Remark: Family 140. Memory–sample lower bounds for noiseless Gaussian regression

For fixed $A>0$, a one-pass learner with $A{d}^2$ persistent bits needs ${\Omega }_A(d\log (1/ϵ))$ noiseless Gaussian samples to recover a unit vector to angular error $0<ϵ\le 1/10$ with probability $2/3$, uniformly in accuracy for large $d$. Computation and randomized updates are unrestricted, but output uses only the terminal state, stopping index and fresh randomness.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.