{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LKKZ6JNY7DBJZI64WTOGUDZZQC","short_pith_number":"pith:LKKZ6JNY","schema_version":"1.0","canonical_sha256":"5a959f25b8f8c29ca3dcb4dc6a0f3980ad06517e37158af6c9e9ebdfec4a78ae","source":{"kind":"arxiv","id":"1204.2334","version":1},"attestation_state":"computed","paper":{"title":"Spurious localized highest-frequency modes in Schr\\\"odinger-type equations solved by finite-difference methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.PS"],"primary_cat":"math-ph","authors_text":"Taras I. Lakoba","submitted_at":"2012-04-11T04:10:13Z","abstract_excerpt":"High-frequency solutions of one or several Schr\\\"odinger-type equations are well known to differ very little from the plane wave solutions $\\exp[\\pm ik x]$. That is, the potential terms impact the envelope of a high-frequency plane wave by only a small amount. However, when such equations are solved by a finite-difference method, the highest-frequency solutions may, under certain conditions, turn out to be localized. In this letter we explain this numerical artifact."},"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":"1204.2334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-11T04:10:13Z","cross_cats_sorted":["math.MP","nlin.PS"],"title_canon_sha256":"49f0509de3da656df4182ef41472cfd3a5833e45300bcc95e9daec2192b02bee","abstract_canon_sha256":"ed529edbfc023d6bd310458fea1571df8942e79ea182ccab8649178296835a3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:12.112186Z","signature_b64":"Nzll0sRd8o/fAvir6E3WfrvDyYknkjLaCgTUt4/n1AJ6WrV6GYXJHh/cJRlAeOCZUN4SyquoDHableI57JcmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a959f25b8f8c29ca3dcb4dc6a0f3980ad06517e37158af6c9e9ebdfec4a78ae","last_reissued_at":"2026-05-18T03:58:12.111400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:12.111400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spurious localized highest-frequency modes in Schr\\\"odinger-type equations solved by finite-difference methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.PS"],"primary_cat":"math-ph","authors_text":"Taras I. Lakoba","submitted_at":"2012-04-11T04:10:13Z","abstract_excerpt":"High-frequency solutions of one or several Schr\\\"odinger-type equations are well known to differ very little from the plane wave solutions $\\exp[\\pm ik x]$. That is, the potential terms impact the envelope of a high-frequency plane wave by only a small amount. However, when such equations are solved by a finite-difference method, the highest-frequency solutions may, under certain conditions, turn out to be localized. In this letter we explain this numerical artifact."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2334","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":"1204.2334","created_at":"2026-05-18T03:58:12.111545+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2334v1","created_at":"2026-05-18T03:58:12.111545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2334","created_at":"2026-05-18T03:58:12.111545+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKKZ6JNY7DBJ","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKKZ6JNY7DBJZI64","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKKZ6JNY","created_at":"2026-05-18T12:27:14.488303+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/LKKZ6JNY7DBJZI64WTOGUDZZQC","json":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC.json","graph_json":"https://pith.science/api/pith-number/LKKZ6JNY7DBJZI64WTOGUDZZQC/graph.json","events_json":"https://pith.science/api/pith-number/LKKZ6JNY7DBJZI64WTOGUDZZQC/events.json","paper":"https://pith.science/paper/LKKZ6JNY"},"agent_actions":{"view_html":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC","download_json":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC.json","view_paper":"https://pith.science/paper/LKKZ6JNY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2334&json=true","fetch_graph":"https://pith.science/api/pith-number/LKKZ6JNY7DBJZI64WTOGUDZZQC/graph.json","fetch_events":"https://pith.science/api/pith-number/LKKZ6JNY7DBJZI64WTOGUDZZQC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC/action/storage_attestation","attest_author":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC/action/author_attestation","sign_citation":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC/action/citation_signature","submit_replication":"https://pith.science/pith/LKKZ6JNY7DBJZI64WTOGUDZZQC/action/replication_record"}},"created_at":"2026-05-18T03:58:12.111545+00:00","updated_at":"2026-05-18T03:58:12.111545+00:00"}