cff-version: 1.2.0
version: '5.19'
message: 'If you use or discuss this paper, please cite it using this metadata.'
title: 'Foundational Paper · The ARC Theory · Law I, the ARC Principle · Recursive Amplification as a Cross-Domain Structural Principle'
authors:
  - family-names: 'Eastwood'
    given-names: 'Michael Darius'
    orcid: 'https://orcid.org/0009-0004-3222-7442'
date-released: '2026-10-05'
url: 'https://www.michaeldariuseastwood.com/research/papers/foundational.html'
license: 'CC-BY-4.0'
identifiers:
  - type: doi
    value: '10.17605/OSF.IO/Y7QGD'
    description: 'OSF component DOI for this paper (foundational)'
  - type: doi
    value: '10.17605/OSF.IO/6C5XB'
    description: 'OSF umbrella DOI for the ARC / Eden Research Programme'
preferred-citation:
  type: article
  title: 'Foundational Paper · The ARC Theory · Law I, the ARC Principle · Recursive Amplification as a Cross-Domain Structural Principle'
  authors:
    - family-names: 'Eastwood'
      given-names: 'Michael Darius'
      orcid: 'https://orcid.org/0009-0004-3222-7442'
  date-published: '2026-02-13'
  url: 'https://www.michaeldariuseastwood.com/research/papers/foundational.html'
  doi: '10.17605/OSF.IO/Y7QGD'
  identifiers:
    - type: doi
      value: '10.17605/OSF.IO/Y7QGD'
      description: 'OSF component DOI for this paper (foundational)'
    - type: doi
      value: '10.17605/OSF.IO/6C5XB'
      description: 'OSF umbrella DOI for the ARC / Eden Research Programme'
    - type: doi
      value: '10.17605/OSF.IO/P8CKQ'
      description: 'Theory-level predictions preregistered on OSF: DOI 10.17605/OSF.IO/P8CKQ, registered 8 September 2026 (version 1.100), updated 13 September 2026 (version 1.102), twenty-two propositions. Companion: Register · The ARC Theory · Operational Definitions, version 1.9.1, 5 October 2026.'
  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:

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