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In the case of a regular Sturm-Liouville problem any diagonalizable PT-symmetric Hamiltonian with the unbroken PT symmetry has a complete set of positive CPT-normalazable eigenfunctions. For non-diagonalizable\n Hamiltonians a complete set of CPT-normalazable functions is possible but the functions belonging to the root subspace corres"},"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":"quant-ph/0503040","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-03-03T16:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"15c7be0ac1539f0161988339952933b15ac7c6fa2812113804eabd87d1b50c9d","abstract_canon_sha256":"421d7a833c9f4e821757fdbc76b975cd24f2d314f990fe9c5df85cc2c0940f88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:03.026001Z","signature_b64":"wSlRLorbZf9rsvJszuTtyw1yNyLj3slBX+N1k6Eml1bhjMFd0iWoCeAMZQBlCiSSwsJiaxhmu13/1dC8AKGpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d40ee4604cc2087c7278f078f2b7dbad018cbce8476992b6e7158fbcc46eeed","last_reissued_at":"2026-05-18T01:05:03.025429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:03.025429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Is the CPT-norm always positive?","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Boris F Samsonov, Pinaki Roy","submitted_at":"2005-03-03T16:12:23Z","abstract_excerpt":"We give an explicit example of an exactly solvable PT-symmetric Hamiltonian with the unbroken PT symmetry which has one eigenfunction with the zero PT-norm. 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