{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:B4XD5KOYNULAQ7SSOKOIFTWVTG","short_pith_number":"pith:B4XD5KOY","schema_version":"1.0","canonical_sha256":"0f2e3ea9d86d16087e52729c82ced599b52dd2f2745614c70d3cc2a3667f3038","source":{"kind":"arxiv","id":"2509.02319","version":3},"attestation_state":"computed","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"},"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":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.02319","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-09-02T13:46:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b33a45db4738d0a309b25c8447aedfdf3c661128f4e32e1ea3f91a6f07190b06","abstract_canon_sha256":"b66f5dd0ed1df03cc3c7a623f4cf685a63c3da7b35c3168e44ebd15acba56552"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:22:26.951181Z","signature_b64":"w5zkSc69WrzCsGItp4T/mK8pwZeS8zcKIQThZTLGhL63yDDnByp2g1tCMHD2LU3pKYn1oJVyPfU7abvSa76tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f2e3ea9d86d16087e52729c82ced599b52dd2f2745614c70d3cc2a3667f3038","last_reissued_at":"2026-07-16T01:22:26.950224Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:22:26.950224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.02319","created_at":"2026-07-16T01:22:26.950689+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.02319v3","created_at":"2026-07-16T01:22:26.950689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02319","created_at":"2026-07-16T01:22:26.950689+00:00"},{"alias_kind":"pith_short_12","alias_value":"B4XD5KOYNULA","created_at":"2026-07-16T01:22:26.950689+00:00"},{"alias_kind":"pith_short_16","alias_value":"B4XD5KOYNULAQ7SS","created_at":"2026-07-16T01:22:26.950689+00:00"},{"alias_kind":"pith_short_8","alias_value":"B4XD5KOY","created_at":"2026-07-16T01:22:26.950689+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG","json":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG.json","graph_json":"https://pith.science/api/pith-number/B4XD5KOYNULAQ7SSOKOIFTWVTG/graph.json","events_json":"https://pith.science/api/pith-number/B4XD5KOYNULAQ7SSOKOIFTWVTG/events.json","paper":"https://pith.science/paper/B4XD5KOY"},"agent_actions":{"view_html":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG","download_json":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG.json","view_paper":"https://pith.science/paper/B4XD5KOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.02319&json=true","fetch_graph":"https://pith.science/api/pith-number/B4XD5KOYNULAQ7SSOKOIFTWVTG/graph.json","fetch_events":"https://pith.science/api/pith-number/B4XD5KOYNULAQ7SSOKOIFTWVTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG/action/storage_attestation","attest_author":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG/action/author_attestation","sign_citation":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG/action/citation_signature","submit_replication":"https://pith.science/pith/B4XD5KOYNULAQ7SSOKOIFTWVTG/action/replication_record"}},"created_at":"2026-07-16T01:22:26.950689+00:00","updated_at":"2026-07-16T01:22:26.950689+00:00"}