{"paper":{"title":"Second-order moment equivalence of twisted Gaussian Schell model beams and orbital angular momentum eigenmodes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Covariance matrices of coherent OAM eigenmodes and twisted Gaussian Schell-model beams are identical","cross_cats":["quant-ph"],"primary_cat":"physics.optics","authors_text":"E. S. G\\'omez, G. Ca\\~nas, G. Lima, G. Santos, Lucas Hutter, S. Ayala, S. P. Walborn, T. Ferreira","submitted_at":"2026-05-14T20:48:36Z","abstract_excerpt":"We show that the covariance matrix of any cylindrically symmetric coherent orbital angular momentum (OAM) eigenmode with quantum number $\\ell$ takes a universal form depending only on $\\langle r^2\\rangle$, $\\langle k_r^2\\rangle$, and $\\ell$, independently of the radial profile, and that this form is identical to the covariance matrix of a twisted Gaussian Schell-model (TGSM) beam.} More specifically, both matrices share the same pattern of zero and nonzero entries, with the off-diagonal blocks proportional to $\\ell$ and the TGSM twist parameter $u$, respectively. This result holds for an arbit"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the covariance matrix of any cylindrically symmetric coherent orbital angular momentum (OAM) eigenmode with quantum number ℓ takes a universal form depending only on ⟨r²⟩, ⟨k_r²⟩, and ℓ, independently of the radial profile, and that this form is identical to the covariance matrix of a twisted Gaussian Schell-model (TGSM) beam","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the covariance matrix alone fully governs second-moment evolution under arbitrary ABCD (symplectic) transformations, as stated in the abstract to conclude that matched beams are second-order indistinguishable at every propagation plane.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Covariance matrices of coherent OAM eigenmodes and TGSM beams share identical structure and zero/nonzero pattern, enabling second-order equivalence under ABCD transformations for arbitrary radial profiles.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Covariance matrices of coherent OAM eigenmodes and twisted Gaussian Schell-model beams are identical","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c057f54f24e692f752484e8e64d334f4df202d3ab03557586076d3cbb3b9cd5c"},"source":{"id":"2605.15408","kind":"arxiv","version":1},"verdict":{"id":"144c696b-927e-45bc-92cc-069088e28cad","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T15:26:51.454751Z","strongest_claim":"the covariance matrix of any cylindrically symmetric coherent orbital angular momentum (OAM) eigenmode with quantum number ℓ takes a universal form depending only on ⟨r²⟩, ⟨k_r²⟩, and ℓ, independently of the radial profile, and that this form is identical to the covariance matrix of a twisted Gaussian Schell-model (TGSM) beam","one_line_summary":"Covariance matrices of coherent OAM eigenmodes and TGSM beams share identical structure and zero/nonzero pattern, enabling second-order equivalence under ABCD transformations for arbitrary radial profiles.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the covariance matrix alone fully governs second-moment evolution under arbitrary ABCD (symplectic) transformations, as stated in the abstract to conclude that matched beams are second-order indistinguishable at every propagation plane.","pith_extraction_headline":"Covariance matrices of coherent OAM eigenmodes and twisted Gaussian Schell-model beams are identical"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15408/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T16:23:43.134020Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T16:01:17.994969Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T15:50:48.572341Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:40:38.815739Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.154719Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.712725Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f83635912a547ee44df259d730b75557926ac864bfce54148c65581188ea3884"},"references":{"count":44,"sample":[{"doi":"","year":1992,"title":"L. 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