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Hasibul Hassan Chowdhury","submitted_at":"2026-02-28T07:49:53Z","abstract_excerpt":"We analyze generalized Bopp shifts and Darboux normalization in two-dimensional noncommutative quantum mechanics (NCQM) from the viewpoint of the unitary representation theory of the kinematical symmetry group \\(G_{\\mathrm{NC}}\\). This group is a step-two nilpotent Lie group with three-dimensional center, and the regular part of its unitary dual \\(\\widehat{G_{\\mathrm{NC}}}\\) is labelled by central characters \\((\\hbar,\\vartheta,B_{\\mathrm{in}})\\). Ordinary two-dimensional quantum mechanics (QM) appears inside \\(\\widehat{G_{\\mathrm{NC}}}\\) as the family of Weyl-Heisenberg representations inflate"},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.00524","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-02-28T07:49:53Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"29aa68a676ea8ba7cfe62df3389d0202977e35e0cb2eda5677a0697338489de7","abstract_canon_sha256":"86b9820d1fc9801348b9507402901509c16ab698c1362d5e1a82999266371bf7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:03.502406Z","signature_b64":"iSqg4BnKsAAnOkpb1z0rBuspfKdwAbZ0kBn3qWfYkcYi+4mAcnMLh+EOiT3jo60sEoaUUcP0Y/AMr43dth+vAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"358686d82c327870f2fbe5be9c15f6ac21eedf77820ca159c3ca4001bdb93df5","last_reissued_at":"2026-05-18T03:10:03.501505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:03.501505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central Characters of $G_{\\mathrm{NC}}$, Darboux Normalization, and the Kinematical Inequivalence of NCQM and QM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Generic noncommutative quantum mechanics sectors are not unitarily equivalent to ordinary quantum mechanics as G_NC representations","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"S. Hasibul Hassan Chowdhury","submitted_at":"2026-02-28T07:49:53Z","abstract_excerpt":"We analyze generalized Bopp shifts and Darboux normalization in two-dimensional noncommutative quantum mechanics (NCQM) from the viewpoint of the unitary representation theory of the kinematical symmetry group \\(G_{\\mathrm{NC}}\\). This group is a step-two nilpotent Lie group with three-dimensional center, and the regular part of its unitary dual \\(\\widehat{G_{\\mathrm{NC}}}\\) is labelled by central characters \\((\\hbar,\\vartheta,B_{\\mathrm{in}})\\). Ordinary two-dimensional quantum mechanics (QM) appears inside \\(\\widehat{G_{\\mathrm{NC}}}\\) as the family of Weyl-Heisenberg representations inflate"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that a generic nondegenerate NCQM sector (ℏ₀,ϑ₀,B₀), with ℏ₀,ϑ₀,B₀≠0 and ℏ₀−B₀ϑ₀≠0, is not unitarily equivalent to the ordinary QM sector (ℏ₀,0,0) as a G_NC-representation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the kinematical symmetry group is correctly identified as the step-two nilpotent Lie group G_NC with three-dimensional center whose regular unitary dual is labelled by central characters (ℏ,ϑ,B_in), and that ordinary QM corresponds exactly to the inflated Weyl-Heisenberg representations with central character (ℏ,0,0).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Generic noncommutative quantum mechanics sectors are not unitarily equivalent to ordinary quantum mechanics as G_NC representations","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0679025efdc3bce0d00b46ade51555bb197953c9e4de5c5ec35c17bd49668fad"},"source":{"id":"2603.00524","kind":"arxiv","version":2},"verdict":{"id":"31ae7cb6-edcb-4d92-ab09-4248e519357c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T18:56:01.113544Z","strongest_claim":"We prove that a generic nondegenerate NCQM sector (ℏ₀,ϑ₀,B₀), with ℏ₀,ϑ₀,B₀≠0 and ℏ₀−B₀ϑ₀≠0, is not unitarily equivalent to the ordinary QM sector (ℏ₀,0,0) as a G_NC-representation.","one_line_summary":"Generic nondegenerate NCQM sectors with nonzero central character parameters are not unitarily equivalent to ordinary QM as representations of G_NC.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the kinematical symmetry group is correctly identified as the step-two nilpotent Lie group G_NC with three-dimensional center whose regular unitary dual is labelled by central characters (ℏ,ϑ,B_in), and that ordinary QM corresponds exactly to the inflated Weyl-Heisenberg representations with central character (ℏ,0,0).","pith_extraction_headline":"Generic noncommutative quantum mechanics sectors are not unitarily equivalent to ordinary quantum mechanics as G_NC representations"},"references":{"count":14,"sample":[{"doi":"","year":1978,"title":"F. 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