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The spectrum of this operator is discrete and contained in the positive half plane. In general, the $\\varepsilon$-pseudospectrum of $H$ will have an unbounded component for any $\\varepsilon>0$ and thus will not approximate the spectrum in a global sense. By exploiting the fact that the semigroup $e^{-tH}$ is immediately compact, we show a complementary result, namely that for eve"},"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":"1505.05719","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-21T13:09:48Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"50f5cef94c5fd3e2ad6afcf5435df8d3463f7b78f32d13950736d6e6b3f8e960","abstract_canon_sha256":"876c856b0bb7fe59a88e90bd15e7e03cbce7f2f5804f2f91bb1c64fee37ea334"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:15.974722Z","signature_b64":"TnfUBenRyq7tNJ8NtgU8KDNFIJn4CfFueOraM9CU+Gzw06/nlpTOf11VKGoxjZYpxLDuHtfi2euAapcdzJpABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f361e72afaccb53be9044bcb28dc5c6b634d2518cd7837dfcb51a0aba59b14c","last_reissued_at":"2026-05-18T00:53:15.974117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:15.974117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank R\\\"osler, Patrick Dorey, Patrick W. 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