{"paper":{"title":"An infinite-dimensional helix invariant under spherical projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Zakhar Kabluchko","submitted_at":"2018-11-23T21:00:03Z","abstract_excerpt":"We classify all subsets $S$ of the projective Hilbert space with the following property: for every point $\\pm s_0\\in S$, the spherical projection of $S\\backslash\\{\\pm s_0\\}$ to the hyperplane orthogonal to $\\pm s_0$ is isometric to $S\\backslash\\{\\pm s_0\\}$. In probabilistic terms, this means that we characterize all zero-mean Gaussian processes $Z=(Z(t))_{t\\in T}$ with the property that for every $s_0\\in T$ the conditional distribution of $(Z(t))_{t\\in T}$ given that $Z(s_0)=0$ coincides with the distribution of $(\\varphi(t; s_0) Z(t))_{t\\in T}$ for some function $\\varphi(t;s_0)$. A basic exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09687","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"}