{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZAOCTQFUI7BKFDVT3QULAQKJXW","short_pith_number":"pith:ZAOCTQFU","canonical_record":{"source":{"id":"1301.1676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T23:49:12Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"919fa363a9b27d32a5008552e154ade2b1ec510913ceff30d74b8130c3a0f3e9","abstract_canon_sha256":"6c644e21e15d8e37e3fcc38b74ff230a7b65d2b8104a815fcc8422d3614f46d3"},"schema_version":"1.0"},"canonical_sha256":"c81c29c0b447c2a28eb3dc28b04149bdabd08432f7311b76d508c08c7a220bef","source":{"kind":"arxiv","id":"1301.1676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1676","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1676v1","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1676","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"ZAOCTQFUI7BK","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZAOCTQFUI7BKFDVT","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZAOCTQFU","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZAOCTQFUI7BKFDVT3QULAQKJXW","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T23:49:12Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"919fa363a9b27d32a5008552e154ade2b1ec510913ceff30d74b8130c3a0f3e9","abstract_canon_sha256":"6c644e21e15d8e37e3fcc38b74ff230a7b65d2b8104a815fcc8422d3614f46d3"},"schema_version":"1.0"},"canonical_sha256":"c81c29c0b447c2a28eb3dc28b04149bdabd08432f7311b76d508c08c7a220bef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:56.118734Z","signature_b64":"QuBBDbeKzZJj8p5EB26/iE52nQ3J1DrSz3zc8Qdsn2SqYwe32NbleZZwc97FtWKvafWkbJcspjZ102Wv71cCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c81c29c0b447c2a28eb3dc28b04149bdabd08432f7311b76d508c08c7a220bef","last_reissued_at":"2026-05-18T03:36:56.118287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:56.118287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1676","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UAP9LHBnAwDcSG8L1Iw6KOXmIy8A9XwdjtjOvEn9Lz1MmDxYvf6z5FYRXdRo650U0pfDKUIJ16BL+0Vo6grPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:59:48.850266Z"},"content_sha256":"d9a5d073a5248b7afb3fc4af2fea76a288da28088835e61a466f78a1fa361559","schema_version":"1.0","event_id":"sha256:d9a5d073a5248b7afb3fc4af2fea76a288da28088835e61a466f78a1fa361559"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZAOCTQFUI7BKFDVT3QULAQKJXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the eigenvalues of some nonhermitian oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Francisco M. Fern/'andez, Javier Garcia","submitted_at":"2013-01-07T23:49:12Z","abstract_excerpt":"We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those oscillators. Comparison of the results of the complex rotation and the Riccati-Pad\\'{e} methods reveals that the optimal rotation angle converts the oscillator into either a PT-symmetric or an Hermitian one. In addition to the real positive eigenvalues the PT-symmetric oscillators exhibit real positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1676","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"raxBylqSYCS1eI4mFC2+wWenTkSUrgZmBXxqi6mKb6sYNIheP/+obb1XINsrJAS8F4GNZjwNGzsVBxAhalx4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:59:48.850937Z"},"content_sha256":"ae781b63ec150ff4616da34ac978c165a6a272e7498c64cb51a4b355a22d2242","schema_version":"1.0","event_id":"sha256:ae781b63ec150ff4616da34ac978c165a6a272e7498c64cb51a4b355a22d2242"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW/bundle.json","state_url":"https://pith.science/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T14:59:48Z","links":{"resolver":"https://pith.science/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW","bundle":"https://pith.science/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW/bundle.json","state":"https://pith.science/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAOCTQFUI7BKFDVT3QULAQKJXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZAOCTQFUI7BKFDVT3QULAQKJXW","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":"6c644e21e15d8e37e3fcc38b74ff230a7b65d2b8104a815fcc8422d3614f46d3","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T23:49:12Z","title_canon_sha256":"919fa363a9b27d32a5008552e154ade2b1ec510913ceff30d74b8130c3a0f3e9"},"schema_version":"1.0","source":{"id":"1301.1676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1676","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1676v1","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1676","created_at":"2026-05-18T03:36:56Z"},{"alias_kind":"pith_short_12","alias_value":"ZAOCTQFUI7BK","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZAOCTQFUI7BKFDVT","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZAOCTQFU","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:ae781b63ec150ff4616da34ac978c165a6a272e7498c64cb51a4b355a22d2242","target":"graph","created_at":"2026-05-18T03:36:56Z","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":"We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those oscillators. Comparison of the results of the complex rotation and the Riccati-Pad\\'{e} methods reveals that the optimal rotation angle converts the oscillator into either a PT-symmetric or an Hermitian one. In addition to the real positive eigenvalues the PT-symmetric oscillators exhibit real positiv","authors_text":"Francisco M. Fern/'andez, Javier Garcia","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T23:49:12Z","title":"On the eigenvalues of some nonhermitian oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1676","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:d9a5d073a5248b7afb3fc4af2fea76a288da28088835e61a466f78a1fa361559","target":"record","created_at":"2026-05-18T03:36:56Z","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":"6c644e21e15d8e37e3fcc38b74ff230a7b65d2b8104a815fcc8422d3614f46d3","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T23:49:12Z","title_canon_sha256":"919fa363a9b27d32a5008552e154ade2b1ec510913ceff30d74b8130c3a0f3e9"},"schema_version":"1.0","source":{"id":"1301.1676","kind":"arxiv","version":1}},"canonical_sha256":"c81c29c0b447c2a28eb3dc28b04149bdabd08432f7311b76d508c08c7a220bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c81c29c0b447c2a28eb3dc28b04149bdabd08432f7311b76d508c08c7a220bef","first_computed_at":"2026-05-18T03:36:56.118287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:56.118287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuBBDbeKzZJj8p5EB26/iE52nQ3J1DrSz3zc8Qdsn2SqYwe32NbleZZwc97FtWKvafWkbJcspjZ102Wv71cCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:56.118734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9a5d073a5248b7afb3fc4af2fea76a288da28088835e61a466f78a1fa361559","sha256:ae781b63ec150ff4616da34ac978c165a6a272e7498c64cb51a4b355a22d2242"],"state_sha256":"f2f99d8cf61492c8e0764a6aef0f2cd32bb347f32b489e6cc8342095fc1c3231"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F4RZ0TJkr4EuN8rUoG+ayakNEixIDXqZuBxJKtcjMF5Tt8O+76wc0OcCTxSyTRr8L4deCM1/yfKL79po1UOyAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:59:48.854838Z","bundle_sha256":"7a500f1cfe980a76158e43c51bd7359e8f9453b6ad67cb0226c4e72765bc5a89"}}