The coupled co-scaling law: what actually keeps a self-improving AI safe
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Stability is set by an exponent inequality, correction must out-scale drift-acceleration, not by growth rate. Paper X in plain English, including what it supersedes.

Canonical path: /research/papers/paper-x-coupled-coscaling-correction.html
Author: Michael Darius Eastwood
Research programme: https://doi.org/10.17605/OSF.IO/6C5XB

The coupled co-scaling law: what actually keeps a self-improving AI safe Michael Darius Eastwood · Independent AI alignment researcher Published 3 July 2026 Michael Darius Eastwood · Foundational theory · 3 July 2026 Michael Darius Eastwood, independent researcher, London: author of the ARC/Eden research programme; the embedded-correction alignment thesis is recorded in a source record dated 8 December 2024 (sent-side SHA-256 f0d1f38f). Paper X argues that the standard reflex to a self-improving AI, cap the growth rate, has been pointed at the wrong variable. Stability depends not on how fast the system grows but on whether its correction machinery grows at least as fast as its drift acceleration. That is a smaller and more testable claim than the programme's earlier framings, and it explicitly supersedes one of them as the operative safety criterion. Paper X argues that the stability of recursive self-improvement is set by a single exponent inequality β greater than k (correction must out-scale drift-acceleration) rather than by growth rate. It supersedes the earlier fixed-exponent framing of U = I × R α as the operative safety criterion. The equation itself and the ARC Bound alpha at most 2 remain live hypotheses; only the earlier unblinded single-model fit of alpha approximately 2.24 was retracted, corrected to approximately 0.49 under blinding. OSF DOI 10.17605/OSF.IO/6C5XB. The question it asks If an AI improves itself in a loop, what governs whether it stays alignable? The dominant safety intuition is "slow it down": pause the run, cap compute, forbid super-linear growth. Paper X models a minimal self-modifying system (a capability C, a blind-scored misalignment magnitude D, and their ratio d) and asks whether the level of the growth rate really decides the outcome, or whether the answer lies in the scaling relationship between drift and correction. What it found Seven theorems within the model. In the additive channel the misalignment fraction never diverges; it either vanishes, holds a permanent gap or saturates at the drift coefficient γ 1 .

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Machine-readable companion. Cite: Eastwood, M. D. (2026). "The coupled co-scaling law: what actually keeps a self-improving AI safe". /research/papers/paper-x-coupled-coscaling-correction.html