{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:SYYWB537EYBJ2MWQ3KPMHNZXYH","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":"ce0f419934b01739dc69e52ff247ffc8f46da45129c017064039ed9bb5d0f398","cross_cats_sorted":["quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2001-06-15T15:25:50Z","title_canon_sha256":"35b27d117d78478614f515afff491659caca9ef8bb98f117adbf0db0b3b56cca"},"schema_version":"1.0","source":{"id":"hep-th/0106138","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0106138","created_at":"2026-05-18T04:22:51Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0106138v4","created_at":"2026-05-18T04:22:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0106138","created_at":"2026-05-18T04:22:51Z"},{"alias_kind":"pith_short_12","alias_value":"SYYWB537EYBJ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"SYYWB537EYBJ2MWQ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"SYYWB537","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:0978431f1502a5fd5251b03ce1b0c3abaa01a582bad178821e1274268f6f5953","target":"graph","created_at":"2026-05-18T04:22:51Z","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 quantum mechanics on the noncommutative plane in the presence of magnetic field $B$. We show, that the model has two essentially different phases separated by the point $B\\theta=c\\hbar^2/e$, where $\\theta$ is a parameter of noncommutativity. In this point the system reduces to exactly-solvable one-dimensional system. When $\\kappa=1-eB\\theta/c\\hbar^2<0$ there is a finite number of states corresponding to the given value of the angular momentum. In another phase, i.e. when $\\kappa>0$ the number of states is infinite. The perturbative spectrum near the critical point $\\kappa=0$ is com","authors_text":"Armen Nersessian, Corneliu Sochichiu, Stefano Bellucci","cross_cats":["quant-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2001-06-15T15:25:50Z","title":"Two phases of the noncommutative quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0106138","kind":"arxiv","version":4},"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:d274d90a0a1cf13f82fe1b98f4a2a244f8c3f79a5cdba40665b2490d97f1f4a8","target":"record","created_at":"2026-05-18T04:22:51Z","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":"ce0f419934b01739dc69e52ff247ffc8f46da45129c017064039ed9bb5d0f398","cross_cats_sorted":["quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2001-06-15T15:25:50Z","title_canon_sha256":"35b27d117d78478614f515afff491659caca9ef8bb98f117adbf0db0b3b56cca"},"schema_version":"1.0","source":{"id":"hep-th/0106138","kind":"arxiv","version":4}},"canonical_sha256":"963160f77f26029d32d0da9ec3b737c1d4da039946c59b276d0c08f54b83e1c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"963160f77f26029d32d0da9ec3b737c1d4da039946c59b276d0c08f54b83e1c2","first_computed_at":"2026-05-18T04:22:51.679040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:51.679040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xSKMtRXTUYZVMA2Jjd6njXhnqNE4cgrkB9lSRDOZnxYGT9R/cmbFfOpUvvxnCfZ1iTDzcae44V9O9sXqKlSNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:51.679598Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0106138","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d274d90a0a1cf13f82fe1b98f4a2a244f8c3f79a5cdba40665b2490d97f1f4a8","sha256:0978431f1502a5fd5251b03ce1b0c3abaa01a582bad178821e1274268f6f5953"],"state_sha256":"9d6797bb61d06ee541fda1e35f82511f3990cec7c4e7389fc0a83b82bd4bb796"}