Why noise wins at depth

Every gate adds load. Every two-qubit gate adds an error of roughly its calibrated rate, and errors compound. After enough gates the state has lost the arrangement that made wrong answers cancel — the amplitudes are scrambled and the ratio falls to 0.500.

That fall is not gradual noise on top of a signal. It is a crossing: under the edge, more depth still buys a better ideal answer; beyond it, more depth buys nothing. The forecast step finds the crossing from today's calibration and your circuit's load, and puts the regime next to every machine.

ROX OS moves the crossing by lowering the load the machine actually carries for the same ideal state: a better loop, fewer native gates, a protected schedule. It does not remove noise after the fact; it asks the machine for less. Where that is not enough, the record shows a loss.

See The edge for the curve and The law behind it for λ ≤ σ.