{"paper":{"title":"Arithmetic Sparsity and Obstructions in Weighted Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Tanush Shaska","submitted_at":"2025-09-02T13:46:16Z","abstract_excerpt":"We study rational and algebraic points of bounded height on weighted projective spaces. A weighted projective space $\\mathbb{P}^n_{\\mathbf{w}}$, with weights $\\mathbf{w} = (q_0, \\dots, q_n)$, carries two natural heights: the tautological height $\\widetilde{h}$, attached to the tautological bundle on the associated stack, and the weighted height $h = H(\\phi(\\,\\cdot\\,))^{1/q}$, the normalized pullback of the Weil height under the Veronese morphism $\\phi : \\mathbb{P}^n_{\\mathbf{w}} \\to \\mathbb{P}^n$, where $q = \\operatorname{lcm}(q_0, \\dots, q_n)$. For $\\widetilde{h}$ we prove a Schanuel-type the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02319","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.02319/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"}