{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HX7XA6LVDLNGZ25YOSH4O2AATT","short_pith_number":"pith:HX7XA6LV","schema_version":"1.0","canonical_sha256":"3dff7079751ada6cebb8748fc768009ccd71881c7f18819a220015e706e3a345","source":{"kind":"arxiv","id":"1512.07725","version":1},"attestation_state":"computed","paper":{"title":"Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Antti Rasila, Tommi Sottinen, Xuxin Yang","submitted_at":"2015-12-24T06:17:26Z","abstract_excerpt":"We show that a constant-potential time-independent Schr\\\"odinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms."},"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":"1512.07725","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-24T06:17:26Z","cross_cats_sorted":["math.AP","math.PR"],"title_canon_sha256":"b804ea7b6ecd8bfa95d26341dd5fd82457780a5751e8546d216ad2faa05e144f","abstract_canon_sha256":"241e9d9533671355ea936b5f24a2e2cdb8a1fc88aaea649915c91c0c6a87538a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:48.036138Z","signature_b64":"fxd9kEMRGOxO/6LhvDQ6Mf/Rwau6JzcEqXy1D/DVv27clcb4Hq9Nty3V+PRwx1+M+6VmIesNhy/Hw/pMTrdICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dff7079751ada6cebb8748fc768009ccd71881c7f18819a220015e706e3a345","last_reissued_at":"2026-05-18T01:23:48.035496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:48.035496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Antti Rasila, Tommi Sottinen, Xuxin Yang","submitted_at":"2015-12-24T06:17:26Z","abstract_excerpt":"We show that a constant-potential time-independent Schr\\\"odinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07725","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":"1512.07725","created_at":"2026-05-18T01:23:48.035598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.07725v1","created_at":"2026-05-18T01:23:48.035598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07725","created_at":"2026-05-18T01:23:48.035598+00:00"},{"alias_kind":"pith_short_12","alias_value":"HX7XA6LVDLNG","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HX7XA6LVDLNGZ25Y","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HX7XA6LV","created_at":"2026-05-18T12:29:25.134429+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/HX7XA6LVDLNGZ25YOSH4O2AATT","json":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT.json","graph_json":"https://pith.science/api/pith-number/HX7XA6LVDLNGZ25YOSH4O2AATT/graph.json","events_json":"https://pith.science/api/pith-number/HX7XA6LVDLNGZ25YOSH4O2AATT/events.json","paper":"https://pith.science/paper/HX7XA6LV"},"agent_actions":{"view_html":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT","download_json":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT.json","view_paper":"https://pith.science/paper/HX7XA6LV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.07725&json=true","fetch_graph":"https://pith.science/api/pith-number/HX7XA6LVDLNGZ25YOSH4O2AATT/graph.json","fetch_events":"https://pith.science/api/pith-number/HX7XA6LVDLNGZ25YOSH4O2AATT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT/action/storage_attestation","attest_author":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT/action/author_attestation","sign_citation":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT/action/citation_signature","submit_replication":"https://pith.science/pith/HX7XA6LVDLNGZ25YOSH4O2AATT/action/replication_record"}},"created_at":"2026-05-18T01:23:48.035598+00:00","updated_at":"2026-05-18T01:23:48.035598+00:00"}