{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:2NPILQM6MVMYKJIH4LDS7CWVIF","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":"cb7c2deec8a6e5df943673166afdce84ceb8d3c4d669c13aba179d555d2da9da","cross_cats_sorted":["gr-qc","hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2003-06-30T09:49:32Z","title_canon_sha256":"ecadc491e583ec982a0deb8094086427677f3a806614daf03fb1ec3ecbec9604"},"schema_version":"1.0","source":{"id":"quant-ph/0306200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0306200","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0306200v2","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0306200","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"2NPILQM6MVMY","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"2NPILQM6MVMYKJIH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"2NPILQM6","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:c29160f41af3956cf9dab1a2d173a176c027b73a14000767e55cdd4b52d86042","target":"graph","created_at":"2026-05-18T01:37:59Z","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 investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution identifies the metric with a positive-definite (Ermakov-Lewis) dynamical invariant of the system. Therefore the geometric phases are determined by the metric. We construct a unitary map relating a given time-independent Hilbert space to the time-dependent Hilbert space defined by a positive-definite dynamical invariant. This map defines a transformation that ","authors_text":"Ali Mostafazadeh","cross_cats":["gr-qc","hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2003-06-30T09:49:32Z","title":"Time-Dependent Hilbert Spaces, Geometric Phases, and General Covariance in Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0306200","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":"sha256:65f389f38b4a04b1f7982eb197b5db5e9fd1a7c9adf3d2db5dd06277a3fd4dfa","target":"record","created_at":"2026-05-18T01:37:59Z","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":"cb7c2deec8a6e5df943673166afdce84ceb8d3c4d669c13aba179d555d2da9da","cross_cats_sorted":["gr-qc","hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2003-06-30T09:49:32Z","title_canon_sha256":"ecadc491e583ec982a0deb8094086427677f3a806614daf03fb1ec3ecbec9604"},"schema_version":"1.0","source":{"id":"quant-ph/0306200","kind":"arxiv","version":2}},"canonical_sha256":"d35e85c19e6559852507e2c72f8ad54175b5afb5e0e5b85f1f84fc5fa87790ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d35e85c19e6559852507e2c72f8ad54175b5afb5e0e5b85f1f84fc5fa87790ed","first_computed_at":"2026-05-18T01:37:59.276193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:59.276193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eax5+RS2JKfYr+CVuWRHqiCQU+rtHPQLTCIp17oAYDO4+uzQLZrAokQmHgyFd1goMe+AOcqeFDpulDiRUcRqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:59.276850Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0306200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65f389f38b4a04b1f7982eb197b5db5e9fd1a7c9adf3d2db5dd06277a3fd4dfa","sha256:c29160f41af3956cf9dab1a2d173a176c027b73a14000767e55cdd4b52d86042"],"state_sha256":"ebd2a4499a8cc8dad86263d9eb429bf9dd878e8c45f0135d1a41f72c2975eefa"}