{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:6T5ZTSWWDNN6Y5BFRRQ2SDIKFG","short_pith_number":"pith:6T5ZTSWW","schema_version":"1.0","canonical_sha256":"f4fb99cad61b5bec74258c61a90d0a298ca3eba217c477466933a0fdc223dc3f","source":{"kind":"arxiv","id":"1012.1337","version":2},"attestation_state":"computed","paper":{"title":"Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Ran Cheng","submitted_at":"2010-12-06T21:10:45Z","abstract_excerpt":"Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a complex tensor with the real part serving as the Riemannian metric that measures the `quantum distance', and the imaginary part being the Berry curvature. Following a physical introduction of the basic formalism, we illustrate its physical significance in both the adiabatic and non-adiabatic systems."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.1337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-06T21:10:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3a8327234b0ceea4030b83e2dc88932d19ee1d89ab60e7d7d66e6e0ffc489a8b","abstract_canon_sha256":"98b7257873eb8a1ef049120446dc8c6fa6cb7634e5b3dac189de6672af477981"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:56.533735Z","signature_b64":"f9JXyFc39SkDnBaRYPAYrQIG6KrZG/nfzxG1aJioUAtQgMfUpzUe3DxRJ19IimxeV6qiaOFm3Nw1VpeXIjBfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4fb99cad61b5bec74258c61a90d0a298ca3eba217c477466933a0fdc223dc3f","last_reissued_at":"2026-05-18T03:28:56.533159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:56.533159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Ran Cheng","submitted_at":"2010-12-06T21:10:45Z","abstract_excerpt":"Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a complex tensor with the real part serving as the Riemannian metric that measures the `quantum distance', and the imaginary part being the Berry curvature. Following a physical introduction of the basic formalism, we illustrate its physical significance in both the adiabatic and non-adiabatic systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1337","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.1337","created_at":"2026-05-18T03:28:56.533255+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.1337v2","created_at":"2026-05-18T03:28:56.533255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1337","created_at":"2026-05-18T03:28:56.533255+00:00"},{"alias_kind":"pith_short_12","alias_value":"6T5ZTSWWDNN6","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"6T5ZTSWWDNN6Y5BF","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"6T5ZTSWW","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.19820","citing_title":"Geometric curvature driven by many-body collective fluctuations","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2601.19152","citing_title":"Evolution of quantum geometric tensor of 1D periodic systems after a quench","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2605.00241","citing_title":"Exploring the Geometric and Dynamical Properties of Spin Systems and Their Interplay with Quantum Entanglement","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG","json":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG.json","graph_json":"https://pith.science/api/pith-number/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/graph.json","events_json":"https://pith.science/api/pith-number/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/events.json","paper":"https://pith.science/paper/6T5ZTSWW"},"agent_actions":{"view_html":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG","download_json":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG.json","view_paper":"https://pith.science/paper/6T5ZTSWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.1337&json=true","fetch_graph":"https://pith.science/api/pith-number/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/graph.json","fetch_events":"https://pith.science/api/pith-number/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/action/storage_attestation","attest_author":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/action/author_attestation","sign_citation":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/action/citation_signature","submit_replication":"https://pith.science/pith/6T5ZTSWWDNN6Y5BFRRQ2SDIKFG/action/replication_record"}},"created_at":"2026-05-18T03:28:56.533255+00:00","updated_at":"2026-05-18T03:28:56.533255+00:00"}