The ARC Principle in plain English
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Three axioms plus Cauchy's 1821 theorem fix every recursive scaling law to one of three shapes. Which one you get is decided by the composition operator.

Canonical path: /research/blog/paper-foundational.html
Author: Michael Darius Eastwood
Research programme: https://doi.org/10.17605/OSF.IO/6C5XB

The ARC Principle in plain English 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). If capability grows with recursion, what shape does that growth take? This foundational paper argues the shape is not a free parameter. Three axioms (separability, cumulative advantage, continuity) plus Cauchy's 1821 classification pin every recursive system to one of three curves: a power law, an exponential, or a saturation curve. Which curve you get is decided by the system's composition operator. Foundational Paper · Formalises the ARC Principle: capability U equals base potential I times a scaling function whose form is determined by the recursive composition operator, with the power law exponent derived from a single self referential coupling constant beta via alpha = 1 / (1 minus beta). OSF DOI 10.17605/OSF.IO/6C5XB. The question it asks Between December 2024 and February 2026, four unrelated programmes (quantum error correction on Google's Willow chip, sequential reasoning in large language models, classical time crystals at NYU, recurrent processing in cortex reported by the COGITATE consortium) each found that recursive or recurrent processing produces gains exceeding linear accumulation. The paper asks whether this is coincidence or a shared structural principle. What it found The paper argues that, under three stated axioms, only three continuous scaling forms are possible: power law, exponential, and saturation. The choice is fixed by the composition operator (multiplicative, additive, or bounded), a consequence of Cauchy's 1821 functional equations. Within the power law regime, the exponent alpha is not a fitted constant but is derived from a coupling constant beta via alpha = 1 / (1 minus beta), an algebraic identity the paper proves and then validates against exact ODE solutions to machine precision.

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Machine-readable companion. Cite: Eastwood, M. D. (2026). "The ARC Principle in plain English". /research/blog/paper-foundational.html