Title: The ARC Principle: Recursive Amplification as a Cross-Domain Structural Principle Author: Michael Darius Eastwood Publication date: 2026-02-13 Version: v5.13 Revised: 2026-08-23 OSF DOI: 10.17605/OSF.IO/Y7QGD Canonical URL: https://www.michaeldariuseastwood.com/research/papers/foundational.html Abstract -------- In the past eighteen months, at least four independent research programmes have discovered that recursive or recurrent processing produces capability gains exceeding linear accumulation, in domains as different as AI reasoning, quantum error correction, acoustic physics, and consciousness science. None set out to study recursion per se. None reference each other's work. Yet they found structurally similar results. This paper asks: is this a coincidence, or are we observing different expressions of a single structural principle? We formalise the question as follows. For AI systems, the equation is: Key findings (quotable) ----------------------- - In the past eighteen months, at least four independent research programmes have discovered that recursive or recurrent processing produces capability gains exceeding linear accumulation, in domains as different as AI reasoning, quantum error correction, acoustic physics, and consciousness science. - Yet they found structurally similar results. - This paper asks: is this a coincidence, or are we observing different expressions of a single structural principle? - For AI systems, the equation is: $$ U = I \times R^{\alpha} $$ The ARC Equation (AI Power-Law Form) where $U$ is effective capability, $I$ is base potential (structured asymmetry), $R$ is recursive depth, and $\alpha$ is the scaling exponent. Priority claims relevant to this paper -------------------------------------- - PC-034 (2026-02-13): The ARC Principle Foundational cross-domain paper was first published on 13 February 2026 under OSF DOI 10.17605/OSF.IO/6C5XB (additional anchors 10.17605/OSF.IO/8FJMA and osf.io/wqnzc). - PC-035 (2026-02-13): The synthesis observation that at least four independent research programmes (AI reasoning, quantum error correction, acoustic physics, consciousness science) converged on recursive or recurrent processing producing capability gains exceeding linear accumulation was first published on 13 February 2026 in the Foundational paper. Synthesis over other researchers' independent work, not a claim of discovering their results. - PC-036 (2026-02-13): Application of the bare alpha = d/(d+1) scaling exponent to recursive AI capability was first published in the Foundational paper on 13 February 2026. The exponent form itself is prior work in the wider scaling-law literature (West-Brown-Enquist 1997; Banavar et al.; Demetrius; He and Chen; Bettencourt; Zhao 2022; Maino et al.); priority is limited to the AI-capability application on this date. - PC-003 (2024-12-08): The ARC Principle - Artificial Recursive Creation, as a named cross-domain framework, was first described in the 8 December 2024 manuscript and formalised in Paper I on 17 January 2026. Recursion as a structural concept is prior work; priority is over Eastwood's specific naming and cross-domain framing under this label. - PC-011 (2026-01-02): The ARC Principle equation - book form U = I x R squared, paper form U = I x R^alpha - was first published as a conjecture in Infinite Architects on 2 January 2026 and formally in Paper I on 17 January 2026. Framing is conjecture throughout. The early alpha of approximately 2.24 is retracted; the robust v13 estimate is approximately 0.49 with interval [-1.3, 2.9] (sub-linear); alpha > 1 remains an open prediction. Bare d/(d+1) form is prior work. Citation -------- Michael Darius Eastwood (2026). The ARC Principle: Recursive Amplification as a Cross-Domain Structural Principle. The ARC Theory (the Theory of Artificial Recursive Creation) ยท ARC/Eden experiments, OSF DOI 10.17605/OSF.IO/Y7QGD. https://www.michaeldariuseastwood.com/research/papers/foundational.html Notes ----- Hardware framings held at the site's already-published two-sentence concept ceiling: safety constraints at hardware level through cryptographic tokens in silicon, TRL 0-1, no prototype. No enabling implementation detail is stated in this companion file. Balanced-ternary computing is prior work (Setun 1958); recursion as a structural concept is prior work (evolutionary theory, self-modifying computation, quantum error correction). Generated from master --------------------- master_path: research/papers/foundational.html master_sha256: 3be709d53d84a5c59974fd68557aae459dd8abcee0ebfed26cbdad13783049a6 builder: scripts/build-paper-companions.py This block records the SHA-256 of the HTML master that produced this .txt. A check tool re-hashing master_path can decide freshness without any external state. If the master's current SHA-256 does not match master_sha256, this file is stale and must not be published: regenerate first with `python3 scripts/build-paper-companions.py --slug foundational`.