{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:MPMPPVEXMVFEOHCMAKHWBAZOMJ","short_pith_number":"pith:MPMPPVEX","canonical_record":{"source":{"id":"2201.05140","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-01-13T18:52:30Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"0c83f60d3fa080aa2bcb5cd6387ff0cf17a7f65431bddf53eb13446e67a6dd73","abstract_canon_sha256":"af79e49db67e970c83e6196a07150ed73349327218d07586e2c8cb96a7b7b167"},"schema_version":"1.0"},"canonical_sha256":"63d8f7d497654a471c4c028f60832e626f04d7f0423de833ef3f22a3c8fe8a41","source":{"kind":"arxiv","id":"2201.05140","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.05140","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"2201.05140v1","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05140","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"MPMPPVEXMVFE","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"pith_short_16","alias_value":"MPMPPVEXMVFEOHCM","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"pith_short_8","alias_value":"MPMPPVEX","created_at":"2026-07-05T05:45:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:MPMPPVEXMVFEOHCMAKHWBAZOMJ","target":"record","payload":{"canonical_record":{"source":{"id":"2201.05140","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-01-13T18:52:30Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"0c83f60d3fa080aa2bcb5cd6387ff0cf17a7f65431bddf53eb13446e67a6dd73","abstract_canon_sha256":"af79e49db67e970c83e6196a07150ed73349327218d07586e2c8cb96a7b7b167"},"schema_version":"1.0"},"canonical_sha256":"63d8f7d497654a471c4c028f60832e626f04d7f0423de833ef3f22a3c8fe8a41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:45:16.950170Z","signature_b64":"6B/iF1I2zc9Krqg7GM1IP2APerQglouZIvn+gKSLtcXUS/32TvIIksvuCsc7FePN3VVlSRLhZLAOUrwBY27/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63d8f7d497654a471c4c028f60832e626f04d7f0423de833ef3f22a3c8fe8a41","last_reissued_at":"2026-07-05T05:45:16.949821Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:45:16.949821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.05140","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":"2026-07-05T05:45:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8fo7ktZ+VVr6XlStBn9x5mIOC/7PlrdaF46mqaUabnFPnAgpE2w/XQZlymqwYEdwhNCTxqlOOOvPaLvZTGNvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:18:58.499795Z"},"content_sha256":"ab28e08ed7a659d67264ab93d93b42b7eab00871d4c839d07bd156e218f4990b","schema_version":"1.0","event_id":"sha256:ab28e08ed7a659d67264ab93d93b42b7eab00871d4c839d07bd156e218f4990b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:MPMPPVEXMVFEOHCMAKHWBAZOMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An introduction to PT-symmetric quantum mechanics -- time-dependent systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Fring","submitted_at":"2022-01-13T18:52:30Z","abstract_excerpt":"I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric, that is they are left invariant under a simultaneous parity transformation (P) and time-reversal (T). I will explain how generalised versions of this antilinear symmetry can be utilised to explain that these type of systems possess real eigenvalue spectra in parts of their parameter spaces and how to set up a consistent quantum mechanical framework for them that enables a unitary time-evolution. In the second part I will explain how to extend this framework to explicitly time-dependent Hamiltonian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05140","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.05140/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:45:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PT8mOXrai/kSrlDNEIIWBcAic1kv2dJH7pZJzfkoHX4G5JQVQlxxGfvaKlZVjnHzQiR6hYnYMrnMzFQo4fzuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T17:18:58.500325Z"},"content_sha256":"237d93f996a0d73463e752381a975c32d2b40d5de00a524b2d048c70ba527584","schema_version":"1.0","event_id":"sha256:237d93f996a0d73463e752381a975c32d2b40d5de00a524b2d048c70ba527584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ/bundle.json","state_url":"https://pith.science/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ/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":"2026-08-03T17:18:58Z","links":{"resolver":"https://pith.science/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ","bundle":"https://pith.science/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ/bundle.json","state":"https://pith.science/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPMPPVEXMVFEOHCMAKHWBAZOMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MPMPPVEXMVFEOHCMAKHWBAZOMJ","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":"af79e49db67e970c83e6196a07150ed73349327218d07586e2c8cb96a7b7b167","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-01-13T18:52:30Z","title_canon_sha256":"0c83f60d3fa080aa2bcb5cd6387ff0cf17a7f65431bddf53eb13446e67a6dd73"},"schema_version":"1.0","source":{"id":"2201.05140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.05140","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"arxiv_version","alias_value":"2201.05140v1","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05140","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"pith_short_12","alias_value":"MPMPPVEXMVFE","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"pith_short_16","alias_value":"MPMPPVEXMVFEOHCM","created_at":"2026-07-05T05:45:16Z"},{"alias_kind":"pith_short_8","alias_value":"MPMPPVEX","created_at":"2026-07-05T05:45:16Z"}],"graph_snapshots":[{"event_id":"sha256:237d93f996a0d73463e752381a975c32d2b40d5de00a524b2d048c70ba527584","target":"graph","created_at":"2026-07-05T05:45:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.05140/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric, that is they are left invariant under a simultaneous parity transformation (P) and time-reversal (T). I will explain how generalised versions of this antilinear symmetry can be utilised to explain that these type of systems possess real eigenvalue spectra in parts of their parameter spaces and how to set up a consistent quantum mechanical framework for them that enables a unitary time-evolution. In the second part I will explain how to extend this framework to explicitly time-dependent Hamiltonian","authors_text":"Andreas Fring","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-01-13T18:52:30Z","title":"An introduction to PT-symmetric quantum mechanics -- time-dependent systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05140","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:ab28e08ed7a659d67264ab93d93b42b7eab00871d4c839d07bd156e218f4990b","target":"record","created_at":"2026-07-05T05:45:16Z","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":"af79e49db67e970c83e6196a07150ed73349327218d07586e2c8cb96a7b7b167","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-01-13T18:52:30Z","title_canon_sha256":"0c83f60d3fa080aa2bcb5cd6387ff0cf17a7f65431bddf53eb13446e67a6dd73"},"schema_version":"1.0","source":{"id":"2201.05140","kind":"arxiv","version":1}},"canonical_sha256":"63d8f7d497654a471c4c028f60832e626f04d7f0423de833ef3f22a3c8fe8a41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63d8f7d497654a471c4c028f60832e626f04d7f0423de833ef3f22a3c8fe8a41","first_computed_at":"2026-07-05T05:45:16.949821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:45:16.949821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6B/iF1I2zc9Krqg7GM1IP2APerQglouZIvn+gKSLtcXUS/32TvIIksvuCsc7FePN3VVlSRLhZLAOUrwBY27/CA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:45:16.950170Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.05140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab28e08ed7a659d67264ab93d93b42b7eab00871d4c839d07bd156e218f4990b","sha256:237d93f996a0d73463e752381a975c32d2b40d5de00a524b2d048c70ba527584"],"state_sha256":"64f5b8163fc22d7aa8f3c902f179e328ac315f1b94f1f8d18b410f4256a5755f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a56hNQ06DY3NU5QGbJr2nbvQGUT/Xi9hXu+oUcg6sAshfuqj1lQt+f11LaYOW4GbQ0u1vDp+CutxZdm7WNPXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T17:18:58.506442Z","bundle_sha256":"b90676b992a932c6a996fce2452105ffb645b5e0c7c5ff15fb64ede3716023fd"}}