{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KIHBC5MDALAPWQAFIO7JIBOZM2","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":"9328e70c186f137e7f29051f2a3fafd0e531d70ffdc8de90e7a6e6df564cbb3d","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-08T10:05:32Z","title_canon_sha256":"880961f23a03df187a64e7e56b535e28e6c33c344d6a44cf226ae4cddcc105fb"},"schema_version":"1.0","source":{"id":"0802.1118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.1118","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"0802.1118v1","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.1118","created_at":"2026-05-18T04:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"KIHBC5MDALAP","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KIHBC5MDALAPWQAF","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KIHBC5MD","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:c4f8e748220c1f2919d43adb0ba42363f9ac1bd3dbf843b1072c3d8d2875265b","target":"graph","created_at":"2026-05-18T04:14:36Z","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 Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schr$\\ddot{o}$dinger equations on noncommutative(NC) space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues.","authors_text":"Kang Li, Sayipjamal Dulat","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-08T10:05:32Z","title":"Landau Problem in Noncommutative Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1118","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":"sha256:39dc4692b7889ec4cf40019a06ffb195229fb44cd23153b675ed6afad094c7e1","target":"record","created_at":"2026-05-18T04:14:36Z","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":"9328e70c186f137e7f29051f2a3fafd0e531d70ffdc8de90e7a6e6df564cbb3d","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-02-08T10:05:32Z","title_canon_sha256":"880961f23a03df187a64e7e56b535e28e6c33c344d6a44cf226ae4cddcc105fb"},"schema_version":"1.0","source":{"id":"0802.1118","kind":"arxiv","version":1}},"canonical_sha256":"520e11758302c0fb400543be9405d966b51d43964a0b4b3c8211af6e8d2e3147","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"520e11758302c0fb400543be9405d966b51d43964a0b4b3c8211af6e8d2e3147","first_computed_at":"2026-05-18T04:14:36.642892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:36.642892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MZpqMkENla88nUi9h08dgeno2kxSsyvB5hCK0aMv6xqMzLHahXBug0bvkfZdwB+Jbsz8nCeXoYHyJdAlXnA/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:36.643329Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.1118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39dc4692b7889ec4cf40019a06ffb195229fb44cd23153b675ed6afad094c7e1","sha256:c4f8e748220c1f2919d43adb0ba42363f9ac1bd3dbf843b1072c3d8d2875265b"],"state_sha256":"4f2fea4ccd5e41387e725395e9703fe50e21a0ff580c6c1047ca85aeb1e2bbbc"}