{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:V6J3EKOUVT4PJZXTWJA37JJU4C","short_pith_number":"pith:V6J3EKOU","canonical_record":{"source":{"id":"1409.6456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-23T09:34:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b291e382cde5e53073747e468c0a497f55b08c6d71de27f0bc484180e8f5a2e3","abstract_canon_sha256":"0b86082863ebc3621eba2a01d1c1bc5b08563954783abcd4fa975cd3e1016b0e"},"schema_version":"1.0"},"canonical_sha256":"af93b229d4acf8f4e6f3b241bfa534e08c3f6581a83818f4033ef58260d51c5c","source":{"kind":"arxiv","id":"1409.6456","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6456","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6456v2","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6456","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"V6J3EKOUVT4P","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V6J3EKOUVT4PJZXT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V6J3EKOU","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:V6J3EKOUVT4PJZXTWJA37JJU4C","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-23T09:34:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b291e382cde5e53073747e468c0a497f55b08c6d71de27f0bc484180e8f5a2e3","abstract_canon_sha256":"0b86082863ebc3621eba2a01d1c1bc5b08563954783abcd4fa975cd3e1016b0e"},"schema_version":"1.0"},"canonical_sha256":"af93b229d4acf8f4e6f3b241bfa534e08c3f6581a83818f4033ef58260d51c5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.741522Z","signature_b64":"KJDHPwYyXAMuP72NFJwvfBAT7MWQKqklztoQMZDtYYy9sLksUSkMHO0NSdUxDeN+BSsJkAKBnDoMyWa0P95bBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af93b229d4acf8f4e6f3b241bfa534e08c3f6581a83818f4033ef58260d51c5c","last_reissued_at":"2026-05-18T01:31:11.740800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.740800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6456","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":"2026-05-18T01:31:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDUh5s2HoqvpshPOARfieUaMdI1MNNuuUWjE5Z2tFk1f74Qmpxtx67R0iDnA6XtvPZEwCrdTCUkSsxBBCsr4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:02:30.821033Z"},"content_sha256":"4db059151f71169a1b6349dea1d0072268f1bd73121ccc4b1efcf33316866a53","schema_version":"1.0","event_id":"sha256:4db059151f71169a1b6349dea1d0072268f1bd73121ccc4b1efcf33316866a53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:V6J3EKOUVT4PJZXTWJA37JJU4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alexander Rush, Eva-Maria Graefe, Hans J\\\"urgen Korsch, Roman Schubert","submitted_at":"2014-09-23T09:34:42Z","abstract_excerpt":"The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6456","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":"2026-05-18T01:31:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cvs1KWdcsxacirw4n2RJXYsiQR3h4lW8N4U/SwUilgbvmapkleo8SaxqlXPQfg3n3dqHdRYsu8+PyEhd1WF8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:02:30.821816Z"},"content_sha256":"92b9ca2571204db5ec0beb6b7a98b0797bf101bf9e1a8cb6a170374dc5f303d2","schema_version":"1.0","event_id":"sha256:92b9ca2571204db5ec0beb6b7a98b0797bf101bf9e1a8cb6a170374dc5f303d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6J3EKOUVT4PJZXTWJA37JJU4C/bundle.json","state_url":"https://pith.science/pith/V6J3EKOUVT4PJZXTWJA37JJU4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6J3EKOUVT4PJZXTWJA37JJU4C/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":"2026-05-31T11:02:30Z","links":{"resolver":"https://pith.science/pith/V6J3EKOUVT4PJZXTWJA37JJU4C","bundle":"https://pith.science/pith/V6J3EKOUVT4PJZXTWJA37JJU4C/bundle.json","state":"https://pith.science/pith/V6J3EKOUVT4PJZXTWJA37JJU4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6J3EKOUVT4PJZXTWJA37JJU4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V6J3EKOUVT4PJZXTWJA37JJU4C","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":"0b86082863ebc3621eba2a01d1c1bc5b08563954783abcd4fa975cd3e1016b0e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-23T09:34:42Z","title_canon_sha256":"b291e382cde5e53073747e468c0a497f55b08c6d71de27f0bc484180e8f5a2e3"},"schema_version":"1.0","source":{"id":"1409.6456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6456","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6456v2","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6456","created_at":"2026-05-18T01:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"V6J3EKOUVT4P","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V6J3EKOUVT4PJZXT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V6J3EKOU","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:92b9ca2571204db5ec0beb6b7a98b0797bf101bf9e1a8cb6a170374dc5f303d2","target":"graph","created_at":"2026-05-18T01:31:11Z","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":"The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the anti-Hermitian part. Closed form expressions for the metric and phase-space trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describes the quantum dynamics of Gaussian wave packets.","authors_text":"Alexander Rush, Eva-Maria Graefe, Hans J\\\"urgen Korsch, Roman Schubert","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-23T09:34:42Z","title":"Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6456","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":"sha256:4db059151f71169a1b6349dea1d0072268f1bd73121ccc4b1efcf33316866a53","target":"record","created_at":"2026-05-18T01:31:11Z","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":"0b86082863ebc3621eba2a01d1c1bc5b08563954783abcd4fa975cd3e1016b0e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-09-23T09:34:42Z","title_canon_sha256":"b291e382cde5e53073747e468c0a497f55b08c6d71de27f0bc484180e8f5a2e3"},"schema_version":"1.0","source":{"id":"1409.6456","kind":"arxiv","version":2}},"canonical_sha256":"af93b229d4acf8f4e6f3b241bfa534e08c3f6581a83818f4033ef58260d51c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af93b229d4acf8f4e6f3b241bfa534e08c3f6581a83818f4033ef58260d51c5c","first_computed_at":"2026-05-18T01:31:11.740800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:11.740800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KJDHPwYyXAMuP72NFJwvfBAT7MWQKqklztoQMZDtYYy9sLksUSkMHO0NSdUxDeN+BSsJkAKBnDoMyWa0P95bBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:11.741522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4db059151f71169a1b6349dea1d0072268f1bd73121ccc4b1efcf33316866a53","sha256:92b9ca2571204db5ec0beb6b7a98b0797bf101bf9e1a8cb6a170374dc5f303d2"],"state_sha256":"601f3984e374345f14644208597868e2aeb9e0c98783f8a80d0904de313803d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RF3GzrS/akLC6+fDNAtq9qh6qPsK9TKQg4sQ5v7mFZWRVbb2/HdgR5N4K8zC0i0gublir6+n7hbRbpeDSY9qAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:02:30.826356Z","bundle_sha256":"53d670ccd8333af1ce60fb4469da7fb954bc40f1c2aa6df4739633f5ac39555d"}}