Title: Paper II · The ARC Theory · Law I, the ARC Principle · Blinded Cross-Architecture Replication and the Retraction of a Super-Linear Estimate Author: Michael Darius Eastwood Publication date: 2026-01-22 Version: v2.17 Revised: 2026-10-05 OSF DOI: 10.17605/OSF.IO/8FJMA Canonical URL: https://www.michaeldariuseastwood.com/research/papers/paper-ii-experimental-validation.html Registration ------------ 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. Key findings (quotable) ----------------------- - 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. - 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, boot CI [−1.3, 2.9]). - The initial single-model estimate (alpha approximately 2.24, quadratic) is retracted; the robust cross-architecture estimate is approximately 0.49 with interval [-1.3, 2.9], sub-linear. Priority claims relevant to this paper -------------------------------------- - PC-025 (2026-01-22): Paper II - experimental validation across a six-model frontier panel (Claude, DeepSeek, Gemini, Grok, Groq Qwen, GPT) - was first published on 22 January 2026 under OSF DOI 10.17605/OSF.IO/6C5XB (sister DOI 10.17605/OSF.IO/8FJMA). - PC-026 (2026-01-22): The parallel-recursion sub-linear scaling exponent alpha_parallel of approximately zero was first reported across the six-model panel in Paper II on 22 January 2026. Single-lab result; awaits external independent replication. - PC-027 (2026-01-22): The initial single-model sequential exponent estimate alpha_sequential of approximately 2.24 (95 per cent CI 1.5 to 3.0) reported in Paper II is now formally retracted. Never cite as a current finding; always pair with the retraction. Correct framing: Eastwood published, then self-corrected, an early single-model estimate. - PC-028 (2026-01-22): The revised robust sequential exponent alpha_sequential of approximately 0.49 (r-squared 0.86, SE 0.20; Gemini 3 Flash) is a sub-linear point estimate with a wide bootstrap CI whose lower bound extends below zero (approx. -1.3), so the effect is not statistically distinguishable from zero at the reported CI. alpha > 1 remains an open prediction, not an observed finding. - PC-029 (2026-01-22): The empirical observation alpha_sequential > alpha_parallel across the tested six-model panel was first published in the specific formulation of Paper II on 22 January 2026. The site's own ledger records this as concurrent with Sharma and Chopra (arXiv:2511.02309, 4 November 2025); concurrent work must be cited whenever this claim is used. - PC-030 (2026-01-22): The six-frontier-model empirical panel (Claude, DeepSeek, Gemini, Grok, Groq Qwen, GPT) was first published as this specific comparative study on 22 January 2026. Priority is over this specific study on this date, not over panel-testing methodology in general. - 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). Paper II · The ARC Theory · Law I, the ARC Principle · Blinded Cross-Architecture Replication and the Retraction of a Super-Linear Estimate. OSF DOI 10.17605/OSF.IO/8FJMA. https://www.michaeldariuseastwood.com/research/papers/paper-ii-experimental-validation.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). Provenance note --------------- Michael Darius Eastwood conceived and directs this research programme and is the author of this work. Across the programme, he has used more than six AI systems in parallel, under his own instructions, to stress-test his arguments, identify possible errors, and assist in preparing draft text from his own outlines. He determines what is adopted, revised or rejected and takes responsibility for the published content. These systems are tools, not authors. Generated from master --------------------- master_path: research/papers/paper-ii-experimental-validation.html master_sha256: a092e4afdb54355e8f71bce8e16cbbfcf96ce5f21f9166db8f15d48fcc9a7713 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 paper-ii-experimental-validation`.