What is the ARC Bound?

The ARC Bound states the law before the value, always in that order. The law: the ceiling of stable self-correctable capability scaling is the reciprocal of the correction shortfall (one minus the correction exponent). The value: feed the law one working assumption, that same-class correctors accumulate corrections the way independent samples do, and the reciprocal of one half is two. The number is derived, not fitted; it comes from the accumulation assumption plus the requirement that correction keep pace with capability.

The ranking is not stylistic. The two propositions are asymmetric under refutation. If the value dies, the law is untouched: measure the correction exponent, report a different ceiling. If the law dies, 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 are aimed at the accumulation assumption, not the digit.

The author's ruling of 8 August 2026 settles the framing on the record: it is proposed as a stable limit, not a hard limit. Nothing says a system cannot exceed quadratic scaling; the claim is that a system whose correction is generated internally cannot remain stably self-correcting beyond it. Crossing the boundary is supercritical, not impossible: the predicted consequence is correction lag, accumulating deviation and drift, not an instant wall. The recorded refutation condition is correspondingly strict: an exponent above 2 sustained without loss of stability. The deciding measurements are written, dated and prepared as draft registrations awaiting human submission. The precise formulations live on the definitions page.