Michael Darius Eastwood · Independent AI alignment researcher
Published
The ARC Principle proposes a single equation for how intelligence scales under recursion. Utility U equals input intelligence I multiplied by a recursion factor R raised to an exponent alpha, where alpha is not a universal constant but a value fixed by the form of recursion the system uses. When recursion is parallel and independent, alpha sits near zero and extra recursion buys almost nothing. When recursion is sequential and chained, alpha is greater than zero and the system can compound its own outputs into progress. The claim, in one sentence, is that the shape of the recursion sets the regime, and the regime sets the returns.
The first appearance of U = I × R is textual, in the manuscript self-emailed on 8 December 2024, at lines 6 to 9 of the file labelled V2. The Gmail Message-ID and the SHA-256 hash of that email are published on the evidence page, so the date is Google-server-timestamped rather than asserted. Papers I and II of the research programme formalise the same relation as U = I × R to the alpha and derive its regime structure. The book, published 2 January 2026 in print and 6 January 2026 as an ebook, presents the R-squared case as its featured formulation and states the general form throughout. The directional half of the claim, that sequential recursion outperforms parallel, was independently reported by Sharma & Chopra in November 2025, whose measurement of 95.6% of tested configurations favouring sequential composition is a stronger empirical result than anything the programme has run internally.
Two caveats sit on the record. The first is that the specific super-linear case, alpha greater than one, is a distinct claim treated separately, and its earliest unblinded single-model measurement (approximately 2.24) was retracted, corrected to approximately 0.49 under blinding after failing cross-architecture replication. Only the measurement was retracted; the equation and the ARC Bound alpha at most 2 that framed it remain live hypotheses. That correction is in the falsification dashboard. The second is that the general regime structure has been demonstrated in the programme's own harness across five models, but a fully independent implementation across three or more task domains has not yet been executed. Priority on the equation and the framing is defensible on the timestamped record; the strength of the quantitative regime prediction depends on external replication.
The falsification contract asks an independent lab to run the serial-versus-parallel comparison at matched compute across at least five models from three families, fit alpha in both conditions, and test whether alpha for serial is greater than alpha for parallel at p<0.05 pooled. A secondary criterion asks whether the three-regime classification of growth form is correct in at least three of four tested domains. If alpha for parallel is at least as large as alpha for serial across a majority of models, the direction of the claim is refuted. If the regime classifier does not beat chance, the second half fails independently of the first.
Related notes: Paper I in plain English for the derivation; the ARC Principle as the book presents it for the accessible-reader U equals I times R squared framing; Claim 10 explained for the sequential-versus-parallel result and the Sharma and Chopra concurrent work; Claim 12 explained for the 2.24-to-0.49 retraction. New to Michael Darius Eastwood: /start-here.html.
From the book Infinite Architects: Intelligence, Recursion, and the Creation of Everything by Michael Darius Eastwood.