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We prove that the mapping V \\mapsto Dim \\pi_{\\mathbb{V}}(B) is almost surely constant for any analytic set B \\subset R^n, where Dim denotes either Hausdorff or packing dimension."},"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":"1208.1876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-08-09T11:19:00Z","cross_cats_sorted":[],"title_canon_sha256":"71162f803ab5797fc7dddfdcc3963251c553840fd8797f8efceb18dacebb1a51","abstract_canon_sha256":"11eaffc5774d94d04eca5c0ff0d5c6fc9c40f69029a1aaa07993320079f56627"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.103609Z","signature_b64":"g3MaySEw8EIKTLah/wolC/5bxGTL8JXE+HSx7yiUuPUFPyj41QXn3wtJ5jnCfWXHppGLMQdrg83fVtqImb2xDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1333a0b19541580d46feba96dfd61aad561e15578ec6ce196cc66723ff66886b","last_reissued_at":"2026-05-18T03:11:24.102850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.102850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constancy results for special families of projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Katrin F\\\"assler, Tuomas Orponen","submitted_at":"2012-08-09T11:19:00Z","abstract_excerpt":"Let {\\mathbb{V} = V x R^l : V \\in G(n-l,m-l)} be the family of m-dimensional subspaces of R^n containing {0} x R^l, and let \\pi_{\\mathbb{V}} : R^n --> \\mathbb{V} be the orthogonal projection onto \\mathbb{V}. 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