Michael Darius Eastwood · Independent AI alignment researcher
Published
The ARC (Artificial Recursive Creation) Principle states that effective capability (U) equals base intelligence (I) multiplied by recursive depth (R) raised to a scaling exponent alpha. Alpha is not a universal constant; it is determined by the composition operator of the specific system. For physical systems embedded in d-dimensional space, alpha = d/(d+1), which is always less than 1. For self-referential systems governed by a coupling parameter beta, alpha = 1/(1 - beta), which can exceed 1 when beta is positive. The principle predicts that sequential recursive processing yields super-linear gains for compatible architectures, while parallel processing yields sub-linear or flat gains.
The equation U = I x R appears in the 8 December 2024 manuscript at Version 2 lines 6-9, described as 'the core of the framework'. Papers I and II formalise this as U = I x R^alpha. The published book presents U = I x R^2 (the alpha equals 2 case) as the featured formulation. Paper X supersedes the fixed-exponent framing as the operative safety criterion and installs the beta greater than k co-scaling stability condition as the current operative quantitative claim. The equation itself was not retracted; only the earlier unblinded single-model fit of alpha approximately 2.24 was retracted, corrected to approximately 0.49 under blinding.
The dimensional formula alpha = d/(d+1) has been independently derived by at least five research groups (West, Brown and Enquist; Banavar; Demetrius; Bettencourt; Zhao). The ARC framework unifies these under a Cauchy-functional-equations synthesis rather than claiming novelty for the exponent itself. Sharma and Chopra's sequential edge result (arXiv:2511.02309, 4 November 2025) precedes the programme's own January 2026 formalisation by approximately 2.5 months and is credited concurrent priority for the quantified finding.
The ARC Principle is measured at architecture-dependent alpha values on current frozen systems in Paper II and its sequel work. The initial universal-alpha-greater-than-1 claim from Paper I has been honestly revised: on the hard tier, alpha is often sub-linear, and the three-tier alignment hierarchy shows positive, flat, and negative scaling depending on model. The fixed-exponent framing as the operative safety criterion has been superseded by Paper X: the load-bearing operative quantitative claim is now the beta greater than k co-scaling criterion for stability. The ARC Bound alpha at most 2 remains a live hypothesis whose real domain, genuine self-improving systems, remains unmeasured; the beta over k programme is that test.
From the book Infinite Architects: Intelligence, Recursion, and the Creation of Everything by Michael Darius Eastwood.