cff-version: 1.2.0
version: '3.4'
message: 'If you use or discuss this paper, please cite it using this metadata.'
title: 'Founding Paper · Recursive Dynamics · The Science of Systems That Improve Themselves'
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/recursive-dynamics-founding-paper.html'
license: 'CC-BY-4.0'
identifiers:
  - type: doi
    value: '10.17605/OSF.IO/HCPBU'
    description: 'OSF component DOI for this paper (recursive-dynamics-founding-paper)'
  - type: doi
    value: '10.17605/OSF.IO/6C5XB'
    description: 'OSF umbrella DOI for the ARC / Eden Research Programme'
preferred-citation:
  type: article
  title: 'Founding Paper · Recursive Dynamics · The Science of Systems That Improve Themselves'
  authors:
    - family-names: 'Eastwood'
      given-names: 'Michael Darius'
      orcid: 'https://orcid.org/0009-0004-3222-7442'
  date-published: '2026-08-31'
  url: 'https://www.michaeldariuseastwood.com/research/papers/recursive-dynamics-founding-paper.html'
  doi: '10.17605/OSF.IO/HCPBU'
  identifiers:
    - type: doi
      value: '10.17605/OSF.IO/HCPBU'
      description: 'OSF component DOI for this paper (recursive-dynamics-founding-paper)'
    - 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: |
    Machines that improve themselves using their own outputs now exist and work, and there is no accepted science of what limits them. This paper founds that science, Recursive Dynamics, and stakes its claim the way thermodynamics was staked in 1824: by computing a bound that any such machine must obey if the claim is right, publishing the instruments that measure its terms, and preregistering by timestamp the experiments whose nulls favour the rival view. The field takes the self-improvement loop as its native object and names five state variables, conjectured to be substrate-independent: capability, recursive depth, correction rate, drift and correction leverage. It carries five laws as named conjectures with statuses declared. One, the ARC Ceiling, is derived in full from two lines of assumption; two, added on 24 September 2026, have their mathematics set out at version 1.0 and are neither registered as laws nor tested. The field locates its identity, as thermodynamics does, in its impossibilities: if the laws hold, self-improvement cannot outrun its own correction, the growth exponent is capped by the reciprocal of the correction shortfall, and no ladder of same-class oversight climbs past its ceiling by adding rungs. The paper states what would make the field wrong, tries to house its questions inside twelve neighbouring fields, gives each of fifty-one objections a disposition, and prints the four results that would dissolve the field. Its honest status is the Carnot stage: one memoir, instruments built, decisive measurements preregistered by timestamp and not run, staked where failure will be as visible as success.

    Keywords: Recursive Dynamics; recursive self-improvement; the ARC Theory; correction and drift; the ARC Ceiling; limit theorems; AI alignment; preregistration

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