{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TOHL22U663NAESAVOLOQLUUJQC","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":"39d70cf9b7fab954700ea49de06abbd746d43461a160d36f91529b95c6a0d451","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T18:16:46Z","title_canon_sha256":"77fc77a2afce2725f311088a2c7d5567680d500d0f15cd7ae3945680abc133d8"},"schema_version":"1.0","source":{"id":"1601.05359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05359","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05359v1","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05359","created_at":"2026-05-18T01:22:15Z"},{"alias_kind":"pith_short_12","alias_value":"TOHL22U663NA","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TOHL22U663NAESAV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TOHL22U6","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:c13877080aef8b0e3cacd3a710bd7c4f39223e1f70f34cd70bd777bc9bdfc62c","target":"graph","created_at":"2026-05-18T01:22:15Z","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 develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to ","authors_text":"A. Kunold, J. C. Sandoval-Santana, J.L. Cardoso, V. G. Ibarra-Sierra","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T18:16:46Z","title":"Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05359","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":"sha256:154ecc000842472c2d3a2eeb1daa7a73dfa0e7306ff157c01de48a2aec5b6120","target":"record","created_at":"2026-05-18T01:22:15Z","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":"39d70cf9b7fab954700ea49de06abbd746d43461a160d36f91529b95c6a0d451","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-01-20T18:16:46Z","title_canon_sha256":"77fc77a2afce2725f311088a2c7d5567680d500d0f15cd7ae3945680abc133d8"},"schema_version":"1.0","source":{"id":"1601.05359","kind":"arxiv","version":1}},"canonical_sha256":"9b8ebd6a9ef6da02481572dd05d28980974b74ebd2cc2413c9b94753fff4427a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b8ebd6a9ef6da02481572dd05d28980974b74ebd2cc2413c9b94753fff4427a","first_computed_at":"2026-05-18T01:22:15.343232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:15.343232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cmkEgitKJQTdH2xGetnpc4NCOLSxI5EBQfAxUznA/hRugnQQTf538AotNvsl3l83lTnMRgKpeXNidM9nXhWwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:15.343888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:154ecc000842472c2d3a2eeb1daa7a73dfa0e7306ff157c01de48a2aec5b6120","sha256:c13877080aef8b0e3cacd3a710bd7c4f39223e1f70f34cd70bd777bc9bdfc62c"],"state_sha256":"dc038a8454ac708497989b4671a51cb5495ffe236f50cbcc4335d970a938beb3"}