{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:5D7X6JNOWRCMQKMT3WIRD3MED3","short_pith_number":"pith:5D7X6JNO","canonical_record":{"source":{"id":"math-ph/0203005","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-03-04T16:34:07Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"e54bad82a02137bf62a890087840543d5a92769216224990cfcb4f83302b5519","abstract_canon_sha256":"638864073949b6e2a493a1591fdc00c37f689beb0ac0afeb2975c2a55f0ac6cd"},"schema_version":"1.0"},"canonical_sha256":"e8ff7f25aeb444c82993dd9111ed841ed295db66ed2dd9b2802608cd90e7023f","source":{"kind":"arxiv","id":"math-ph/0203005","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0203005","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0203005v2","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0203005","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"5D7X6JNOWRCM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"5D7X6JNOWRCMQKMT","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"5D7X6JNO","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:5D7X6JNOWRCMQKMT3WIRD3MED3","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0203005","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-03-04T16:34:07Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"e54bad82a02137bf62a890087840543d5a92769216224990cfcb4f83302b5519","abstract_canon_sha256":"638864073949b6e2a493a1591fdc00c37f689beb0ac0afeb2975c2a55f0ac6cd"},"schema_version":"1.0"},"canonical_sha256":"e8ff7f25aeb444c82993dd9111ed841ed295db66ed2dd9b2802608cd90e7023f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:34.255095Z","signature_b64":"0tGfSwnwUlMufJJbNa6vB6Q0NEKc5AfMffiAAB2qv+/FxhNyqJpmh86Imp+LGyB119kUq4+bJuPt0Yl945+sBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8ff7f25aeb444c82993dd9111ed841ed295db66ed2dd9b2802608cd90e7023f","last_reissued_at":"2026-05-18T01:38:34.254337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:34.254337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0203005","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFey2dzxPonPdevac+MgtGUZzylT273/N8yfJ5cX4VJAGot/VGu+ljI0Gz1VmDzRXzWumsa2e0r5shew6+VPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:26:17.862302Z"},"content_sha256":"80146ba60bebf10d2138ad28dd283c8e4590d037c047273f7745d393a05a4607","schema_version":"1.0","event_id":"sha256:80146ba60bebf10d2138ad28dd283c8e4590d037c047273f7745d393a05a4607"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:5D7X6JNOWRCMQKMT3WIRD3MED3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries","license":"","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Ali Mostafazadeh","submitted_at":"2002-03-04T16:34:07Z","abstract_excerpt":"We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real or come in complex conjugate pairs if and only if H possesses such a symmetry. In particular, the reality of the spectrum of H implies the presence of an antilinear symmetry. We further show that the spectrum of H is real if and only if there is a positive-definite inner-product on the Hilbert space with respect to which H is Hermitian or alternatively there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0203005","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6AvgnxMmnKBf822qZSayxLkhxdqJ7VUAY4PP9Sp8+VJzW5Ak9N4ycFZgu8p+JTiPQCr7xVrD2vrL3X7Hb6jeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:26:17.862755Z"},"content_sha256":"daabdfe51f1aaef421b6eb93c5078cc5aef23792a7c683768e7e592fa2d2989f","schema_version":"1.0","event_id":"sha256:daabdfe51f1aaef421b6eb93c5078cc5aef23792a7c683768e7e592fa2d2989f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5D7X6JNOWRCMQKMT3WIRD3MED3/bundle.json","state_url":"https://pith.science/pith/5D7X6JNOWRCMQKMT3WIRD3MED3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5D7X6JNOWRCMQKMT3WIRD3MED3/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":"2026-05-25T14:26:17Z","links":{"resolver":"https://pith.science/pith/5D7X6JNOWRCMQKMT3WIRD3MED3","bundle":"https://pith.science/pith/5D7X6JNOWRCMQKMT3WIRD3MED3/bundle.json","state":"https://pith.science/pith/5D7X6JNOWRCMQKMT3WIRD3MED3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5D7X6JNOWRCMQKMT3WIRD3MED3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:5D7X6JNOWRCMQKMT3WIRD3MED3","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":"638864073949b6e2a493a1591fdc00c37f689beb0ac0afeb2975c2a55f0ac6cd","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2002-03-04T16:34:07Z","title_canon_sha256":"e54bad82a02137bf62a890087840543d5a92769216224990cfcb4f83302b5519"},"schema_version":"1.0","source":{"id":"math-ph/0203005","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0203005","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0203005v2","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0203005","created_at":"2026-05-18T01:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"5D7X6JNOWRCM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"5D7X6JNOWRCMQKMT","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"5D7X6JNO","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:daabdfe51f1aaef421b6eb93c5078cc5aef23792a7c683768e7e592fa2d2989f","target":"graph","created_at":"2026-05-18T01:38:34Z","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 show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real or come in complex conjugate pairs if and only if H possesses such a symmetry. In particular, the reality of the spectrum of H implies the presence of an antilinear symmetry. We further show that the spectrum of H is real if and only if there is a positive-definite inner-product on the Hilbert space with respect to which H is Hermitian or alternatively there ","authors_text":"Ali Mostafazadeh","cross_cats":["hep-th","math.MP","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-03-04T16:34:07Z","title":"Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0203005","kind":"arxiv","version":2},"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":"sha256:80146ba60bebf10d2138ad28dd283c8e4590d037c047273f7745d393a05a4607","target":"record","created_at":"2026-05-18T01:38:34Z","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":"638864073949b6e2a493a1591fdc00c37f689beb0ac0afeb2975c2a55f0ac6cd","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2002-03-04T16:34:07Z","title_canon_sha256":"e54bad82a02137bf62a890087840543d5a92769216224990cfcb4f83302b5519"},"schema_version":"1.0","source":{"id":"math-ph/0203005","kind":"arxiv","version":2}},"canonical_sha256":"e8ff7f25aeb444c82993dd9111ed841ed295db66ed2dd9b2802608cd90e7023f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8ff7f25aeb444c82993dd9111ed841ed295db66ed2dd9b2802608cd90e7023f","first_computed_at":"2026-05-18T01:38:34.254337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:34.254337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tGfSwnwUlMufJJbNa6vB6Q0NEKc5AfMffiAAB2qv+/FxhNyqJpmh86Imp+LGyB119kUq4+bJuPt0Yl945+sBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:34.255095Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0203005","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80146ba60bebf10d2138ad28dd283c8e4590d037c047273f7745d393a05a4607","sha256:daabdfe51f1aaef421b6eb93c5078cc5aef23792a7c683768e7e592fa2d2989f"],"state_sha256":"bdb799159dc54711db052ab7aa8721cfdb343e0182586a65a2508a6cbde9bec5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FKjRdTyW9cmBohM6Us4rKWqPQtHvsT8xOmC4lBV3a7q3XJGbCCSiFeXkXzgGCYoNFdxhK4UxxuaJtdm0WE2vBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:26:17.866563Z","bundle_sha256":"05f8de05b6c99964e21d3a89220961c24424fc8d498f594e916bf7d7bf22885a"}}