{"paper":{"title":"Exponential concentration for quantum periods via mirror symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Quantum periods of Fano manifolds satisfy the exponential concentration property when they admit convenient weak Landau-Ginzburg models with non-negative coefficients.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hua-Zhong Ke, Jianxun Hu, Jingwei Lu","submitted_at":"2026-05-15T15:19:10Z","abstract_excerpt":"We investigate power series satisfying the exponential concentration property, and show that suitable modifications of hypergeometric series respect this property. As a geometric application, we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Fano manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients (extracted from the abstract statement of the geometric application).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Modified hypergeometric series respect the exponential concentration property, implying the same for quantum periods of Fano manifolds admitting convenient weak Landau-Ginzburg models with non-negative coefficients.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quantum periods of Fano manifolds satisfy the exponential concentration property when they admit convenient weak Landau-Ginzburg models with non-negative coefficients.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5897ea168761b8bac297369a0363c87952d6174831df25c28227d5924f8297f6"},"source":{"id":"2605.16051","kind":"arxiv","version":1},"verdict":{"id":"f5d88e23-707a-44f3-a7fc-55bd5f5b17fb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:16:53.282766Z","strongest_claim":"we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients.","one_line_summary":"Modified hypergeometric series respect the exponential concentration property, implying the same for quantum periods of Fano manifolds admitting convenient weak Landau-Ginzburg models with non-negative coefficients.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Fano manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients (extracted from the abstract statement of the geometric application).","pith_extraction_headline":"Quantum periods of Fano manifolds satisfy the exponential concentration property when they admit convenient weak Landau-Ginzburg models with non-negative coefficients."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16051/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:18.999651Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:31:00.518763Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:41.555114Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.528310Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"79ce526609db03712fe56e54c40f44e1a966e48b8ff7e8435c387064a67b2260"},"references":{"count":13,"sample":[{"doi":"","year":2013,"title":"Gamma conjecture I for flag varieties","work_id":"54738610-bd8a-436f-819e-959d6bacdd45","ref_index":1,"cited_arxiv_id":"2501.13221","is_internal_anchor":true},{"doi":"","year":2022,"title":"Databases of quantum periods for Fano manifolds","work_id":"aafe0434-572a-4d22-966e-0f64c644b4eb","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"The conifold point","work_id":"fc06f1e2-b485-4914-8687-3c7621bbcc78","ref_index":3,"cited_arxiv_id":"1404.7388","is_internal_anchor":true},{"doi":"","year":2016,"title":"On the quantum product of Schubert classes","work_id":"a6a93303-0278-4306-899c-c63ddb93dee1","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Adv. 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