{"paper":{"title":"Associative half-densities on symplectic groupoids and quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Symplectic groupoids admit associative half-densities that classify the semiclassical corrections needed to quantize the underlying Poisson manifold.","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Alejandro Cabrera, Gabriel Gonzalo Ledesma Valenotti","submitted_at":"2026-04-09T13:03:01Z","abstract_excerpt":"In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold. We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphis"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphism and its Kashiwara-Vergne extensions as a canonical associative enhancement.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The structural motivation that an associativity condition on half-densities supplies the complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold; this premise is invoked to justify the entire construction but is not independently verified in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Associative half-densities on symplectic groupoids exist, admit classification, and canonically recover semiclassical factors from Kontsevich quantization and the Duflo isomorphism in linear cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symplectic groupoids admit associative half-densities that classify the semiclassical corrections needed to quantize the underlying Poisson manifold.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"36f0f3ea71bb2e1cfdd987648b6de7097007bb52ca91136a601f6c7833ad04d7"},"source":{"id":"2604.08201","kind":"arxiv","version":2},"verdict":{"id":"0068d035-38fa-432e-886f-51044cc15d49","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T17:26:16.650677Z","strongest_claim":"We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphism and its Kashiwara-Vergne extensions as a canonical associative enhancement.","one_line_summary":"Associative half-densities on symplectic groupoids exist, admit classification, and canonically recover semiclassical factors from Kontsevich quantization and the Duflo isomorphism in linear cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The structural motivation that an associativity condition on half-densities supplies the complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold; this premise is invoked to justify the entire construction but is not independently verified in the abstract.","pith_extraction_headline":"Symplectic groupoids admit associative half-densities that classify the semiclassical corrections needed to quantize the underlying Poisson manifold."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.08201/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}