{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:WI5FQNAPUGNXS53N2GWPLDQN4P","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":"8a64f5e5942dc6332e761ed2b7ef25ea45065ec30a217ce928ff2356dfdf6311","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2000-07-05T07:42:34Z","title_canon_sha256":"a5fc786c11f4da483fb0efffbe88c1357f682818d41d7e9f1992b4eb6f9fd6b7"},"schema_version":"1.0","source":{"id":"math-ph/0007006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0007006","created_at":"2026-07-04T16:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0007006v1","created_at":"2026-07-04T16:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0007006","created_at":"2026-07-04T16:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"WI5FQNAPUGNX","created_at":"2026-07-04T16:21:10Z"},{"alias_kind":"pith_short_16","alias_value":"WI5FQNAPUGNXS53N","created_at":"2026-07-04T16:21:10Z"},{"alias_kind":"pith_short_8","alias_value":"WI5FQNAP","created_at":"2026-07-04T16:21:10Z"}],"graph_snapshots":[{"event_id":"sha256:362199580cf9dd886768c8702bf3dbadb3f42be8f9002d02a6b6d0892af09760","target":"graph","created_at":"2026-07-04T16:21:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0007006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the non-Hermitian Hamiltonian H= -\\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \\geq 1 with all nonnegative real coefficients (possibly P\\equiv 0). It is proved that the eigenvalues \\lambda must be in the sector | arg \\lambda | \\leq \\frac{\\pi}{2n+3}. Also for the case H=-\\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\\prime and we find some other interesting properties of eigenfunctions.","authors_text":"K. C. Shin","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2000-07-05T07:42:34Z","title":"On the eigenproblems of PT-symmetric oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0007006","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:a591028a1f1a6f6a893626e1933afcf128cb6ad702c6bd1bea24cc76303d7819","target":"record","created_at":"2026-07-04T16:21:10Z","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":"8a64f5e5942dc6332e761ed2b7ef25ea45065ec30a217ce928ff2356dfdf6311","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2000-07-05T07:42:34Z","title_canon_sha256":"a5fc786c11f4da483fb0efffbe88c1357f682818d41d7e9f1992b4eb6f9fd6b7"},"schema_version":"1.0","source":{"id":"math-ph/0007006","kind":"arxiv","version":1}},"canonical_sha256":"b23a58340fa19b79776dd1acf58e0de3dc7ed7c48d9b055464d98b1792007642","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b23a58340fa19b79776dd1acf58e0de3dc7ed7c48d9b055464d98b1792007642","first_computed_at":"2026-07-04T16:21:10.867362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:21:10.867362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"msuQ2pfpp1S/8dhFHjONJbF7cPRsivUX87OcLcf8L3k+g4w3nJmnjg0MEx1tSA6pYLuelpltxaTMMhLaHlnCDg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:21:10.867699Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0007006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a591028a1f1a6f6a893626e1933afcf128cb6ad702c6bd1bea24cc76303d7819","sha256:362199580cf9dd886768c8702bf3dbadb3f42be8f9002d02a6b6d0892af09760"],"state_sha256":"f5ac2a6b7e1353dedf795a32dbbd8565ae2d852c6999dce6a023e1397663b082"}