{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BZW3H2Q6I77SJPTCDBS3ML5AE2","short_pith_number":"pith:BZW3H2Q6","schema_version":"1.0","canonical_sha256":"0e6db3ea1e47ff24be621865b62fa026bed46a37746673348e5a1e3c76ac2b73","source":{"kind":"arxiv","id":"1602.07629","version":1},"attestation_state":"computed","paper":{"title":"A sharp exceptional set estimate for visibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2016-02-24T18:22:27Z","abstract_excerpt":"A Borel set $B \\subset \\mathbb{R}^{n}$ is visible from $x \\in \\mathbb{R}^{n}$, if the radial projection of $B$ with base point $x$ has positive $\\mathcal{H}^{n - 1}$ measure. I prove that if $\\dim B > n - 1$, then $B$ is visible from every point $x \\in \\mathbb{R}^{n} \\setminus E$, where $E$ is an exceptional set with dimension $\\dim E \\leq 2(n - 1) - \\dim B$. This is the sharp bound for all $n \\geq 2$.\n  Many parts of the proof were already contained in a recent previous paper by P. Mattila and the author, where a weaker bound for $\\dim E$ was derived as a corollary from a certain slicing theo"},"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":"1602.07629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-02-24T18:22:27Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"3a9c605dfcea0e7af0cca73fb27f99214e157924dea4ac712236cf98724ae07f","abstract_canon_sha256":"83b6c084daae3c97fb27cf62c0a001d7828efea06f35757c7852506d1e66fca6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:49.150503Z","signature_b64":"fU6vv5IRlZy0kC0SumFGhq7COLfasSF+xgZTVv+2/bYyHCYVgW2w60w5aBO8uAMtrSU5ounsx8bNW0rVbaLXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e6db3ea1e47ff24be621865b62fa026bed46a37746673348e5a1e3c76ac2b73","last_reissued_at":"2026-05-18T00:30:49.149783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:49.149783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp exceptional set estimate for visibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2016-02-24T18:22:27Z","abstract_excerpt":"A Borel set $B \\subset \\mathbb{R}^{n}$ is visible from $x \\in \\mathbb{R}^{n}$, if the radial projection of $B$ with base point $x$ has positive $\\mathcal{H}^{n - 1}$ measure. I prove that if $\\dim B > n - 1$, then $B$ is visible from every point $x \\in \\mathbb{R}^{n} \\setminus E$, where $E$ is an exceptional set with dimension $\\dim E \\leq 2(n - 1) - \\dim B$. This is the sharp bound for all $n \\geq 2$.\n  Many parts of the proof were already contained in a recent previous paper by P. Mattila and the author, where a weaker bound for $\\dim E$ was derived as a corollary from a certain slicing theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07629","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":""},"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":"1602.07629","created_at":"2026-05-18T00:30:49.149893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.07629v1","created_at":"2026-05-18T00:30:49.149893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07629","created_at":"2026-05-18T00:30:49.149893+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZW3H2Q6I77S","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZW3H2Q6I77SJPTC","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZW3H2Q6","created_at":"2026-05-18T12:30:09.641336+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/BZW3H2Q6I77SJPTCDBS3ML5AE2","json":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2.json","graph_json":"https://pith.science/api/pith-number/BZW3H2Q6I77SJPTCDBS3ML5AE2/graph.json","events_json":"https://pith.science/api/pith-number/BZW3H2Q6I77SJPTCDBS3ML5AE2/events.json","paper":"https://pith.science/paper/BZW3H2Q6"},"agent_actions":{"view_html":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2","download_json":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2.json","view_paper":"https://pith.science/paper/BZW3H2Q6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.07629&json=true","fetch_graph":"https://pith.science/api/pith-number/BZW3H2Q6I77SJPTCDBS3ML5AE2/graph.json","fetch_events":"https://pith.science/api/pith-number/BZW3H2Q6I77SJPTCDBS3ML5AE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2/action/storage_attestation","attest_author":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2/action/author_attestation","sign_citation":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2/action/citation_signature","submit_replication":"https://pith.science/pith/BZW3H2Q6I77SJPTCDBS3ML5AE2/action/replication_record"}},"created_at":"2026-05-18T00:30:49.149893+00:00","updated_at":"2026-05-18T00:30:49.149893+00:00"}