The quadratic ceiling is a ceiling of what, exactly?
Of stable, internally self-correctable capability scaling. Not of growth, size or speed in general. State the law first: the ceiling is the reciprocal of the correction shortfall (one minus the correction exponent). State the value second: feed it the assumption that internally accumulated correction strengthens at most like the square root of what it has accumulated, and the reciprocal of one half is two.
Every summary of the programme compresses to the ceiling, and the compression is where readers go wrong, so here is the uncompressed object with its two propositions ranked in the order they must be told.
The law comes first: the ceiling of stable self-correctable capability scaling is the reciprocal of the correction shortfall (one minus the correction exponent). The ceiling is on the scaling exponent of a self-improving system's capability, under the condition that the system remain stable because its internally generated correction must keep pace. It is not a ceiling on growth itself, and exceeding it is not impossible; it is supercritical, with drift as the predicted consequence.
The value comes second, and only after the law. Feed the law one working assumption, that internally accumulated correction strengthens at most like the square root of what it has accumulated, and the fastest correctable growth is the reciprocal of one half, which is two. The number is derived, not fitted.
The ranking survives the two ways the claim can die. If the accumulation assumption is wrong, the law is untouched: measure a different correction exponent, report a different reciprocal. If the law is wrong, the value has nothing holding it up, because the book printed the square without deriving it and the derivation arrived eighteen months later through the reciprocal. Tests aim at the assumption, not the digit. Challenge the square-root premise and the ceiling moves with it; the tests that decide are written, dated and prepared as draft registrations awaiting human submission. What cannot be done is to keep the premise and argue for a different number.