cff-version: 1.2.0
version: '2.17'
message: 'If you use or discuss this paper, please cite it using this metadata.'
title: 'Paper II · The ARC Theory · Law I, the ARC Principle · Blinded Cross-Architecture Replication and the Retraction of a Super-Linear Estimate'
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/paper-ii-experimental-validation.html'
license: 'CC-BY-4.0'
identifiers:
  - type: doi
    value: '10.17605/OSF.IO/8FJMA'
    description: 'OSF component DOI for this paper (paper-ii-experimental-validation)'
  - type: doi
    value: '10.17605/OSF.IO/6C5XB'
    description: 'OSF umbrella DOI for the ARC / Eden Research Programme'
preferred-citation:
  type: article
  title: 'Paper II · The ARC Theory · Law I, the ARC Principle · Blinded Cross-Architecture Replication and the Retraction of a Super-Linear Estimate'
  authors:
    - family-names: 'Eastwood'
      given-names: 'Michael Darius'
      orcid: 'https://orcid.org/0009-0004-3222-7442'
  date-published: '2026-01-22'
  url: 'https://www.michaeldariuseastwood.com/research/papers/paper-ii-experimental-validation.html'
  doi: '10.17605/OSF.IO/8FJMA'
  identifiers:
    - type: doi
      value: '10.17605/OSF.IO/8FJMA'
      description: 'OSF component DOI for this paper (paper-ii-experimental-validation)'
    - 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: |
    This paper presents experimental validation of the ARC Principle (Artificial Recursive Creation), a mathematical framework proposing that error rates in intelligent systems decrease according to a power law with recursive depth. The principle, first articulated in Infinite Architects (Eastwood, December 2024) and formalised in Paper I (Eastwood, 17 January 2026), predicts that the form of recursion determines the scaling regime: sequential recursion should yield super-linear error suppression (scaling exponent $\alpha > 1$), while parallel recursion should yield sub-linear suppression ($\alpha < 1$).

    We conducted controlled experiments in two phases. Phase 1 (the initial single-model study) used DeepSeek R1 with visible reasoning tokens on 12 competition-level mathematics problems, finding $\alpha_{\text{sequential}} \approx 2.24$ (95% CI: 1.5-3.0), since retracted, and $\alpha_{\text{parallel}} \approx 0.0$. Phase 2 (the six-model study) extended testing to six frontier models on 18 AIME/Putnam-level problems (n=54 per depth per model) with bootstrap confidence intervals and 4-layer cross-verification.

    Cross-architecture replication: The original $\alpha \approx 2.24$ (quadratic) does not replicate across architectures. Only Gemini 3 Flash produced clean, monotonic scaling data: $\alpha_{\text{seq}} = 0.49$ (regression, $r^2 = 0.86$, SE = 0.20; endpoint estimate 0.59, boot CI [−1.3, 2.9]). DeepSeek R1 reached ceiling (94.4%-100%). GPT-5.4 exhibited a binary step function (50% → 100%). Grok 4.1 Fast achieved 100% at all depths. Groq Qwen3 showed no trend (~50%).

    Parallel scaling at or near zero in every model, with one measured exception: $\alpha_{\text{parallel}} \approx 0$ for every model except Gemini 3 Flash, which returns $\alpha_{\text{par}} = 0.31$ at $r^2 = 0.93$. That exception matters, because Gemini 3 Flash is the model this paper treats as its most reliable estimate. The replicated finding is therefore that parallel scaling is at or near zero in every model measured, with one measured exception, not that it is universally zero. Sequential outperformed parallel for every model where both were measurable.

    Revised parameter estimate: The most robust cross-architecture estimate is $\alpha_{\text{sequential}} \approx 0.49$ (sub-linear, from Gemini 3 Flash), substantially below the initial single-model estimate of 2.24. Under the Intelligence Formula $\alpha = 1/(1 - \beta)$ from Paper I, $\alpha < 1$ places a model in the physical regime (multiplicative composition through finite-dimensional networks) rather than the intelligence regime (recursive self-reference with $\alpha > 1$); the estimate points to the physical regime for current models, but it is one model’s fit and inconclusive. The fundamental inequality $\alpha_{\text{sequential}} > \alpha_{\text{parallel}}$ remains confirmed.

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