{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HYZAERDHUP57RRIRXI5TL3MJHE","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":"6bb575551a559f6d1ef7bb271f1a088ecd4e23d9c51071ce46efa2eb42239d0a","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2014-04-15T07:35:54Z","title_canon_sha256":"fbb60d4466beef5cf8914c6b2754da5d32b7315d7d6e27827584971723caaddc"},"schema_version":"1.0","source":{"id":"1404.3837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3837","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3837v1","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3837","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"HYZAERDHUP57","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYZAERDHUP57RRIR","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYZAERDH","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:e980a7872a4e7e25061424156180a7d1df757a6472e7b7484877fe6e4191c56b","target":"graph","created_at":"2026-05-18T02:54:13Z","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 consider the quantum mechanics of an electron trapped on an infinite band along the $x$-axis in the presence of the Morse-like perpendicular magnetic field $\\vec{B}=-B_{0}e^{-\\frac{2\\pi}{a_{0}}x}\\hat{k}$ with $B_{0}>0$ as a constant strength and $a_{0}$ as the width of the band. It is shown that the square integrable pure states realize representations of $su(1,1)$ algebra via the quantum number corresponding to the linear momentum in the $y$-direction. The energy of the states increases by decreasing the width $a_{0}$ while it is not changed by $B_{0}$. It is quadratic in terms of two quan","authors_text":"B. Mojaveri, H. Fakhri, M.A. Gomshi Nobary","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2014-04-15T07:35:54Z","title":"Landau Levels as a Limiting Case of a Model with the Morse-Like Magnetic Field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3837","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":"sha256:8f3af0646fa9b31ac9db43900e6f2d400763adc6bffd3ef1b27ca14353ab82bc","target":"record","created_at":"2026-05-18T02:54:13Z","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":"6bb575551a559f6d1ef7bb271f1a088ecd4e23d9c51071ce46efa2eb42239d0a","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2014-04-15T07:35:54Z","title_canon_sha256":"fbb60d4466beef5cf8914c6b2754da5d32b7315d7d6e27827584971723caaddc"},"schema_version":"1.0","source":{"id":"1404.3837","kind":"arxiv","version":1}},"canonical_sha256":"3e32024467a3fbf8c511ba3b35ed893938c63f0ec67370383912f1e38994bdfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e32024467a3fbf8c511ba3b35ed893938c63f0ec67370383912f1e38994bdfd","first_computed_at":"2026-05-18T02:54:13.511253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:13.511253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gk9ufneeqjKiF2Ku3AKCSm0W/ZOPiT91AJMjOVz+f9RCfYCYJkkMazm9kivd2DZPQ/3MS46grnnnJ+SDpQ+HDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:13.511880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f3af0646fa9b31ac9db43900e6f2d400763adc6bffd3ef1b27ca14353ab82bc","sha256:e980a7872a4e7e25061424156180a7d1df757a6472e7b7484877fe6e4191c56b"],"state_sha256":"90001fc8931a83fe6c4234739aedc5e79c7128497f136be29ab6ed36779cffab"}