{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:PEQVQTL3G5R5ZDOJ6OYDFOVCJO","short_pith_number":"pith:PEQVQTL3","schema_version":"1.0","canonical_sha256":"7921584d7b3763dc8dc9f3b032baa24b84713e3bd4f17be2e2c642a09d4f12cb","source":{"kind":"arxiv","id":"physics/9712001","version":3},"attestation_state":"computed","paper":{"title":"Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry","license":"","headline":"","cross_cats":["cond-mat","hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Carl M. Bender (Washington University, Clark Atlanta University), CTSPS, Los Alamos, Stefan Boettcher (CNLS, St. Louis)","submitted_at":"1997-11-29T04:37:49Z","abstract_excerpt":"The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These ${\\cal PT}$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories."},"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":"physics/9712001","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1997-11-29T04:37:49Z","cross_cats_sorted":["cond-mat","hep-th","math.MP","quant-ph"],"title_canon_sha256":"04d962c5fd8b572e7bfb84d0f1722b5c2fd109eb64589941b9f20e1f5a133364","abstract_canon_sha256":"b2d88c9b834a0bdb58e53aaf136dd01df0b28570ef2e19c84ee979451fd05ad3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:06:25.648839Z","signature_b64":"77j5CyyUXyGqbywj+WMi5PFyKVkpCDaBedeBLvT7KxpBfqBXM5ZQHc1TqQYFFZnwqXeAWlj/pdp2st9qhJpTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7921584d7b3763dc8dc9f3b032baa24b84713e3bd4f17be2e2c642a09d4f12cb","last_reissued_at":"2026-07-04T16:06:25.648436Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:06:25.648436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry","license":"","headline":"","cross_cats":["cond-mat","hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Carl M. Bender (Washington University, Clark Atlanta University), CTSPS, Los Alamos, Stefan Boettcher (CNLS, St. Louis)","submitted_at":"1997-11-29T04:37:49Z","abstract_excerpt":"The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These ${\\cal PT}$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/9712001","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/physics/9712001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"physics/9712001","created_at":"2026-07-04T16:06:25.648492+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/9712001v3","created_at":"2026-07-04T16:06:25.648492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/9712001","created_at":"2026-07-04T16:06:25.648492+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEQVQTL3G5R5","created_at":"2026-07-04T16:06:25.648492+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEQVQTL3G5R5ZDOJ","created_at":"2026-07-04T16:06:25.648492+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEQVQTL3","created_at":"2026-07-04T16:06:25.648492+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":14,"internal_anchor_count":11,"sample":[{"citing_arxiv_id":"2606.18629","citing_title":"Holographic Dual of PT Symmetric BCFT","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2606.14208","citing_title":"Real-time pseudo entropy and modular-Hamiltonian correlations","ref_index":31,"is_internal_anchor":true},{"citing_arxiv_id":"2606.13251","citing_title":"Kubo-Martin-Schwinger conditions for non-Hermitian systems","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2606.01405","citing_title":"Trajectories of Critical Unstable Qubits in and on the Bloch Sphere","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2606.31697","citing_title":"Hadronic exceptional points","ref_index":184,"is_internal_anchor":true},{"citing_arxiv_id":"2606.13251","citing_title":"Kubo-Martin-Schwinger conditions for non-Hermitian systems","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2606.28814","citing_title":"CFT Dual for Timelike Geodesic in Lorentzian dS","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2606.08143","citing_title":"Pathways to Real Composite Operators from Non-Hermitian Fermions","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2411.16843","citing_title":"Mobility edges in pseudo-unitary quasiperiodic quantum walks","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2511.11059","citing_title":"Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2602.02649","citing_title":"Non-Hermitian free-fermion critical systems and logarithmic conformal field theory","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2604.22421","citing_title":"Two flavor neutrino oscillations in presence of non-Hermitian dynamics","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21348","citing_title":"Ghost Degrees of Freedom Without Quantum Runaway: Exact Moment Bounds from an Operator Conservation Law","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2604.13358","citing_title":"Atiyah--Singer Index Theorem for Non-Hermitian Dirac Operators","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO","json":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO.json","graph_json":"https://pith.science/api/pith-number/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/graph.json","events_json":"https://pith.science/api/pith-number/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/events.json","paper":"https://pith.science/paper/PEQVQTL3"},"agent_actions":{"view_html":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO","download_json":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO.json","view_paper":"https://pith.science/paper/PEQVQTL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/9712001&json=true","fetch_graph":"https://pith.science/api/pith-number/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/graph.json","fetch_events":"https://pith.science/api/pith-number/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/action/storage_attestation","attest_author":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/action/author_attestation","sign_citation":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/action/citation_signature","submit_replication":"https://pith.science/pith/PEQVQTL3G5R5ZDOJ6OYDFOVCJO/action/replication_record"}},"created_at":"2026-07-04T16:06:25.648492+00:00","updated_at":"2026-07-04T16:06:25.648492+00:00"}