Decoupling Spatial Interaction from Corpus State: Re-centring Without Re-coupling

A spatial interface over a personal corpus of embeddings has two requirements: writing a note must not move the ones already placed, and navigating must re-centre the view on the note being consulted. Global dimensionality reduction such as UMAP or t-SNE, the usual choice for such canvases, keeps a layout current by refitting, which relocates placed points even with a fixed seed and reads the whole corpus again. Any fixed linear map meets the first requirement without reading the corpus; the second is where methods differ. We present the Polar Projector, a local O(d) operator that places an incoming vector against an active frame, an anchor plus a contrast dipole, without reading the corpus, returning a clamped projection coefficient λ ∈ [−1, 1] and an orthogonal residual d_esc ≥ 0. Its collinear configurations do not degenerate (Proposition 2), its residual decomposition is exact when λ is unsaturated (Proposition 3), and an algebraically equivalent scalar form of d_esc loses all precision below d_esc/‖r‖₂ ≈ 10⁻⁶, at two points undetectably. Re-anchoring the frame on the query re-centres the view without re-coupling it, beyond a codebook built once.Per-stimulus cost is 4.66 µs with a prepared frame, and a stateless call stays flat to 2.7% across corpora of 1,000 to 25,000 vectors. On 2,221 chunks of Spinoza's Ethics, re-anchoring raises the recall of a query's 15 nearest neighbours 29×, from 0.019 to 0.543, while a local PCA refit reads the corpus again and recovers 0.023. A radial coordinate centred on the query bounds the operator at 0.981 on this instrument, which rewards any view ordered by distance from the query; rendering λ in length units lifts the operator to 0.925 in an exploratory ablation. No user took part, so whether any of this helps a person navigate remains open.