Figure reachability · A Small Switch in a Vast Machine

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Eight anchors share one coordinate chart. Desired blue vectors remain fixed while one matrix moves all violet vectors together; gold residuals remain at the computed optimum. — Reachability · Exact mathematical model
Eight requested changes must share one matrix. In this constructed example, even the best fit leaves a residual: the matrix cannot move every input independently.
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Exact eight-input toy with $F=I$ . Blue arrows show requested changes and violet arrows the changes produced by one shared matrix. The animation varies that matrix from zero to $\Delta W^*=VA^+=\operatorname{diag}(.35,.55)$ . Gold segments join the realized and requested endpoints in the same chart; vectors share one display scale. At the solution, the residual norm is 65.6% of the requested field norm. This is an analytic interpolation, not Astra’s search or a field measured from Qwen.
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