{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GOVGRDELW2DHMMADQHVZK5JH7G","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":"e424cbd36f37de17e07dd1dd907ffe84908624db70468aff03d1ccd66cec0e16","cross_cats_sorted":["hep-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-06-24T11:08:37Z","title_canon_sha256":"b4d7f73a2d0015cc677f34f4c7b1208ac9be01ee096a894fb3b78e3338b88997"},"schema_version":"1.0","source":{"id":"1006.4748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4748","created_at":"2026-05-18T02:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4748v1","created_at":"2026-05-18T02:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4748","created_at":"2026-05-18T02:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"GOVGRDELW2DH","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GOVGRDELW2DHMMAD","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GOVGRDEL","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:89972685a992bf6df0f333495ff2c0fe6cb1710b5cc9d2c8a764bbb6a347d805","target":"graph","created_at":"2026-05-18T02:33:16Z","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":"A long time ago, it has been conjectured that a Hamiltonian with a potential of the form x^2+i v x^3, v real, has a real spectrum. This conjecture has been generalized to a class of so-called PT symmetric Hamiltonians and some proofs have been given. Here, we show by numerical investigation that the divergent perturbation series can be summed efficiently by an order-dependent mapping (ODM) in the whole complex plane of the coupling parameter v^2, and that some information about the location of level crossing singularities can be obtained in this way. Furthermore, we discuss to which accuracy t","authors_text":"J. Zinn-Justin, U. D. Jentschura","cross_cats":["hep-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-06-24T11:08:37Z","title":"Order-dependent mappings: strong coupling behaviour from weak coupling expansions in non-Hermitian theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4748","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":"sha256:546a5be98990660117407e41abdbf5e6573a7db62ba004b839797ed64f00bc5d","target":"record","created_at":"2026-05-18T02:33:16Z","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":"e424cbd36f37de17e07dd1dd907ffe84908624db70468aff03d1ccd66cec0e16","cross_cats_sorted":["hep-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-06-24T11:08:37Z","title_canon_sha256":"b4d7f73a2d0015cc677f34f4c7b1208ac9be01ee096a894fb3b78e3338b88997"},"schema_version":"1.0","source":{"id":"1006.4748","kind":"arxiv","version":1}},"canonical_sha256":"33aa688c8bb68676300381eb957527f98a4eb82779fe096fe1e5c336ede40ee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33aa688c8bb68676300381eb957527f98a4eb82779fe096fe1e5c336ede40ee9","first_computed_at":"2026-05-18T02:33:16.108760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:16.108760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GuQnvQv8Q/c5Tn+nVeOOnPAUXxYppUo8/GO13UG8r30pay23WmoRRXw0W/8XhYB3D56Px3jYCkfxTJ6VFUmGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:16.109424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.4748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:546a5be98990660117407e41abdbf5e6573a7db62ba004b839797ed64f00bc5d","sha256:89972685a992bf6df0f333495ff2c0fe6cb1710b5cc9d2c8a764bbb6a347d805"],"state_sha256":"6b157e4443089be155606899325e8568f8dcfc43b078c1e8c96905bb26c35552"}