Why quadratic, and not just superlinear?

Quadratic is not a chosen number: growth stays correctable only while the brakes keep pace, a system’s internal brakes improve at best like the square root of what they have accumulated, and the reciprocal of one half is two, so quadratic is precisely the fastest growth the best possible internal correction can still catch.

Superlinear says only “faster than linear” and names no limit; the framework forces an exact one. A corrector built inside the system improves by accumulating its own corrections, and accumulated corrections combine the way independent measurements do, where averaging a thousand samples improves your accuracy not a thousandfold but about thirty-two-fold, the square root. That square-root law caps how fast internal correction can strengthen, at exponent one half. Stability demands correction keep pace with growth, so the fastest correctable growth is the reciprocal of that cap, and one over a half is two. Quadratic, exactly, is where the best brakes the system can build out of itself finally break even with the engine.

The one assumption doing the work is that corrections combine like independent samples, and that assumption is not defended rhetorically, it is filed for measurement: if correction turns out to combine better than independence allows, the ceiling moves with it, and the tests that decide are already registered. The measured value today is 0.49, sub-linear, far inside the proposed ceiling. The number two is the central potential discovery of Michael Darius Eastwood’s research programme, and the whole of it is told at the page below.