{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3DVI5PDTQRBLO4FHU2JNIK3TNR","short_pith_number":"pith:3DVI5PDT","schema_version":"1.0","canonical_sha256":"d8ea8ebc738442b770a7a692d42b736c46d2181e85d3897cc61e90b9a4e34e47","source":{"kind":"arxiv","id":"1708.01247","version":2},"attestation_state":"computed","paper":{"title":"Appropriate Inner Product for PT-Symmetric Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Philip D. Mannheim","submitted_at":"2017-08-03T17:52:05Z","abstract_excerpt":"A Hamiltonian $H$ that is not Hermitian can still have a real and complete energy eigenspectrum if it instead is $PT$ symmetric. For such Hamiltonians three possible inner products have been considered in the literature, the $V$ norm, the $PT$ norm, and the $C$ norm. Here $V$ is the operator that implements $VHV^{-1}=H^{\\dagger}$, the $PT$ norm is the overlap of a state with its $PT$ conjugate, and $C$ is a discrete linear operator that always exists for any Hamiltonian that can be diagonalized. Here we show that it is the $V$ norm that is the most fundamental as it is always chosen by the the"},"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":"1708.01247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-08-03T17:52:05Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"80381b304caaacad263431f8152193218a03387a29df188492b84587e71e8f4b","abstract_canon_sha256":"3ebf1917e6f85e2d63efeaa85ae1548d85c4aa40892f215b9cbcf61f44e80afb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:16.805256Z","signature_b64":"8evx70jjwNBHe+8/8sU6IAepprtaeSWL50t5B36zJck2SDx+wfkOopUFQnin4zwWCncLfG8Qml4qUIXdtlQlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8ea8ebc738442b770a7a692d42b736c46d2181e85d3897cc61e90b9a4e34e47","last_reissued_at":"2026-05-18T00:24:16.804733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:16.804733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Appropriate Inner Product for PT-Symmetric Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Philip D. Mannheim","submitted_at":"2017-08-03T17:52:05Z","abstract_excerpt":"A Hamiltonian $H$ that is not Hermitian can still have a real and complete energy eigenspectrum if it instead is $PT$ symmetric. For such Hamiltonians three possible inner products have been considered in the literature, the $V$ norm, the $PT$ norm, and the $C$ norm. Here $V$ is the operator that implements $VHV^{-1}=H^{\\dagger}$, the $PT$ norm is the overlap of a state with its $PT$ conjugate, and $C$ is a discrete linear operator that always exists for any Hamiltonian that can be diagonalized. Here we show that it is the $V$ norm that is the most fundamental as it is always chosen by the the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01247","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.01247","created_at":"2026-05-18T00:24:16.804813+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.01247v2","created_at":"2026-05-18T00:24:16.804813+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01247","created_at":"2026-05-18T00:24:16.804813+00:00"},{"alias_kind":"pith_short_12","alias_value":"3DVI5PDTQRBL","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3DVI5PDTQRBLO4FH","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3DVI5PDT","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.22421","citing_title":"Two flavor neutrino oscillations in presence of non-Hermitian dynamics","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR","json":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR.json","graph_json":"https://pith.science/api/pith-number/3DVI5PDTQRBLO4FHU2JNIK3TNR/graph.json","events_json":"https://pith.science/api/pith-number/3DVI5PDTQRBLO4FHU2JNIK3TNR/events.json","paper":"https://pith.science/paper/3DVI5PDT"},"agent_actions":{"view_html":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR","download_json":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR.json","view_paper":"https://pith.science/paper/3DVI5PDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.01247&json=true","fetch_graph":"https://pith.science/api/pith-number/3DVI5PDTQRBLO4FHU2JNIK3TNR/graph.json","fetch_events":"https://pith.science/api/pith-number/3DVI5PDTQRBLO4FHU2JNIK3TNR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR/action/storage_attestation","attest_author":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR/action/author_attestation","sign_citation":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR/action/citation_signature","submit_replication":"https://pith.science/pith/3DVI5PDTQRBLO4FHU2JNIK3TNR/action/replication_record"}},"created_at":"2026-05-18T00:24:16.804813+00:00","updated_at":"2026-05-18T00:24:16.804813+00:00"}