{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:27JZV3K3ST5JDRCU7R4ECRSR6N","short_pith_number":"pith:27JZV3K3","schema_version":"1.0","canonical_sha256":"d7d39aed5b94fa91c454fc78414651f343d5211f97537f447dff3d11c775283e","source":{"kind":"arxiv","id":"1803.10541","version":1},"attestation_state":"computed","paper":{"title":"Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jussi Korpela, Lauri Oksanen, Matti Lassas","submitted_at":"2018-03-28T11:41:49Z","abstract_excerpt":"An inverse boundary value problem for the 1+1 dimensional wave equation $(\\partial_t^2 - c(x)^2 \\partial_x^2)u(x,t)=0,\\quad x\\in\\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are given the boundary value of the wave, $u(0,t)$, that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed $\\widetilde c$, satisfying a H\\\"older type estimate $\\| \\widetilde c-c\\|\\leq C \\epsilon^{\\gamma}$, where $\\epsilon$ is the noise level."},"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":"1803.10541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T11:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"e283934346d828975d616d86bd1f3c2d6b7bfc22da77e5fbba31e25610535a7b","abstract_canon_sha256":"258e8e0f0afb150a9bfa5c5829220dffc96dcad0f000e9c5fc4f92ca0700f75d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:54.964602Z","signature_b64":"v+6A3pnd0aBz3/B5v8SuseKX9YbUbO2s94rLWyhegcWpRCeEVEOTWLif1m2YrQZUIJO85Zy6j9pioxAkcTp2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7d39aed5b94fa91c454fc78414651f343d5211f97537f447dff3d11c775283e","last_reissued_at":"2026-05-18T00:19:54.963852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:54.963852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jussi Korpela, Lauri Oksanen, Matti Lassas","submitted_at":"2018-03-28T11:41:49Z","abstract_excerpt":"An inverse boundary value problem for the 1+1 dimensional wave equation $(\\partial_t^2 - c(x)^2 \\partial_x^2)u(x,t)=0,\\quad x\\in\\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are given the boundary value of the wave, $u(0,t)$, that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed $\\widetilde c$, satisfying a H\\\"older type estimate $\\| \\widetilde c-c\\|\\leq C \\epsilon^{\\gamma}$, where $\\epsilon$ is the noise level."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10541","kind":"arxiv","version":1},"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":"1803.10541","created_at":"2026-05-18T00:19:54.963957+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.10541v1","created_at":"2026-05-18T00:19:54.963957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10541","created_at":"2026-05-18T00:19:54.963957+00:00"},{"alias_kind":"pith_short_12","alias_value":"27JZV3K3ST5J","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"27JZV3K3ST5JDRCU","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"27JZV3K3","created_at":"2026-05-18T12:31:59.375834+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/27JZV3K3ST5JDRCU7R4ECRSR6N","json":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N.json","graph_json":"https://pith.science/api/pith-number/27JZV3K3ST5JDRCU7R4ECRSR6N/graph.json","events_json":"https://pith.science/api/pith-number/27JZV3K3ST5JDRCU7R4ECRSR6N/events.json","paper":"https://pith.science/paper/27JZV3K3"},"agent_actions":{"view_html":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N","download_json":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N.json","view_paper":"https://pith.science/paper/27JZV3K3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.10541&json=true","fetch_graph":"https://pith.science/api/pith-number/27JZV3K3ST5JDRCU7R4ECRSR6N/graph.json","fetch_events":"https://pith.science/api/pith-number/27JZV3K3ST5JDRCU7R4ECRSR6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N/action/storage_attestation","attest_author":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N/action/author_attestation","sign_citation":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N/action/citation_signature","submit_replication":"https://pith.science/pith/27JZV3K3ST5JDRCU7R4ECRSR6N/action/replication_record"}},"created_at":"2026-05-18T00:19:54.963957+00:00","updated_at":"2026-05-18T00:19:54.963957+00:00"}