991","sha256:7bddfe756a502dc6e5e4b040be6eb035f8f9fee9647b737eea9afe8fadf89538"],"state_sha256":"28f208fa2ef1256a520ae2b33ac1d8c401c918f96c599ebfab25fa2ec54fafd2"}