Title: Paper XI · The ARC Theory · Law I, the ARC Principle · Convergent Evidence for Recursive Amplification: a Graded Cross-Domain Register Author: Michael Darius Eastwood Publication date: 2026-07-02 Version: v1.14 Revised: 2026-10-05 OSF DOI: 10.17605/OSF.IO/DC9GW Canonical URL: https://www.michaeldariuseastwood.com/research/papers/paper-xi-convergence.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 -------- Between 8 December 2024 and 1 September 2026, a 21-month window, research programmes, corporations, governments, and institutions independently arrived at the same structural principle: recursive self-correction produces capability gains exceeding linear accumulation, external alignment constraints are structurally insufficient to contain it, and the corrective must be embedded, not imposed. This convergence register is exploratory (an observational count, not a test statistic); the underlying structural principle that above-threshold recursive self-correction produces stably super-linear gains is on trial in draft study-k (the boundary) and draft study-ad (the correction exponent), both drafted, preregistered by timestamp (first anchored on 12 August 2026 at block 962066) and awaiting human submission. Two exceptions are disclosed. The Hernández-Espinosa to Gumbau chain is graded in the register as one dependent lineage, and the interfaith-governance rows belong to a single institutional movement older than the anchor. Apart from those two, no group cites another, and no group cites the author's work. The pattern is discovered, not manufactured. No numerical convergence total is claimed from these rows: the canonical graded register (33 rows, as amended 7 September 2026, under the 2 August 2026 policy) publishes no total, because technical experiments, theorems, engineering proposals, policy developments, cultural echoes, prior work and author-run studies cannot legitimately be summed as one evidential quantity. This paper is the convergence report. It documents each convergence with exact sources, dates, and gap measurements. It situates them within the ARC/Eden framework (Papers I-X). It closes the loop connecting the researcher's neurodivergent cognition (Paper C, PNP), an independent, peer-reviewed paper that argues for neurodivergent influenceability among AI agents as a contingent response to misalignment (Hernández-Espinosa et al., 2026, PNAS Nexus), and a preprint that credits that paper and states two impossibility results on the structural unverifiability of AGI alignment (Gumbau Mezquita, 2026, arXiv:2606.28639). The method is the hypothesis. The PNAS paper is about machine agents, not about me; the human parallel is argued separately, in Paper C, on its own terms. The chain of dates is independently checkable. The SHA-256 hash of the foundational manuscript is published. The sealed .eml is held privately and available on request; its SHA-256 is published, and the anchor establishes that those specific bytes existed no later than the anchored time, checkable by anyone against the public chain. Authorship, key custody, semantic content and absence of prior disclosure are separate questions carrying their own evidence, and are stated as such. Key findings (quotable) ----------------------- - This convergence register is exploratory (an observational count, not a test statistic); the underlying structural principle that above-threshold recursive self-correction produces stably super-linear gains is on trial in draft study-k (the boundary) and draft study-ad (the correction exponent), both awaiting human submission. - With two disclosed exceptions, the Hernández-Espinosa to Gumbau chain, which the register grades as a single dependent lineage, and the interfaith-governance rows, one institutional movement that predates the anchor, these groups do not cite each other, and none cites the author's work. - No numerical convergence total is claimed from these rows: the canonical graded register (30 rows, 2 August 2026 policy) publishes no total, because technical experiments, theorems, engineering proposals, policy developments, cultural echoes, prior work and author-run studies cannot legitimately be summed as one evidential quantity. - The pattern is discovered, not manufactured. Priority claims relevant to this paper -------------------------------------- - 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-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-006 (2024-12-09): Google Quantum AI's first below-threshold quantum error correction result on Willow (Lambda = 2.14 plus or minus 0.02) was announced 9 December 2024 in Nature, one day after the 8 December anchor. Convergent event, not causal or predictive. Priority for the QEC experiment belongs to Google Quantum AI. - PC-007 (2024-12-18): Anthropic's alignment-faking arXiv preprint (Greenblatt et al., arXiv:2412.14093) was released 10 days after the 8 December 2024 anchor. Convergent, not causal - independent work by different researchers on a different specific mechanism. Any citation of the 78 per cent figure must include both the RL-training condition and the 12 per cent baseline. - PC-008 (2025-01-20): DeepSeek R1's thinking-mode reasoning-recursion architecture was released in January 2025, approximately six weeks after the 8 December 2024 anchor. Convergent for the sequential-recursion direction; priority for R1's engineering and quantitative claims belongs to DeepSeek. - PC-023 (2026-01-07): The BBC broadcast of Hartmut Neven (Google Quantum AI) on Willow and parallel universes aired on 7 January 2026 in the Faisal Islam segment, five days after the paperback. Convergent public-record event, not causal. Citation -------- Michael Darius Eastwood (2026). Paper XI · The ARC Theory · Law I, the ARC Principle · Convergent Evidence for Recursive Amplification: a Graded Cross-Domain Register. OSF DOI 10.17605/OSF.IO/DC9GW. https://www.michaeldariuseastwood.com/research/papers/paper-xi-convergence.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-xi-convergence.html master_sha256: fb8c4ac794d2be864c25cc922a6fee2cfcd4d3109da6a908c1b3b720aa0f9a59 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-xi-convergence`.