{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:3OLVQDLHW5K5VBWUAVH5IKCAZS","short_pith_number":"pith:3OLVQDLH","schema_version":"1.0","canonical_sha256":"db97580d67b755da86d4054fd42840cc96254857ddf9e80e0cb49758c7a34fdb","source":{"kind":"arxiv","id":"2309.04097","version":1},"attestation_state":"computed","paper":{"title":"Discretized Radial Projections in $\\mathbb{R}^d$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.CA","authors_text":"Kevin Ren","submitted_at":"2023-09-08T03:25:08Z","abstract_excerpt":"We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an $\\epsilon$-improvement in Kaufman's projection theorem for hyperplanes and an unconditional discretized radial projection theorem in the spirit of Orponen-Shmerkin-Wang. Our proof relies on a new incidence estimate for $\\delta$-tubes and a quasi-product set of $\\delta$-balls in $\\mathbb{R}^d$."},"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":"2309.04097","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2023-09-08T03:25:08Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"ccad0cd5576dcd4986f26dc25405f017b0de46ef3aca7678f812f2481222c050","abstract_canon_sha256":"96fc468805fd8ef1f78739bc5f9d8e267567add787119e09f1dbf967a5b295fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:55.139268Z","signature_b64":"5p50GutYNardXcq4ZVSdx8sad2uK6habcQvn8bYceUg4kBKImwWYCuzrI2lCT0SJmMkoizwPWzg1jFWe8HZTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db97580d67b755da86d4054fd42840cc96254857ddf9e80e0cb49758c7a34fdb","last_reissued_at":"2026-07-05T06:48:55.138763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:55.138763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discretized Radial Projections in $\\mathbb{R}^d$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.CA","authors_text":"Kevin Ren","submitted_at":"2023-09-08T03:25:08Z","abstract_excerpt":"We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an $\\epsilon$-improvement in Kaufman's projection theorem for hyperplanes and an unconditional discretized radial projection theorem in the spirit of Orponen-Shmerkin-Wang. Our proof relies on a new incidence estimate for $\\delta$-tubes and a quasi-product set of $\\delta$-balls in $\\mathbb{R}^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.04097","kind":"arxiv","version":1},"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/2309.04097/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":"2309.04097","created_at":"2026-07-05T06:48:55.138822+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.04097v1","created_at":"2026-07-05T06:48:55.138822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.04097","created_at":"2026-07-05T06:48:55.138822+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OLVQDLHW5K5","created_at":"2026-07-05T06:48:55.138822+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OLVQDLHW5K5VBWU","created_at":"2026-07-05T06:48:55.138822+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OLVQDLH","created_at":"2026-07-05T06:48:55.138822+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.17985","citing_title":"Pinned Dot Product Set Estimates","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS","json":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS.json","graph_json":"https://pith.science/api/pith-number/3OLVQDLHW5K5VBWUAVH5IKCAZS/graph.json","events_json":"https://pith.science/api/pith-number/3OLVQDLHW5K5VBWUAVH5IKCAZS/events.json","paper":"https://pith.science/paper/3OLVQDLH"},"agent_actions":{"view_html":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS","download_json":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS.json","view_paper":"https://pith.science/paper/3OLVQDLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.04097&json=true","fetch_graph":"https://pith.science/api/pith-number/3OLVQDLHW5K5VBWUAVH5IKCAZS/graph.json","fetch_events":"https://pith.science/api/pith-number/3OLVQDLHW5K5VBWUAVH5IKCAZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS/action/storage_attestation","attest_author":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS/action/author_attestation","sign_citation":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS/action/citation_signature","submit_replication":"https://pith.science/pith/3OLVQDLHW5K5VBWUAVH5IKCAZS/action/replication_record"}},"created_at":"2026-07-05T06:48:55.138822+00:00","updated_at":"2026-07-05T06:48:55.138822+00:00"}