{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:CWHD525WY6R5ZK5T3GTY46RM5W","short_pith_number":"pith:CWHD525W","schema_version":"1.0","canonical_sha256":"158e3eebb6c7a3dcabb3d9a78e7a2cedbcd31ae3a4f79eb363c89df151ce06e1","source":{"kind":"arxiv","id":"2509.11951","version":2},"attestation_state":"computed","paper":{"title":"X-ray imaging from nonlinear waves: numerical reconstruction of a cubic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Markus Harju, Suvi Anttila, Teemu Tyni","submitted_at":"2025-09-15T14:08:56Z","abstract_excerpt":"We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a direct numerical reconstruction method for the Radon transform of $q$, which can then be inverted using standard X-ray tomography techniques to determine $q$. Our implementation introduces a spectral regularization procedure to stabilize the numerical differentiation step required in the reconstruction, improving robustness with respect to noise in the bound"},"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":"2509.11951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-09-15T14:08:56Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"490fb878a789581e59dc6db7a406ac3c8e8aa2adfa864d13fc81f2e061949430","abstract_canon_sha256":"9cdcac0542ea731fb83d8a96a4fb6f5b33f03acc7785c4693871b3e30f25c21f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:47.762506Z","signature_b64":"FAzhekxmuZNIBc93Fy2wDRgN/00R6Z5fo48H/MwpDmf4rzZeeK6JxO+lHgMRidT8G7Tg7B9shtL12+3LRcV8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"158e3eebb6c7a3dcabb3d9a78e7a2cedbcd31ae3a4f79eb363c89df151ce06e1","last_reissued_at":"2026-06-19T16:12:47.762083Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:47.762083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"X-ray imaging from nonlinear waves: numerical reconstruction of a cubic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Markus Harju, Suvi Anttila, Teemu Tyni","submitted_at":"2025-09-15T14:08:56Z","abstract_excerpt":"We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a direct numerical reconstruction method for the Radon transform of $q$, which can then be inverted using standard X-ray tomography techniques to determine $q$. Our implementation introduces a spectral regularization procedure to stabilize the numerical differentiation step required in the reconstruction, improving robustness with respect to noise in the bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.11951","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.11951/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2509.11951","created_at":"2026-06-19T16:12:47.762148+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.11951v2","created_at":"2026-06-19T16:12:47.762148+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.11951","created_at":"2026-06-19T16:12:47.762148+00:00"},{"alias_kind":"pith_short_12","alias_value":"CWHD525WY6R5","created_at":"2026-06-19T16:12:47.762148+00:00"},{"alias_kind":"pith_short_16","alias_value":"CWHD525WY6R5ZK5T","created_at":"2026-06-19T16:12:47.762148+00:00"},{"alias_kind":"pith_short_8","alias_value":"CWHD525W","created_at":"2026-06-19T16:12:47.762148+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.28023","citing_title":"Gauge symmetry and uniqueness in inverse problems for the JMGT equation","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W","json":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W.json","graph_json":"https://pith.science/api/pith-number/CWHD525WY6R5ZK5T3GTY46RM5W/graph.json","events_json":"https://pith.science/api/pith-number/CWHD525WY6R5ZK5T3GTY46RM5W/events.json","paper":"https://pith.science/paper/CWHD525W"},"agent_actions":{"view_html":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W","download_json":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W.json","view_paper":"https://pith.science/paper/CWHD525W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.11951&json=true","fetch_graph":"https://pith.science/api/pith-number/CWHD525WY6R5ZK5T3GTY46RM5W/graph.json","fetch_events":"https://pith.science/api/pith-number/CWHD525WY6R5ZK5T3GTY46RM5W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W/action/storage_attestation","attest_author":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W/action/author_attestation","sign_citation":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W/action/citation_signature","submit_replication":"https://pith.science/pith/CWHD525WY6R5ZK5T3GTY46RM5W/action/replication_record"}},"created_at":"2026-06-19T16:12:47.762148+00:00","updated_at":"2026-06-19T16:12:47.762148+00:00"}