{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:LTLWLUTPCWGPTJ2WVBVG7FXBUE","short_pith_number":"pith:LTLWLUTP","schema_version":"1.0","canonical_sha256":"5cd765d26f158cf9a756a86a6f96e1a11eb10fb55dde6e51f0c64194fc37a69c","source":{"kind":"arxiv","id":"0806.2022","version":1},"attestation_state":"computed","paper":{"title":"Perfectly matched layers for the stationary Schrodinger equation in a periodic structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Victor Kalvin","submitted_at":"2008-06-12T08:59:47Z","abstract_excerpt":"We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show that solution to this problem approximates a solution to the original problem with an error that exponentially tends to zero as the length of perfectly matched layer tends to infinity."},"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":"0806.2022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-06-12T08:59:47Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"deb3fbff1aca52db5b959e739d5a3c94e615a10f7d3e16f69b39ce8f9f793476","abstract_canon_sha256":"98d7ddf9a92a02ec431c1f724b90fd5ec116dc8045d1d0a15d2211ec5e68720e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:37.081291Z","signature_b64":"npAIYmGXXSaZan+bQSIbAse/7gY2ZJXjMzZBQHvds/XmetJZHybv+X8gc9Gp6Ys6+LWI/rplJ7u/5gMW6u77DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cd765d26f158cf9a756a86a6f96e1a11eb10fb55dde6e51f0c64194fc37a69c","last_reissued_at":"2026-05-18T04:28:37.080846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:37.080846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfectly matched layers for the stationary Schrodinger equation in a periodic structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Victor Kalvin","submitted_at":"2008-06-12T08:59:47Z","abstract_excerpt":"We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvability of the problem with perfectly matched layer of finite length and show that solution to this problem approximates a solution to the original problem with an error that exponentially tends to zero as the length of perfectly matched layer tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.2022","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":"0806.2022","created_at":"2026-05-18T04:28:37.080912+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.2022v1","created_at":"2026-05-18T04:28:37.080912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.2022","created_at":"2026-05-18T04:28:37.080912+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTLWLUTPCWGP","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTLWLUTPCWGPTJ2W","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTLWLUTP","created_at":"2026-05-18T12:25:57.157939+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/LTLWLUTPCWGPTJ2WVBVG7FXBUE","json":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE.json","graph_json":"https://pith.science/api/pith-number/LTLWLUTPCWGPTJ2WVBVG7FXBUE/graph.json","events_json":"https://pith.science/api/pith-number/LTLWLUTPCWGPTJ2WVBVG7FXBUE/events.json","paper":"https://pith.science/paper/LTLWLUTP"},"agent_actions":{"view_html":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE","download_json":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE.json","view_paper":"https://pith.science/paper/LTLWLUTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.2022&json=true","fetch_graph":"https://pith.science/api/pith-number/LTLWLUTPCWGPTJ2WVBVG7FXBUE/graph.json","fetch_events":"https://pith.science/api/pith-number/LTLWLUTPCWGPTJ2WVBVG7FXBUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE/action/storage_attestation","attest_author":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE/action/author_attestation","sign_citation":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE/action/citation_signature","submit_replication":"https://pith.science/pith/LTLWLUTPCWGPTJ2WVBVG7FXBUE/action/replication_record"}},"created_at":"2026-05-18T04:28:37.080912+00:00","updated_at":"2026-05-18T04:28:37.080912+00:00"}