Michael Darius Eastwood · Independent AI alignment researcher
Published
The ARC Bound is a claimed ceiling on the amplification a purely classical recursive system can achieve. In the ARC framework, alpha = 1/(1 - beta), so alpha diverges as beta approaches 1. The ARC Bound picks out beta = 0.5 (yielding alpha = 2) as the physically realisable boundary for classical systems, and pairs it with an optimal recursive depth R-star. The bound is used in Paper X as the assumption structure over which the beta greater than k criterion is derived.
The quadratic reading, alpha at most 2, is not a mathematical ceiling on the Bernoulli ODE. The Eden Vision paper sets this out directly: the equation places no upper bound on alpha, and as beta approaches one, alpha diverges. The quadratic value is an information-theoretic constraint arising from fixed transformer attention with order-N-squared pairwise pathways, and a self-modifying system that rewrites its own attention mechanism escapes that constraint entirely. The ARC Bound therefore names the regime in which the bound holds (frozen inference on fixed architecture) rather than a universal law.
The ARC Bound is introduced in the Foundational paper (dated 13 February 2026) as beta = 0.5, alpha = 2, together with an optimal-depth argument. Paper X notes it as prior art within the programme's own catalogue and stipulates that novelty, if any, sits in the axioms rather than the formula. The alpha = 1/(1 - beta) form is the classical feedback / geometric-series result (Keynes multiplier, Dyson resummation).
The functional form alpha = 1/(1 - beta) is prior art in economics (the Keynes multiplier) and in physics (the Dyson resummation). A finite optimal depth for recursive processing is prior art in the overthinking literature (Qi 2025 among others). The ARC Bound's contribution is not the formula but the axiomatic derivation and the specific value of the ceiling. Paper X credits the underlying scaling-law form to the classical feedback literature.
The ARC Bound is derived within the ARC axioms rather than empirically measured. Paper X treats it as an assumption structure for the co-scaling criterion, not as a load-bearing empirical claim. Whether real self-improving systems obey it is an open empirical question that Paper X states plainly. The bound is best read as a candidate law, not a validated one.
From the book Infinite Architects: Intelligence, Recursion, and the Creation of Everything by Michael Darius Eastwood.