{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:X2S3GIZQIXMXZR6ELIGA3IKL44","short_pith_number":"pith:X2S3GIZQ","schema_version":"1.0","canonical_sha256":"bea5b3233045d97cc7c45a0c0da14be71588b87cb0e0cba8b3f2e31a400f4db7","source":{"kind":"arxiv","id":"1112.2993","version":2},"attestation_state":"computed","paper":{"title":"Solution of the propeller conjecture in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"cs.CC","authors_text":"Assaf Naor, Aukosh Jagannath, Steven Heilman","submitted_at":"2011-12-13T18:27:03Z","abstract_excerpt":"It is shown that every measurable partition ${A_1,..., A_k}$ of $\\mathbb{R}^3$ satisfies $$\\sum_{i=1}^k||\\int_{A_i} xe^{-\\frac12||x||_2^2}dx||_2^2\\le 9\\pi^2.\\qquad(*)$$ Let ${P_1,P_2,P_3}$ be the partition of $\\mathbb{R}^2$ into $120^\\circ$ sectors centered at the origin. The bound is sharp, with equality holding if $A_i=P_i\\times \\mathbb{R}$ for $i\\in {1,2,3}$ and $A_i=\\emptyset$ for $i\\in \\{4,...,k\\}$ (up to measure zero corrections, orthogonal transformations and renumbering of the sets $\\{A_1,...,A_k\\}$). This settles positively the 3-dimensional Propeller Conjecture of Khot and Naor (FOCS"},"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":"1112.2993","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-13T18:27:03Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"80b262354473009f09086dc328a868197fe636f7fa33fba20c2694f681c8d3e5","abstract_canon_sha256":"8706d15dcaf2f69e7c2a0a79b6f233fe964d9bfb5b82c52ad14f01817df354b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.359083Z","signature_b64":"zH6jZpHlXVb3T+Pg1GejndIlHEzLCYfPUgcpOBKr+4TDEG6f+OcxcyAhXRJ083Zn6UM1lwRRv3SzOiPXhsBjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bea5b3233045d97cc7c45a0c0da14be71588b87cb0e0cba8b3f2e31a400f4db7","last_reissued_at":"2026-05-18T02:54:47.358702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.358702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solution of the propeller conjecture in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"cs.CC","authors_text":"Assaf Naor, Aukosh Jagannath, Steven Heilman","submitted_at":"2011-12-13T18:27:03Z","abstract_excerpt":"It is shown that every measurable partition ${A_1,..., A_k}$ of $\\mathbb{R}^3$ satisfies $$\\sum_{i=1}^k||\\int_{A_i} xe^{-\\frac12||x||_2^2}dx||_2^2\\le 9\\pi^2.\\qquad(*)$$ Let ${P_1,P_2,P_3}$ be the partition of $\\mathbb{R}^2$ into $120^\\circ$ sectors centered at the origin. The bound is sharp, with equality holding if $A_i=P_i\\times \\mathbb{R}$ for $i\\in {1,2,3}$ and $A_i=\\emptyset$ for $i\\in \\{4,...,k\\}$ (up to measure zero corrections, orthogonal transformations and renumbering of the sets $\\{A_1,...,A_k\\}$). 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