{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N2KRU62MEK5H4HSOMLM3W7R6KW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a0badb43937302cc99322364830574ac987635ee4e62bdd17f12980dac77eba7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-16T13:08:04Z","title_canon_sha256":"e66c57ea218c05e69e23ef5addbc3c82b08b853a36d8cab597e4f8fab7e2cce9"},"schema_version":"1.0","source":{"id":"1512.05163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05163","created_at":"2026-05-18T01:16:24Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05163v2","created_at":"2026-05-18T01:16:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05163","created_at":"2026-05-18T01:16:24Z"},{"alias_kind":"pith_short_12","alias_value":"N2KRU62MEK5H","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N2KRU62MEK5H4HSO","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N2KRU62M","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:0328c7733aadd0575e7fcc2cbf89fbcf7c9c1e45ac6c9907c1b81fcaa98a8de1","target":"graph","created_at":"2026-05-18T01:16:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction method can transform the transmission eigenvalue solving in the finest finite element space to a sequence of linear problems and some transmission eigenvalue solving in a very low dimensional spaces. Since the main computational work is to solve the sequence of linear problems, the multilevel correction method improves the overfull efficiency of the transmissio","authors_text":"Hehu Xie, Xinming Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-16T13:08:04Z","title":"A Multilevel Correction Method for Interior Transmission Eigenvalue Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05163","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1b9ae433de8545b591d9ec903f27fe930854de8cd38500e078e8477369d56df4","target":"record","created_at":"2026-05-18T01:16:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a0badb43937302cc99322364830574ac987635ee4e62bdd17f12980dac77eba7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-16T13:08:04Z","title_canon_sha256":"e66c57ea218c05e69e23ef5addbc3c82b08b853a36d8cab597e4f8fab7e2cce9"},"schema_version":"1.0","source":{"id":"1512.05163","kind":"arxiv","version":2}},"canonical_sha256":"6e951a7b4c22ba7e1e4e62d9bb7e3e5595efbd51722096f2240fe662ae2cfeea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e951a7b4c22ba7e1e4e62d9bb7e3e5595efbd51722096f2240fe662ae2cfeea","first_computed_at":"2026-05-18T01:16:24.460452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:24.460452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ITotq68lYcLnsNbq9hpkPcN2bcImc+pN8GZUFrcNYVSZRSO4+5A5QdvGb6VGgUqemFXmcufW2zIe5n25VFJXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:24.461023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b9ae433de8545b591d9ec903f27fe930854de8cd38500e078e8477369d56df4","sha256:0328c7733aadd0575e7fcc2cbf89fbcf7c9c1e45ac6c9907c1b81fcaa98a8de1"],"state_sha256":"fc62d9d3174cb2ebd21f4ad85245bf7ff384af3adfff789a0aebfc619a086a65"}