{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KN3A6TDPZYUMC2CP7DWOOQNBSI","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":"a9d72a8aee336b534af129a352ef5d8e6eca88242b5cd6952a75fd7eb12b9b6a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-24T17:55:09Z","title_canon_sha256":"cf820c99a283c700b4ea21a97d6c8c1e3873f5fda9649beaeb71684ef7829662"},"schema_version":"1.0","source":{"id":"1102.5051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5051","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5051v1","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5051","created_at":"2026-05-18T04:01:13Z"},{"alias_kind":"pith_short_12","alias_value":"KN3A6TDPZYUM","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KN3A6TDPZYUMC2CP","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KN3A6TDP","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:03734b406545295e40901d5a7caf50feb21acb79884c942fb64be079f032a4e7","target":"graph","created_at":"2026-05-18T04:01:13Z","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":"The Laplacian in an unbounded tubular neighbourhood of a hyperplane with non-Hermitian complex-symmetric Robin-type boundary conditions is investigated in the limit when the width of the neighbourhood diminishes. We show that the Laplacian converges in a norm resolvent sense to a self-adjoint Schroedinger operator in the hyperplane whose potential is expressed solely in terms of the boundary coupling function. As a consequence, we are able to explain some peculiar spectral properties of the non-Hermitian Laplacian by known results for Schroedinger operators.","authors_text":"David Krejcirik, Denis Borisov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-24T17:55:09Z","title":"The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5051","kind":"arxiv","version":1},"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:e4b2781e95f7bad2888aaf1b7755a762e7d54d08db8cc3479d500c797abbb15b","target":"record","created_at":"2026-05-18T04:01:13Z","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":"a9d72a8aee336b534af129a352ef5d8e6eca88242b5cd6952a75fd7eb12b9b6a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-02-24T17:55:09Z","title_canon_sha256":"cf820c99a283c700b4ea21a97d6c8c1e3873f5fda9649beaeb71684ef7829662"},"schema_version":"1.0","source":{"id":"1102.5051","kind":"arxiv","version":1}},"canonical_sha256":"53760f4c6fce28c1684ff8ece741a19236c25095b285426e25ab36a1d548bf91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53760f4c6fce28c1684ff8ece741a19236c25095b285426e25ab36a1d548bf91","first_computed_at":"2026-05-18T04:01:13.219948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:13.219948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HbWvVej3xqHtm0plP91h9a94Wr6ehb/wdcxOUVeCpUe8Ezc+yMbLPMsF3mn/t6EJ/eei8IrCiJzHDEuoxG5TBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:13.220500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4b2781e95f7bad2888aaf1b7755a762e7d54d08db8cc3479d500c797abbb15b","sha256:03734b406545295e40901d5a7caf50feb21acb79884c942fb64be079f032a4e7"],"state_sha256":"a3e22cdaac0621123feb6328ca987297c6f48f685a96c270eac1f8bf5aea0975"}