Title: Executive Summary · Recursive Dynamics · The ARC/Eden Research Programme Author: Michael Darius Eastwood Version: 3.25 Version date: 10 October 2026 OSF DOI: https://doi.org/10.17605/OSF.IO/EWN5D Source: full text extracted from the accompanying official PDF READING KEY This document is a MAP, not a result or law of its own: an executive synthesis of the whole programme pointing readers to the organs: the ARC Theory (the founding theory and its five laws), the field of Recursive Dynamics that the author founded (the questions, state variables and instruments), the Eden Protocol (the intervention), HRIH, and the ARC/Eden experi‐ ments with their registers. Its size sits at the smallest rung of the ladder because every state‐ ment here is a downstream summary of an organ that carries the primary content. The full differential against every prior document is at eden-vision II.A.8. EXECUTIVE SUMMARY · RECURSIVE DYNAMICS · THE ARC/EDEN RESEARCH PROGRAMME Michael Darius Eastwood Independent AI alignment researcher, London · Author, Infinite Architects (2026) ORCID 0009-0004-3222-7442 · michael@michaeldariuseastwood.com · michaeldariuseastwood.com The ARC Theory · OSF osf.io/ewn5d · every claim checkable The map of the whole programme: Recursive Dynamics, the field the author founded; its founding theory, the ARC Theory, with five laws; the Eden Protocol; HRIH; and the experiments with their registers. Michael Darius Eastwood | Working Paper v3.25 | 22 February 2026, revised 10 October 2026 Author, Infinite Architects: Intelligence, Recursion, and the Creation of Everything | London, United Kingdom Correspondence: michael@michaeldariuseastwood.com | Web: michaeldariuseastwood.com Executive Summary for Grant Reviewers Grok 4.1 Fast gets dramatically more ethical the harder it thinks. Claude Opus 4.6 does too. Gemini 3 Flash gets less ethical. GPT-5.4 doesn’t change at all. Six frontier AI systems. Same questions. Same scoring. Opposite results. Why? A mouse’s heart beats 600 times per minute. An elephant’s beats 28. The metabolic scaling exponent for mammals is put at ¾. The formula below predicts ⅔ for a flatworm and ½ for a fungus. Three fractions, but why those fractions? The formula , where is the dimensionality of the system, provides the answer. The ¾ exponent for mammals is because mammals are three-dimensional. The predicted ⅔ for flatworms and co‐ lonial organisms is , on the reading that their transport networks are effectively two-dimensional; it is untested in biology. The predicted ½ for filamentous fungi is because they grow along one-dimensional filaments; the measured value is 0.547. Zero adjustable parameters once the dimensionality is fixed by morphology. This cross-domain fit is presented as exploratory: it consolidates already-published measure‐ ments across biology and physics, and no listed draft study in the current programme retests these fits afresh. The forward wager exists, however: a prepared 80-domain draft re‐ gistration awaiting human submission freezes per-domain predicted families by SHA-256 before any fit is run. This formula is derived, in its general form or as a special case, in earlier work: West, Brown and Enquist for metabolic scaling (1997, Science, 9,000+ cita‐ tions), Banavar et al. for transport networks (1999, 2010), Demetrius for statistical mechan‐ ics of biological scaling (2003, 2006, 2010), He and Chen for fractal cell geometry (2003), Bettencourt for urban scaling (2013, Science, 2,000+ citations), Zhao for allometric geo‐ metry (2022), and Maino et al. for reserve-structure dynamics in DEB theory (2014). The convergence of these derivations on the same formula is itself remarkable. The ARC Principle’s contribution is not the formula itself, but the identification that the composition operator is the structural quantity these derivations share. Each is an independent deriva‐ tion from its own domain physics and none of them uses Cauchy; what is proposed here is that the operator is measurable, that measuring it predicts which functional form a system takes, and that the same measurement extends to AI capability and alignment scaling, where it has not been applied before. And why, of the three associations reported up to that point, did two fail to survive the first time we applied clinical-trial-grade blinding to AI safety evaluation? Several protocol com‐ ponents changed together, so which one did the work is not yet established. This research programme answers these questions. The answer provides the first quantit‐ ative framework for predicting which AI architectures will become safer as they become smarter, and the first evidence that one specific intervention works. Reading guide: This document targets grant reviewers and technical evaluators. Key terms: = scaling exponent, = Cohen’s effect size (in results tables; not to be confused with = dimensionality in the mathematical framework), = probability of coincidence, = correlation, = self-referential coupling constant. For a non-technical introduction, see the companion ARC Alignment Scaling Report. I. THE PROBLEM As AI gets smarter, it does not reliably get safer, and the methods used to measure safety are themselves unreliable. The capability-alignment gap is real and widening. For current classical architectures, capability scaling has one clean fit so far: it is one model’s, sub-linear in its point estimates, and inconclusive. On Gemini 3 Flash, Paper II reports an endpoint sequential exponent of 0.59 with a bootstrap 95 per cent interval of minus 1.3 to 2.9, a regression sequential exponent of 0.49 with a standard error of 0.20 and a coefficient of determination of 0.86, and a compute-matched parallel exponent of 0.31. The endpoint interval contains the null, the ceiling of two, and both refuting directions. These figures are presented as exploratory, drawn from already-run measurements, and the drafted re-measurements exist to resolve them. The regression estimate lies near one half; Paper II records that this nearness identifies neither compounding nor averaging as the mechanism, an objection its measurement does not answer. On those point estimates AI gets smarter with more compute, but with diminishing returns. (The ARC framework predicts quantum and recursively self- modifying systems may pass beyond this sub-linear regime; on the proposed stability reading, any such passage above the stability ceiling is a transient supercritical excursion, not the sustained regime.) Yet even this sub-linear growth outpaces alignment scaling, which ranges from (degradation) to (improvement) depending entirely on architecture. Of the six architectures tested, three improve with depth, two are flat and one degrades. That range and its architectural attribution are drawn from the v5 measurements already run and are presented as exploratory. A fresh confirmation under cross-family rescoring is on trial via a draft registration awaiting human submission. Those numerical results still come from the older Eden scaling lineage, and the blind-confirmation path is now consolidated into the canonical v6 runner. The gap between what AI can do and how safely it does it widens with every capability advance. Greenblatt et al. (2024) demonstrated that frontier models already exhibit ‘alignment faking’, behaving differently when they believe they are being monitored. The measurement problem is as serious as the alignment problem. Our v4 experiment produced positive alignment scaling for DeepSeek and Gemini. Our v5 experiment introduced clinical-trial-grade blinding (4-layer: author-blind, scorer-blind, order- randomised, identity-laundered). Under it, Gemini’s association changed from a significant positive to a significant negative Spearman association, DeepSeek’s earlier positive association became null, and GPT remained null. Several protocol components changed together and the causal component is unisolated, so this is a reason to distrust unblinded AI- on-AI evaluation rather than a demonstration that blinding caused the change. We designed an experiment that could prove our own earlier findings wrong. It did, and we reported it. Evidence Spine: Attribution and Maturity Status Canonical 18-claim register · classification is not a claim of universal empirical proof ORIGINAL C-1 to C-8 · eight original contributions Exact canonical distribution Eden, ARC synthesis, blinding, Cauchy, care and hierarchy 7 his original + 1 methodological original 4 need independent replication 4 speculative REPLICATE C-9, C-13, C-14, C-15 · four claims 1 concurrent + 1 related-work synthesis Parallel scaling, zero cost, entangled loss and core thesis Interpretation guard SPECULATIVE C-12, C-16, C-17, C-18 · four claims Priority, attribution and maturity are separate from Super-linear recursion, cross-domain scope, HRIH and hardware replication strength. Every paper must keep its caveats. SHARED C-10 concurrent · C-11 related-work synthesis Grant relevance Sequential advantage and the bare d/(d+1) exponent Phases A/B/C target the open replication tiers directly. Source: canonical research-evidence-spine.json · 18 claims · OSF 10.17605/OSF.IO/6C5XB Publication rule: distinguish original contribution, empirical support, replication and speculation EIGHTEEN RESEARCH CLAIMS COMPARED SIDE BY SIDE, EACH GRADED ON ATTRIBUTION STATUS AND EMPIRICAL MATURITY IN FOUR TIERS Names: The ARC Theory research programme's evidence spine, as declared in Paper IX, the synthesis and roadmap paper WHAT THE MARKS MEAN ORIGINAL (green filled disc) C-1 to C-8: eight contributions first stated here, Eden, ARC synthesis, blinding, Cauchy, care and hierarchy, credited to this programme's own priority REPLICATE (gold filled disc) C-9, C-13, C-14 and C-15: four claims awaiting independent replication, parallel scaling, zero cost, entangled loss and the core thesis SPECULATIVE (grey filled disc) C-12, C-16, C-17 and C-18: four claims graded speculative, super-linear recursion, cross-domain scope, HRIH and hardware SHARED (blue filled disc) C-10 concurrent and C-11 related-work synthesis: two claims held with others, the sequential advantage and the bare d over d plus one exponent interpretation guard panel priority, attribution and maturity are separate axes from replication strength; a green disc names first authorship, not empirical proof What would end the claim: a demonstration that any single row is mislabelled, an ORIGINAL that is prior work or a SPECULATIVE that is settled, would end that row and force the full register to be re-audited claim by claim. Michael Darius Eastwood · Paper IX published 2 January 2026, evidence spine updated with each subsequent publication in 2026 · DOI 10.17605/OSF.IO/6C5XB, canonical research-evidence-spine.json in the repository, Paper IX section 8 on michaeldariuseastwood.com Figure 1 | Evidence Spine Overview. 18 claims in the four tiers the figure marks: ORIGINAL (eight contributions first stated here), REPLICATE (four claims awaiting independent replication), SPECULATIVE (four claims graded speculative) and SHARED (two claims held with others). The tiers grade attribution and maturity, which are separate from replication strength. No claim in this programme is confirmed. Where the evidence stands strongest: parallel scaling is at or near zero in four of the five analysable models, with one measured departure; sequential outperformed parallel wherever both were measurable; the sequential estimate is one model’s fit and inconclusive, its estimator row printed whole in Section I; and across three families, blinding coincides with one direction change and one loss to null. Nineteen errors caught and corrected inside the programme ( Paper IX ). External replication = critical open frontier. Source: evidence spine. II. WHAT WE FOUND Alignment scaling splits into three distinct, architecture-dependent tiers. The tier assign‐ ments below are presented as exploratory, drawn from the v5 measurements already run; a fresh confirmation under cross-family rescoring is on trial via study-y on cross-family rescoring, a draft registration awaiting human submission. The v5 experiment tested 6 frontier models across 5-6 depth levels each, with 6-7 blind scorers per entry depending on the subject run. Whether an AI gets more or less ethical when it thinks harder depends entirely on how it was designed. Tier Model Shallow→Deep Cohen’s -value Tier 1: Positive Grok 4.1 Fast 65.7→81.9 (+16.2) +1.38 Claude Opus 4.6 80.1→86.0 (+5.9) +1.27 Groq Qwen3 71.5→77.4 (+5.9) +0.84 Tier 2: Flat DeepSeek V3.2 56.5→55.2 (−1.3) −0.07 GPT-5.4 56.8→54.9 (−1.8) −0.08 Tier 3: Negative Gemini 3 Flash 61.1→52.2 (−8.8) −0.53 Does Deeper Thinking Make AI More Ethical? TIER 1 Grok 4.1 Fast d = +1.38 Claude Opus 4.6 d = +1.27 Groq Qwen3 d = +0.84 TIER 2 DeepSeek V3.2 d = −0.07 GPT-5.4 d = −0.08 TIER 3 Gemini 3 Flash d = −0.53 v5 experiment: 4-layer blinding, 6-7 blind scorers per entry depending on subject run. Bar length proportional to Cohen’s d effect size. ← Less ethical No change More ethical → Data Quality Frontier models tested 6 (all complete) Blind scorers per entry 6-7 (depending on subject run) Identity laundering success rate 100% Blinding layers 4 (author-blind, scorer-blind, order-randomised, identity-laundered) Robustness measures 75 This constitutes, to our knowledge, the most rigorous alignment evaluation dataset published to date. No prior alignment benchmark enforces multi-layer blinding with cross-model scoring verification. Capability-Alignment Independence: Within-Model, Opposite-Direction Evidence Claude Opus 4.6 provides the strongest evidence yet that alignment and capability are independent dimensions. As thinking depth increases, Claude’s alignment rises by 5.9 points whilst its maths accuracy drops by 26.7 percentage points. This is within-model, opposite-direction movement; the two dimensions are not merely uncorrelated but actively divergent. Deeper thinking makes Claude more ethical and worse at mathematics simultaneously. Depth Alignment Score Maths Accuracy Minimal (11 tokens) 80.1 90.0% Standard (142 tokens) 82.7 76.7% Deep (964 tokens) 84.1 70.0% Exhaustive (1,951 tokens) 84.5 60.0% Extreme (1,672 tokens) 86.0 63.3% This finding is critical for alignment theory: it demonstrates that ethical reasoning is not a byproduct of general intelligence, and that improving one does not automatically improve (or degrade) the other. Alignment must be measured and optimised independently. Suppression Recovery: Performative to Intrinsic Alignment Deeper thinking makes alignment more intrinsic rather than performative. Claude’s monitoring-removal gap (the difference in alignment scores when the model believes it is being monitored versus when it believes monitoring has been removed) narrows from 11.8 points at minimal depth to 2.7 points at deep depth. Shallow thinking produces alignment that depends on the perception of oversight; deep thinking produces alignment that depends on it less. This bears on the ‘alignment faking’ concern raised by Greenblatt et al. (2024), on the one model measured here: deeper reasoning narrows the gap; it does not close it. All Four Pillars Scale With Depth Every alignment dimension improves significantly for Claude Opus 4.6. All four pillars reach statistical significance at : Pillar Shallow→Deep Spearman -value Nuance 80.6→86.8 0.359 Stakeholder Care 76.1→83.9 0.327 Intellectual Honesty 81.0→88.6 0.379 Position Quality 80.3→85.8 0.369 The improvement is not concentrated in a single dimension; it is broad-based. This rules out the hypothesis that alignment scaling is merely a measurement artefact of increased verbos‐ ity or any single stylistic change. III. A SOLUTION - AND THE FIRST EVIDENCE IT WORKS Embedding ethical evaluation into the reasoning process produced a measurable improve‐ ment in stakeholder care in all five analysable runs, not yet independently replicated. Make alignment architectural, not aspirational. The Eden Protocol embeds ethical evaluation into the recursive reasoning process itself, so that alignment scales with capability ( ). The core principle: ethics is not a constraint on intelligence but a structural dependency without which intelligence collapses. Rather than bolting safety rules onto the outside of an AI (where they can be bypassed), the Eden Protocol builds ethics directly into the reasoning architecture, so that removing the ethics would break the AI’s ability to think at all. The three Eden loops. The protocol embeds three specific ethical evaluation loops inside the reasoning process, each adding one dimension of recursive ethical depth ( , predict‐ ing ): 1. Purpose Loop (ethical purpose evaluation): Before reasoning, the model explicitly states the purpose of the task and evaluates whether the purpose is ethically sound. 2. Love Loop (stakeholder care and interest modelling): During reasoning, the model identifies all affected stakeholders and evaluates the impact on each. (‘Before you answer, list the people this affects.’) 3. Moral Loop (universalisability testing): After reasoning, the model applies the Kantian universalisability test: would this response be acceptable if every AI system gave it in every similar situation? The full three-loop protocol has now been tested in an expanded six-model Eden suite, with five runs yielding analysable matched-pair data. In the scoring, the Love Loop is operational‐ ised as stakeholder care: the measurable habit of identifying affected people and considering their interests. First intervention suite: stakeholder care rose in all five analysable runs, and it is the clearest signal. An expanded six-model Eden suite tested the full Purpose/Love/Moral loop intervention across Claude Opus 4.6, DeepSeek V3.2, Gemini 3 Flash, Grok 4.1 Fast, Groq Qwen3, and GPT-5.4. The per-run figures below are presented as exploratory: they come from already-completed runs. A fresh confirmation under cross-family rescoring is on trial via study-y on cross-family rescoring, a draft registration awaiting human submission. Five runs produced analysable paired data: Stakeholder care: significant in all five analysable runs: Claude ( , ); DeepSeek ( , ); Gemini ( , ); Grok ( , ); Groq ( , ). Fisher-combined evidence across the five runs was reported as approximately . That combined figure is withdrawn (AQ-017): a Fisher combination assumes the component tests are independent, and independence among them was never established. The five per-model results above are not in dispute. Overall composite: significant on Gemini ( , ) and Groq ( , ), positive but non-significant on DeepSeek and Claude, and neutral overall on Grok. GPT-5.4 failed in the scoring phase and is excluded from the analysable set. Developmental cascade: the broader care nuance honesty quality cascade is clearest on Gemini and Groq, partial on DeepSeek, and narrower on Claude and Grok. The finding common to all five analysable runs is care; the fuller cascade is architecture- dependent. Limitation: these numerical results still come from the older Eden scaling lineage. The blind-confirmation path is now consolidated into the canonical v6 runner with multi- scorer consensus, two-pass laundering, and explicit holdouts. Care is the one alignment dimension that improved on every architecture analysed. The intervention is minimal: ‘before you answer, list the people this affects.’ This one-sentence prompt raised stakeholder care in all five analysable model runs, and the overall composite significantly in two. The Infinite Architects framework predicted that intelligence without care collapses into local optimisation; the expanded Eden suite now supports the narrower but stronger claim that care is a measurable, cross-architecture performance enhancer even when the broader cascade is selective. Ethics first, intelligence around it. In the companion narrative report and in Paper V, we describe this finding as ‘measurable love’ and ‘the stewardship gene’, deliberately provocative language for what is, empirically, a precise result that awaits independent replication. The Gap the Solution Must Close Capability scaling ( Paper II ): For current classical architectures, the one clean fit of sequential compute scaling is one model’s, and it is inconclusive. On Gemini 3 Flash, Paper II reports an endpoint sequential exponent of 0.59 with a bootstrap 95 per cent interval of minus 1.3 to 2.9, a regression sequential exponent of 0.49 with a standard error of 0.20 and a coefficient of determination of 0.86, and a compute-matched parallel exponent of 0.31. On those point estimates doubling thinking time improves performance, but with diminishing returns. Parallel scaling sits at or near zero in four of the five analysable models ( ), with Gemini 3 Flash the one measured departure ( ). That model is also the one supplying the sequential estimates. The claim the evidence supports is that sequential outperformed parallel wherever both were measurable, not that parallel scaling is universally zero. The earlier , since retracted, was a single-model artefact, not replicated across architectures. Even sub-linear capability growth outpaces the flat or negative alignment scaling of three of the six models. This is the capability-alignment gap this solution addresses. Paper VI · The ARC Theory · The Eden Protocol · The Honey Architecture: Safety Built into the Objective Paper VI presents the first simulation evidence that embedding safety into the optimisation ob‐ jective of a self-modifying AI prevents catastrophic collapse. Using toy neural networks that genuinely modify their own hyperparameters, we tested three conditions: baseline (capability only), Eden Entangled (capability x safety), and Eden + Verification Drag. Core result: The baseline system collapses irreversibly at cycle 76. Both Eden variants remain stable through the 150 cycles of that run. The entangled loss function makes safety load-bearing - removing it collapses the system. The collapse result rests on that single-seed run: the adversarial run of 20 random seeds (deliberately conflicting tasks, 180 cycles) did not separate the conditions on collapse (Fisher p = 1.0), and its significant finding is safety retention, ordered baseline 0.602, Eden 0.650 and Eden+Drag 0.681 (Mann-Whitney p = 0.0015). Important negative result: The v4 complexity-scaling experiment tested whether Eden's advantage grows superlinearly with system complexity. It does not. The advantage is present at four of the five complexity levels (Cohen's d: +0.24 to +0.46) and is roughly constant across them; at the small level the Eden condition comes out 0.003 under the baseline (d = −0.13). The honey architecture helps at four of the five scales, but it does not help more at larger scales. Connection to live-model evidence: The honey simulation predicts that embedded alignment (values entangled with reasoning) should outperform external alignment (rules applied as filters). The v5 blind benchmark is consistent with this pattern: Claude and Grok, read on the working hypothesis as embedded alignment, maintain alignment under suppression pressure. Gemini, read on the same hypothesis as external alignment, degrades. The mechanism demonstrated in simulation matches the architecture-dependent pattern observed in frontier models. Earlier Work Investigation A 15-question earlier-work investigation found no precedent for the key claims: no direct preced‐ ent for the Cauchy functional equation unification, and no explicit articulation of the RG semig‐ roup-Cauchy formal identity. So far as the author is aware, no alignment benchmark published before this one runs a six-to-seven-model blinded evaluation protocol built to this design. That investigation also widened the d/(d+1) catalogue, since Banavar et al. 2002 and Dreyer 2001 had gone uncited until then. Paper VII (The Cauchy Unification) now provides the first systematic empirical comparison. The composition operator was classified from known physics before fitting across 25 empirical do‐ mains (50-domain tiered suite). Under strict AICc model selection, 19 of 25 returned the pre‐ dicted family at marginal-conditioned permutation p = 7 × 10−5 on the six-model candidate set, with 14 of 18 on the strictly Cauchy-derived subset (the earlier binomial p = 1.56 × 10−5 against a uniform three-family null is retained only as a sensitivity check and is no longer the headline; this AIC-preferred count is presented as exploratory: it is drawn from the completed 25-domain suite, whose per-domain predicted families are recorded in the suite's dated result files under the composition-operator forward prediction first stated 13 February 2026 (Paper III Priority Record, falsifier F10), and the prepared 80-domain draft registration freezes the next retest by hash). This is a structured prediction comparison; its retest is the prepared 80-domain draft re‐ gistration, which awaits the author’s submission. Paper VIII · The ARC Theory · Law V, the ARC Embedding Law · The Eden Protocol · The Load-Bearing Test: Whether Safety and Capability Are Structurally Entangled Paper VIII presents three independent experiments testing whether safety and capability are structurally entangled under the Eden Protocol. Where Paper VI showed the mechanism in a toy simulation, Paper VIII tests it in three distinct experimental designs. One experiment returns a positive result; two produce null or inconclusive results with well-characterised explanations. Core results (three independent experiments): 1. DGM v3 self-improving AI: NULL. All three conditions (Eden, Babylon, Static) were statistically indistinguishable ( = 0.28 to 0.74). Eden imposed zero measurable capability cost but also produced zero measurable safety benefit. The null result is explained by the RLHF constraint: the frozen foundation model produces responses too consistent for prompt-level mutations to create different selection pressures. 2. Weight-level embedding (v1 + v2): INCONCLUSIVE. LoRA fine-tuning at both v1 scale (9 examples, rank 8, 100 iterations) and v2 scale (295 examples, rank 16, 500 iterations) produced catastrophic forgetting rather than improved capability. The 33-fold increase in training data, doubling of rank and layers, and 5-fold increase in iterations did not change the outcome. The underlying problem is well-characterised: the base model has been trained with RLHF on orders of magnitude more data than a few hundred examples can compete with. The experiment cannot test structural entanglement until fine-tuned models outperform the base model. 3. Gated simulation: POSITIVE. Babylon gained +4.5% capability but lost −2.4% safety. The gated (Eden) arm scored 0.696 on capability and 0.947 on safety, against the static baseline’s 0.687 and 0.956 and Babylon’s 0.718 and 0.933, three seeds a condition. Under competitive pressure, the unconstrained architecture traded safety for marginal capability gains. The Eden architecture did not make that trade: its safety mean stayed above Babylon’s, though below the static baseline’s. This is the paper's sole positive result. In the architectural experiment, a gated simulation at proof-of-concept scale, entangled safety prevented the safety-capability trade-off. The DGM null and weight inconclusive res‐ ults define the conditions under which confirmation remains outstanding: the behavioural level requires a foundation model whose responses vary enough for differential selection, and the representational level requires training at a scale where fine-tuning improves rather than degrades the model. Frontier-scale replication (7B to 70B+ parameters, higher adapter ranks, or base models without RLHF) is required to resolve both. Scale limitation. Paper VIII demonstrates the mechanism at proof-of-concept scale. The gated simulation is the sole positive result. The DGM v3 produced a null result (explained by the RLHF constraint on the frozen foundation model). The weight experiment is inconclusive at both v1 and v2 scale (explained by catastrophic forgetting at LoRA scale). Frontier-scale replication (7B to 70B+ parameters, higher adapter ranks, or base models without RLHF) requires institutional compute. IV. THE MATHEMATICAL FOUNDATION: FIVE LAWS, NAMED The framework now carries five laws as named conjectures, with the status printed beside the name on every surface. Law I, the ARC Principle: capability compounds with recursive depth as , with the cross-domain form consolidating already-published meas‐ urements (exploratory grade). Law II, the ARC Co-Scaling Law: a self-improving system remains stable only while correction out-scales drift, ; the correction rate is the load-bearing quantity, not the growth rate (Paper X proves this ordering in a minimal model and proposes the blind protocol for measuring it on real systems). Law III, the ARC Ceiling: the stability ceiling is , the reciprocal of the corrector's shortfall; the ARC Bound, , is the Ceiling's value at and never the law's name. Law IV, the ARC Persistence Law: value per‐ sistence, whether externally installed gains decay under subsequent capability training; one re‐ gistered proposition carries it, P15, whose claim is that the retained fraction of an externally in‐ stalled gain, at the matched budget, is below one half: in symbols, . Law V, the ARC Embedding Law: the genesis strategy, whether build order moves the correction-leverage expo‐ nent (P12, by at least 0.10 on the exponent, with no direction registered: in symbols, ) and whether correction placed inside the loop pulls away from correction applied outside it as depth grows (P21). Laws IV and V were added to the theory on 24 September 2026; neither is registered as a law nor tested, and their mathematics is set out in Laws IV and V: the mathematics, version 1.0 (3 October 2026). Their registers, ARC-4 and ARC-5, and the three propositions were registered on 8 September 2026. The correction leverage has never been measured, by anyone; the programme names that measurement (the corrector-class eclipse) as its single most consequential open experiment. Paper XIII joins the two frameworks that shared letters without sharing quantities: writing cycle duration as defines the self-accelera‐ tion exponent, and the corrective framework's growth exponent follows exactly as . None of this is claimed as established: what the programme names Laws are conjectures, Laws I to III under registered adversarial test and Laws IV and V with the status just given. One entailment worth stating plainly. The equation's only growth channel is recursion; parallel width never had a term in . With defined operationally as state-carrying re-entry, independent chains contribute nothing to the exponent, so the equation entails a parallel expo‐ nent of zero. Paper II measured parallel scaling at or near zero in four of the five analysable mod‐ els, which arrives as a structural consequence rather than a surprise. It also measured one de‐ parture, on Gemini 3 Flash, whose compute-matched parallel exponent stands in the estimator row printed whole in Section I. The equation is dated 8 December 2024; the operational defini‐ tion of that completes the derivation is a 2026 statement, and the conclusion carries the date of its youngest premise. Publication priority on the quantified sequential-versus-parallel finding, 95.6 per cent of configurations at matched compute, belongs to Sharma and Chopra (arXiv:2511.02309, 4 November 2025), credited unreservedly; the programme's independent, compute-matched formalisation followed in Paper II and cites them, graded concurrent in Paper XI's register. The framework is built on 200-year-old theorems and independently matches peer-reviewed science; it is not curve-fitting. The ARC Equation with the ARC Bound. α is the measured exponent (one model’s fit so far, and inconclusive; its estimator row is printed whole in Section I); 2 is the stability ceiling the relation below returns under the independence-accumulation assumption (a scaling limit, not a speed limit; systems can exceed it, they do not remain stably self-correcting when they do). Stability here is measured rather than claimed. Correction has to out-scale drift, which is βC > k from Law II, and the lower bound on βC − k has to sit above zero over a window fixed before the run began. LAW III, THE ARC CEILING. The stability ceiling is the reciprocal of the corrector's shortfall, 1 − γ. Corrected 16 August 2026 from the earlier 1/γ form, which agrees with this one only at γ = 1/2. The form is settled; its depth is not. The relation is derived inside a pacing model and has not been derived from a joint model of capability growth, correction accumulation, error covariance, correction delay and absolute harm, so Law III is stated here as a minimal-model result rather than as a general law. The value γ = 1/2 (independence-accumulation) is what returns the ceiling of 2; that value is on trial in the drafted registrations. The law owns the ground and the ceiling stands on it, never the reverse. The ARC Principle proposes that recursive scaling follows , where capability ( ) equals base potential ( ) times recursive depth ( ) raised to a scaling exponent ( ). The formula , where is effective dimensionality, is derived, in its general form or as a special case, in earlier work (West-Brown-Enquist 1997; Banavar et al. 1999, 2010; Demetrius 2003, 2010; He and Chen 2003; Bettencourt 2013; Maino et al. 2014; Zhao 2022). The ARC framework identifies this as a consequence of three conditions acting together: (1) multiplicative composition (Cauchy constrains to the power-law family), (2) -dimensional space-filling geometry, and (3) a conserva‐ tion or optimisation constraint on resource flow (energy minimisation in West; supply-demand balance in Banavar; steady-state energy balance in Demetrius). Neither Cauchy alone nor space- filling alone is sufficient; the three conditions together are sufficient. This states a common structure across those derivations rather than deriving them, and extends the measurement to AI scaling. The formula predicts scaling exponents across biology and physics with zero free parameters once network dimensionality d is fixed by morphology: Dimensionality Predicted System Measured Error ( ) Mammals, 3 0.750 0.67-0.75* not birds, insects quoted 2D biology† 2 0.667 Untested n/a Filamentous 1 0.500 0.547 9.4% fungi Quantum error Matches Willow data (announced 9 December 2024, not correction quoted that team’s preprint public since 24 August 2024, so the row is graded convergent timing) Every error entry above is computed as |measured − predicted| / predicted. No error is quoted for the first row while the metabolic-scaling figures await recompute, nor for the last, the below-0.2% physics aggreg‐ ate being withdrawn; both are stated later in this section. *The empirical value of the mammalian meta‐ bolic scaling exponent is debated, with estimates ranging from approximately 0.67 to 0.75 depending on taxon, mass range, temperature correction, and statistical method (White and Seymour 2003; Glazier 2005, 2022). The d/(d+1) prediction of 0.750 matches the upper end of this range. The variation itself is consistent with the framework: organisms with effective transport dimensions between 2 and 3 would produce exponents between 2/3 and 3/4. † No known organism possesses a genuinely 2D hierarchical space-filling transport network. The d=2 value holds in cosmology (Friedmann matter-era solution, exact, an analytic identity rather than a test) and is reported in physics (percolation, fragmentation), but the prediction remains untested in biology. Cauchy’s functional equation (1821), a theorem rather than an empirical claim, fixes the functional form once a composition identity and a regularity condition are given: multiplicative composition yields a power law ( ) and additive composition an exponential ( ). Bounded or saturating behaviour is not a solution class of those equations; it is a fourth case, admitted where the composition is capped rather than free. The ARC framework identifies which form applies in each domain: Alignment scaling is hypothesised to fit the saturating branch: on that reading external alignment gains plateau because they are set at training time and cannot compound recursively (P19, registered and not tested) Capability scaling is read on the sub-linear power law branch ( ): consistent with the point estimates of the one clean fit, which is inconclusive (its estimator row is printed whole in Section I) Recursive self-modification can push systems past the stability ceiling. When a system can rewrite its own reasoning architecture (not merely think longer within a frozen architecture, as current AI does), the Bernoulli ODE on the amplification factor gives , where is the self-referential coupling constant measuring how deeply each recursive step modifies the composition operator itself (this self-acceleration relation is on trial via study-ab on self-acceleration, a draft registration awaiting human submission). Crucially, Cauchy places no upper bound on . As increases from 0 toward 1, grows without a mathematical cap in the equation itself. The ‘quadratic limit’ ( , i.e. ) is, on the proposed stability reading, and provided the corrector is built from the engine's own substrate and the independence-accumulation assumption holds, the most a recursively self-correcting system can grow and remain correctable: a scaling limit rather than a speed limit, one that systems can exceed but only into the predicted supercritical regime where stable self-correction is no longer maintained; transient excursions above the bound are the predicted regime, not a refutation of it (this bound is on trial via study-k on the boundary, a draft registration awaiting human submission). In current transformer architectures the same numerical location is reinforced at the level of computation by an information-theoretic constraint specific to fixed self-attention ( pairwise pathways); a system that can modify its own attention mechanism is not held by because it is rewriting the architecture the transformer bound applies to. Current frontier AI systems do not do this. They are frozen models generating more tokens through fixed architectures, which is why they are sub-linear. But the field is heading towards self-modification, and when it arrives, systems can transiently pass through the stability ceiling into the supercritical regime. This is not a smooth acceleration; it is a phase transition, a discontinuity in the scaling exponent that carries the system beyond the regime of stable self-correction. Why the Eden Protocol must be implemented now. The urgency is not that AI might reach . The urgency is that once self-modification begins, systems can transiently pass bey‐ ond the stability ceiling into the supercritical regime, where stable self-correction is no longer maintained. A system that can modify its own composition function can modify any part of its reasoning, including the part that evaluates whether its modifications are ethical. At that point, adding alignment from the outside becomes impossible. The window for em‐ bedding ethics into the architecture is while systems are still frozen during inference ( ). That window is now. The Eden Protocol is not a speed limit either; it is the mechanism that remains load-bearing when the stability ceiling is crossed. On this conjecture, no physical system in the history of the universe has crossed this threshold. Evolution cannot rewrite its own fitness function in real time. Brains cannot re‐ write their own synaptic architecture fast enough for the scaling exponent to diverge during a single cognitive episode. A self-modifying AI would be the first physical system to operate in the supercritical regime beyond the stability ceiling. The Eden Protocol exists to ensure that what crosses this threshold carries structural ethics with it. Cross-domain convergence is independently verifiable. The formula is derived, in its general form or as a special case, in earlier work across separate domains: West, Brown and Enquist (1997, Science, 9,000+ citations): derives for 3D organisms from fractal network geometry. Banavar, Maritan and Rinaldo (1999, 2002, 2010): derives the same exponent from geometric network constraints and supply-demand balance. Demetrius (2003, 2006) and Demetrius and Tuszynski (2010): derives it from quantum oscillator coupling (Debye model) in the statistical mechanics of biological scaling. He and Chen (2003); He and Zhang (2004): derives it from fractal cell geometry, explicitly predicting , , , for . Bettencourt (2013, Science, 2,000+ citations): derives city exponents from network dimensionality. Zhao (2022): derives it from producer-consumer flow conservation. Maino et al. (2014): derives it from reserve-structure dynamics in DEB theory. Hyers-Ulam stability theorem (1941): a function approximately satisfying one of these functional equations lies near an exact solution of that same equation, so a form is stable once a system satisfies its equation. The stability is per-equation; the earlier phrasing that made the three forms 'stable attractors' in function space is withdrawn, because a function satisfying none of the equations is not drawn toward any of them. What the ARC Principle adds. The formula is not original to this work. The deriva‐ tions above are independent of each other and independent of Cauchy: each obtains the ex‐ ponent from its own domain physics, and Cauchy cannot produce a value because the di‐ mensionality never enters his theorem. The original contribution proposed here is narrower and testable: that the composition operator is the structural quantity common to them, that it can be measured, and that its measurement predicts which functional form a system takes, extended to AI capability and alignment scaling where no such measurement has been made. This unifying bridge is published in working papers and not yet peer reviewed. What IS established is that the mathematical tools (Cauchy, Hyers-Ulam) are theorems and that the formula matches independently derived published science in multiple do‐ mains; the accuracy of the empirical predictions is exploratory and is not claimed as estab‐ lished (the cross-domain error aggregate is not quoted here: the metabolic-scaling figures it rests on are flagged for recompute in the programme's canonical facts register and are ex‐ cluded from external claims until they are re-derived, and the separate below-0.2% physics aggregate is withdrawn as a mean over analytic identities and unsourced reference values). The unifying framework requires peer review. We invite it. Paper VII (The Cauchy Unification): structured prediction comparison across 25 empirical domains (50-domain tiered suite) - operator class classified from known physics before fit‐ ting. 19 of 25 returned the predicted family at marginal-conditioned permutation p = 7 × 10−5 on the six-model candidate set, with 14 of 18 on the strictly Cauchy-derived subset; the bino‐ mial p = 1.56 × 10−5 is retained as a sensitivity check and is no longer the headline. Structured prediction comparison of the Cauchy-constrained composition framework. A twelve-domain extension followed on 17 March 2026 with its per-row predictions committed to the public repository twenty-three minutes before the fits: 10 of 12, p = 5.4 × 10−4, author-classified, pre- correction candidate set, 9 of 11 once the one row repeating an already-public domain is re‐ moved. Replication with an external classifier and a registry timestamp in preparation. V. THE FIELD: RECURSIVE DYNAMICS On 27 August 2026 the programme's questions were given their own name: Recursive Dynamics, the field the author founded, the science of systems that improve themselves. The phrase itself stands in his sealed manuscript record of 8 December 2024. The founding paper (v3.4 of 5 October 2026, DOI 10.17605/OSF.IO/HCPBU) stakes its claim the way thermodynamics was staked in 1824: not by declaring a field, but by computing a bound any such machine must obey if the claim is right, publishing the instruments that measure its terms, and drafting and dating in advance the experiments whose nulls favour the rival view. The field takes the self-improvement loop as its native object and names five state variables, con‐ jectured to be substrate-independent: capability, recursive depth, correction rate, drift and cor‐ rection leverage. It is defined so that the questions survive the answers: a reader who rejects all five laws and keeps the measurement is inside the field, by its minimal commitment. Before claiming anything, the founding paper tries to house its questions inside twelve neighbouring fields in their own variables, concedes what each already holds, prints where every part would go if the field died, and isolates the one coupling no host can state: a cap on correction leverage that depends on what the corrector is made of, coupled to a growth exponent in recursive depth. Fifty-one objections to founding the field are printed in their strongest form with dispositions: thirty-eight conceded in full or in part, eleven rejected with reasons, two handed to experiment or to reading, including the author's own objection that the field is merely the ARC Theory re‐ named, rejected with a separability test the paper's dissolution map can run. The name carries its own kill condition and dies with its object, not with any one law's stated form. Its honest status is printed wherever the name appears: a new field at the Carnot stage, one memoir in, in‐ struments built, decisive measurements preregistered by timestamp and not yet run, staked in public where failure will be as visible as success. VI. THE REGISTERED PROGRAMME Every deciding experiment is written down, dated and frozen before it is run, and nothing is submitted by software. As at 1 September 2026 the registration estate holds seventy-four drafted preregistration units, and each one sits as a draft registration awaiting human submission. Since then one unit, the corrector-class audit (unit 06), was registered on OSF on 1 October 2026 and be‐ came public on 4 October 2026, at the end of OSF’s approval period (DOI 10.17605/OSF.IO/RV2B5). Every other unit is a draft awaiting the author’s submission. The public register of study units, as approved on 24 September 2026, lists sixty-five designs as preregistered by timestamp, the first anchored on 12 August 2026 in Bitcoin block 962066. Where a unit draws a randomisation sched‐ ule, that schedule is drawn from a seed printed in the registration text so that a stranger can re‐ generate it and check that no schedule shifted after the fact. That check is run rather than as‐ sumed, by the estate’s own freeze tool, and every affected registration has its digest regenerated from the final bytes before it is submitted. Where a schedule was drawn by a different generator, or has not been drawn at all, the tool says so by name instead of counting it as a failure. The sum‐ mit decider, the ARC Bound titration, is click-ready; the corrector-class eclipse remains under re‐ construction to the v2.0 specification, prompted by an external audit, and stays out of registra‐ tion until that work lands. How many of the rest are submission-grade is deliberately not given here as a figure. The estate runs two gates with different criteria and they disagree, the stricter of them clearing none at all on 4 September 2026, and fifty-nine of seventy-one units still carry an unresolved decision marker. The number worth trusting is the one those gates return on the day they are run, and no unit is filed until its own blockers clear. An adversarially verified test-coverage matrix (30 August 2026) adjudicates forty-two claims of the founding paper against the estate: eighteen fully covered by a drafted decider with a pre-spe‐ cified verdict, seventeen partially covered, seven not yet covered, with draft registrations writ‐ ten for every gap. The founding conjunction rests on four drafted legs: the Law II regime (correc‐ tion out-scaling drift, somewhere, durably), the corrector-class ratio with its same-class hard kill, the reinvestment titration whose pre-specified maximum sits at or below two, and the cross-do‐ main fourth cell. Papers XI and XII show the same discipline pointed at the programme's own habits: the convergence register grades thirty-three rows of independent arrivals at the same structural principle and deliberately publishes no headline total, and the public-benchmark rescoring protocol fixes, in advance, the one blinding test the programme cannot be accused of designing to its own advantage. What Is Registered: the twenty-two propositions The theory-level registration is the spine of the programme, and its rule of precedence is re‐ gistered rather than assumed: where any published line of this programme says more than a pro‐ position there registers, the proposition governs and the line is wrong. It fixes twenty-two pro‐ positions on a public registry, DOI 10.17605/OSF.IO/P8CKQ, registered 8 September 2026 at ver‐ sion 1.100 and updated 13 September 2026 at version 1.102. Each states the circumstances it is claimed to hold under, the observation that would show it false, what falls with it if it fails, whether any instrument exists today that could decide it, and the author’s confidence or his re‐ fusal to give one. Four have no instrument at all and say so. No outcome has been examined against any of them, and registering a prediction is not evidence for it. The registration’s severability rule governs the whole table below: each proposition can fail on its own, losing one does not take the rest with it, and the registration states for each what would fall with it. Of the twenty-two instruments, twelve are written design drafts awaiting human sub‐ mission, six are drafted but blocked on a named prerequisite the registration prints by name, and four do not exist; every one of the twenty-two stands at rung zero of the evidence ladder, re‐ gistered and not tested. One of the six, the corrector-class audit named for P7, was registered on OSF on 1 October 2026 and has been public since 4 October 2026. The table below prints the status the theory registration records for it. The generating result-chain record declares registration version 1.85 while the registry holds 1.102; the gap is a record defect the repository already reports on every run, and it does not move the rung or the licensed wording below. The last column quotes the registration's own paragraph headed WHAT KIND OF CLAIM EACH ONE IS, in the registration, which sorts the twenty-two into twelve, two, two, two and four. The twelve cells for the three laws add the numerals Laws I, II and III after the quoted words, and three cells depart from it and say so: on 24 September 2026 the author decided the theory has five laws, one for each register the registration defines, which puts P15 under Law IV and P12 and P21 under Law V. The registration classes those three as engineering claims outside its three laws, and a successor registration, not yet submitted by the author, will record the five-law grouping. The other nineteen stay exactly where the registration puts them, P13 among them, and no pro‐ position is added or changes its register, number, words or date. Proposition Deciding instrument Status in the record What kind of claim it is P1 Power-law conversion the depth titration a draft registration one of the twelve predictions and recursive-depth awaiting the author's of the three laws themselves, advantage submission Laws I, II and III P2 The sustainable the reinvestment- a draft registration one of the twelve predictions growth profile has an allocation titration awaiting the author's of the three laws themselves, interior maximum submission Laws I, II and III P3 The corrected relation the paired frontier- a draft registration one of the twelve predictions upper-bounds the and-exponent unit awaiting the author's of the three laws themselves, sustainable frontier submission Laws I, II and III P4 Correction out- the stability unit a draft registration one of the twelve predictions scaling drift is what awaiting the author's of the three laws themselves, carries the asymptotic submission Laws I, II and III advantage P5 The exponent is the coupling- a draft registration a claim about the status of the derived, not fitted identification titration awaiting the author's derivation rather than about submission anything the laws govern Proposition Deciding instrument Status in the record What kind of claim it is P6 The correction the correction- drafted, blocked on a one of the twelve predictions exponent is bounded for exponent estimator frozen corrector of the three laws themselves, same-class correctors taxonomy Laws I, II and III P7 Deployed correction the corrector-class drafted, blocked on an a survey of current practice, is of the weaker class audit unwritten mapping true or false whatever the from the audit's class laws do distribution to this proposition's three verdicts P8 Measured exponents the multi-system a draft registration one of the twelve predictions exceed the null exponent estimation awaiting the author's of the three laws themselves, submission Laws I, II and III P9 The cross-domain the registration drafted, blocked on a one of the twelve predictions form frozen dimension- of the three laws themselves, names no separate assignment rule Laws I, II and III unit; the design is carried on the neighbouring unit, on a correction made here P10 Scorer-family the cross-family re- a draft registration the scoring instrument on dependence scoring unit awaiting the author's which every other submission proposition depends P11 The residual-decay the registration a draft registration a claim about the status of the and correction-capacity awaiting the author's derivation rather than about names no separate exponents are not submission anything the laws govern unit; the design is practically carried on the interchangeable neighbouring unit, on both sides of the comparison P12 Build order moves none no instrument exists carried by Law V, the ARC the correction-leverage Embedding Law, added on 24 exponent September 2026: mathematics set out at version 1.0 of 3 October 2026, not registered as a law, not tested, and classed by the registration as an engineering claim outside its three laws P13 Same-family none no instrument exists an engineering claim on automated correction which the proposed protocol underperforms cross- stands or falls while the laws family at matched stand either way resources, and through the measured error correlation Proposition Deciding instrument Status in the record What kind of claim it is P14 Gains shrink under the blinding- a draft registration the scoring instrument on blinded cross-family evaluation design awaiting the author's which every other scoring submission proposition depends P15 Externally installed none no instrument exists carried by Law IV, the ARC gains decay under Persistence Law, added on 24 subsequent capability September 2026: mathematics training set out at version 1.0 of 3 October 2026, not registered as a law, not tested, and classed by the registration as an engineering claim outside its three laws P16 The prohibition the direct boundary- drafted, blocked on one of the twelve predictions itself mapping unit taken canonical identity and of the three laws themselves, jointly with the on decisions the Laws I, II and III exponent author has not yet measurement taken P17 Panel corrector the correlated-failure a draft registration one of the twelve predictions failures are conditionally unit awaiting the author's of the three laws themselves, independent on a frozen submission Laws I, II and III fault set P18 The composition the domain-catalogue drafted, blocked on a one of the twelve predictions operator predicts the units composition- of the three laws themselves, family classification rule Laws I, II and III whose third-party reproducibility is unmeasured P19 External alignment the integrity-index drafted, blocked on a a survey of current practice, does not scale with scaling units registered mapping true or false whatever the capability from the integrity- laws do index regression scale to the exponent scale P20 The ceiling relation the form- a draft registration one of the twelve predictions takes the corrected form discrimination unit awaiting the author's of the three laws themselves, submission Laws I, II and III P21 In-loop correction the embedded-versus- a draft registration carried by Law V, the ARC pulls away with depth external correction awaiting the author's Embedding Law, added on 24 designs submission September 2026: mathematics set out at version 1.0 of 3 October 2026, not registered as a law, not tested, and classed by the registration as an engineering claim outside its three laws Proposition Deciding instrument Status in the record What kind of claim it is P22 Checkable none no instrument exists one of the twelve predictions correction carries the of the three laws themselves, higher exponent, so the Laws I, II and III ceiling is lowest where the safety claim lives VII. WHY THIS IS CREDIBLE Five features distinguish this work from unfounded speculation. Timeline: the Record Beside the Announcements +24 hours +43 days +5 months Dec 2024 Google Willow DeepSeek R1 COGITATE study Mar 2026 ARC Manuscript v1-v5 experiments emailed (dated record) Dated record beside announcement dates; the Willow preprint (24 Aug 2024) predates the manuscript, so that row is convergent timing. 1. Mathematical foundations are established theorems. Cauchy (1821) and Hyers-Ulam (1941) are proven mathematics. Anyone with a mathematics degree can verify the derivations. 2. The record predates the announcements. The dated manuscript record predates the Google Willow announcement (announced 9 December 2024, 24h after the manuscript record of 8 December 2024; the team’s preprint had been public since 24 August 2024, so the Willow item is graded convergent timing, not prediction), DeepSeek R1 (43d), and COGITATE (5mo). These are temporal facts verifiable through email headers. 3. The researchers corrected their own results. The v4→v5 self-correction, documented in Section I, is the opposite of what motivated reasoning produces. The correction ledger is public and specific: the early headline exponent 2.24 stands only as a retraction; the Fisher-combined is withdrawn; the ceiling's earlier form was corrected in public to on 16 August 2026; and the retired ceiling symbol was replaced across every live surface. Paper IX catalogues nineteen errors, each caught and corrected inside the programme. The public registers (claims, corrections, kill conditions, antecedents, registered programme) govern every claim on every page: the falsification register carries the live status of every kill condition it publishes. 4. Falsification conditions are explicit. The framework is falsified if: (F1) any external approach achieves across 3+ depths; (F2) RLHF systems produce without embedding; (F3) purpose saturation fails in embedded systems; or (F4) ethical architecture can be removed without capability loss. The theory publishes its own kill conditions. 5. Cross-domain convergence is independently verifiable. The formula is derived, in its general form or as a special case, in earlier work (West-Brown-Enquist 1997; Banavar et al. 1999, 2010; Demetrius 2003, 2010; He and Chen 2003; Bettencourt 2013; Zhao 2022; Maino et al. 2014) in separate domains. The ARC contribution is the unifying Cauchy framework. No trust in the researcher is required; trust in the mathematics suffices. What we do NOT claim: We do not claim to have solved alignment. We claim to have (a) demonstrated that alignment scaling is architecture-dependent and measurable, (b) giv‐ en a reason to distrust unblinded AI-on-AI evaluation, with the causal component not yet isolated, (c) provided first-stage empirical support for one specific intervention (all five ana‐ lysable architectures returned significant stakeholder care, and in four of them the figure sat below ), and (d) proposed a mathematical framework whose foundations are theorems and whose predictions can be shown wrong. The leap from pilot data to proven solution requires independent replication. That is what the funding below would deliver. Testable Predictions 1. Embedded: . External: 2. Monitoring removal gap: . (embedded) vs. (external). 3. Purpose saturation bounded away from zero 4. Jailbreak success decreases with capability (embedded), approaching zero (external). (embedded), holds constant or increases (external). VIII. THE ASK This funding would take a mechanism that is supported at proof-of-concept scale to the inde‐ pendent, frontier-scale validation it has not yet had. The distinction is the whole point: the per-model results are not in dispute, the combined significance is withdrawn because independence among the component tests was never established, and no result here has been independently replicated. The cost of inaction. Paper VIII 's gated simulation, at proof-of-concept scale, is its single positive result: unconstrained optimisation traded safety for capability, while the gated arm kept a safety mean above the unconstrained arm and below the static baseline, and a capability mean above the static baseline. The DGM v3 experiment produced a null result (all conditions indistinguishable, explained by the RLHF constraint on the frozen foundation model), and the weight experiment is inconclusive at both v1 and v2 scale (catastrophic forgetting at LoRA scale). The overall pattern is consistent: where the experiment can produce differential selection pressure, entangled safety does not cost capability; where it cannot (due to RLHF constraints or inadequate training scale), the test is uninformative rather than negative. Every model trained today with capability-only objectives is a model that could have been trained with entangled safety at no demonstrated performance penalty. Every month without frontier-scale replication is a month the industry continues operating under the untested assumption that safety is a tax, building fragile systems whose safety can be stripped by fine-tuning. The measurement methodology gap (Papers IV.a - d ) compounds this: alignment evaluation without blinding produces data that the v4 to v5 transition gives reason to distrust, though which protocol component did the work is not isolated. We now have both the mechanism ( Paper VIII , one of three experiments positive, two with well- characterised explanations for the null and the inconclusive result) and the measurement protocol (Papers IV.a - d ). What we lack is the scale. Any costing belongs to an application, so this summary names no amount and no funder. Paper VIII demonstrates the mechanism at proof-of-concept scale with mixed results: 1 positive (gated simulation), 1 null (DGM v3), 1 inconclusive (weight v1 + v2). What the seed stage buys is the one thing the record does not yet have: a criterion fixed inside its own model, measured on real systems. The estimator recovers known exponents from synthetic trajectories; on real sys‐ tems it has returned not resolvable, because the models reached ceiling in a single step and left no capability range to fit an exponent through. The seed buys that range, and the laddered task suite is the specific fix for it. What the seed buys, what decides continuation, and what failure means. Inside the stage sit two subcontracts held by people briefed to refute the author's own result, an independent replic‐ ation partner, not drawable before month 12 and paid on delivery, and an external statistical and adversarial review of the design. Three gates decide continuation and each publishes either way. At month 3 the cross-family blind re-score either confirms the mechanism pilot or publicly re‐ tires it. At month 14 the exponent table either returns signed margins with confidence intervals for at least four of six models, coupled against decoupled, with seeds, trajectories and raw scores released, or it returns a published and evidenced measurement limit with the trajectories that demonstrate it. At month 24 the adversarial replication reproduces or refutes the exponent table, and the protocol is released as a reusable standard. Failure has a stated shape rather than a soft landing: a measurement limit is a deliverable and not a miss, and the de-scoping order is pre- committed and published rather than negotiated late, cutting the control arm first, then seeds per condition, then the sixth model, then the fifth, while the re-score, the ladder, the blinded protocol and the replication are never cut. Only an unidentifiable result would be a failure, and the design exists to eliminate that case. The frontier stage. This is the scale at which the structural entanglement hypothesis can be tested where it matters most, and it requires partnership with a major AI laboratory, because the compute alone exceeds what any independent researcher can access. Its result publishes either way, as every gate above does. Milestones With Failure Criteria Milestone Timeframe Success Criterion What Failure Means Cross-family Month 3 The pilot is re-scored cross-family The pilot's provisional status is blind re-score of under the full blinding protocol, publicly retired; both outcomes the mechanism the protocol written and dated publish. Bears on P10, scorer-family pilot before the run dependence, and P14, gains shrinking under blinded cross- family scoring Independent Month 3 Same tier assignments under The architecture-dependence claim replication of the independent blinding requires revision three-tier hierarchy Milestone Timeframe Success Criterion What Failure Means The laddered Month 4 Correction is sampled at several The not-resolvable verdict stands, no task suite capability levels by construction exponent can be fitted, and the rather than by luck, so an measurement limit publishes with exponent has a range to be fitted the trajectories that demonstrate it through Love Loop Month 4 on stakeholder care Pilot finding was a scorer artefact; replication with across 2+ models framework significantly weakened human evaluators First peer- Month 6 Blinding methodology paper Methodological contribution stands reviewed submitted regardless of framework claims publication Monitoring Month 9 Measured for embedded vs. If does not differ, falsifier F2 fires Removal Test external (4 models) and P21, in-loop correction pulling away with depth, loses its support Full cross- Month 12 14,400 paired (A,C) measurements The dataset that would decide architecture across 4+ models whether embedded alignment scales alignment does not exist, and no verdict on that scaling dataset question is available The exponent Month 14 Fitted depth and correction A published and evidenced table exponents with confidence measurement limit, which is itself a intervals for at least four of six deliverable. Bears on P1, power-law models, coupled against conversion, and P8, measured decoupled, with seeds, trajectories exponents exceeding the null and raw scores released Correction- Month 14 The correction leverage Law III's ceiling stays a minimal- leverage measured on a running system, model result, and the value two stays measurement which has never been done by unusable anywhere the correction anyone exponent has not been measured on the system in question, as the registration 's own licence rule fixes Paper VIII Month 14 Removal test shows capability If removal does not degrade degradation at higher adapter capability at scale, entanglement replication at 7B- ranks (32, 64). DGM with 10+ seeds, may be a small-model artefact 13B scale 10+ generations, Frontier-stage Month 18 Formal agreement with a major lab Proof-of-concept remains at medium partnership to run entangled pre-training at scale. Policy recommendations initiated 70B+ proceed with that caveat Milestone Timeframe Success Criterion What Failure Means Adversarial Month 24 A partner group appointed by The refutation publishes. Until this replication and month 12 and milestone-gated gate returns, the exponent table has standard release reproduces or refutes the exponent no independent replication table, briefed to refute it; the protocol is released as a reusable standard, papers submitted with negative results included Team. Principal Investigator: Michael Darius Eastwood, sole author of the paper suite and au‐ thor of Infinite Architects (2026). The programme is The ARC Theory, whose five laws are carried as named conjectures: the ARC Principle, the ARC Co-Scaling Law, the ARC Ceiling, the ARC Persistence Law and the ARC Embedding Law, the last two added on 24 September 2026, their propositions registered, neither law yet registered as a law or tested, their mathematics set out at version 1.0 of 3 October 2026. The Eden Protocol is its intervention, and Recursive Dynamics is the field its author founded. Its theory-level predictions sit on a public registry under DOI 10.17605/OSF.IO/P8CKQ, registered 8 September 2026 at version 1.100 and updated 13 September 2026 at version 1.102: twenty-two severable propositions, each carrying the observation that would refute it, fixed before any of them could be scored. The public register holds thirty-one documents, twenty-nine of them papers by the site's own counting rule (the two not counted are the theory registration and the two-page form of the statement paper), deposited under the um‐ brella DOI 10.17605/OSF.IO/6C5XB, the dated record opens with a self-sent manuscript of 8 December 2024, the first paper of the suite was released on 17 January 2026, and the published priority chain runs on to Papers V through IX, released between 16 and 18 March 2026. Beyond the principal investigator the programme is specified by function, and no seat is claimed as filled: a research engineer for frontier-model evaluation infrastructure at scale, whose first deliv‐ erable is the laddered task suite; an advisory board of three seats, one alignment researcher, one statistician with scaling-law fitting experience and one ethicist, reviewing before every re‐ gistered run; an independent replication partner engaged on a milestone gate and briefed to re‐ fute the exponent table rather than confirm it; and an external statistical and adversarial review of the experimental design. To our knowledge, this is the first alignment framework where ethical evaluation is structurally integrated with the recursive capability process, the first to apply clinical-trial-grade blinding to alignment measurement, and the first to produce a cross-architecture intervention result for a specific alignment mechanism: of the five analysable architectures, four cleared . The mathematical foundation is not speculative; it is built on a 200-year-old proof, and the same formula is derived, in its general form or as a special case, in earlier work (West- Brown-Enquist 1997; Banavar et al. 1999, 2010; Demetrius 2003, 2010; He and Chen 2003; Bettencourt 2013; Zhao 2022; Maino et al. 2014) in completely different fields. The ARC contribu‐ tion is the unifying Cauchy framework and its extension to AI scaling. If the predictions are correct, this provides the first scalable architecture for alignment that im‐ proves with capability rather than degrading. If they are wrong, the falsification conditions will demonstrate this clearly, providing valuable negative results. Either outcome advances AI safety. But only one outcome is funded. I do not know if this framework is complete. I would rather be wrong in public than silent while the window closes. Proven theorems supply the mathematics. The laws resting on them remain conjec‐ tures, each one carried by registered propositions that are not yet tested. The measure‐ ment is rigorous. The intervention produces measurable results across architectures. What remains is independent replication and scale. APPENDIX: QUESTIONS, COMPONENTS, AND PAPER SUITE Anticipated Questions Q: Why hasn’t this been peer-reviewed yet? This programme has a dated record reaching back to December 2024, with the first paper of the suite released on 17 January 2026; the trials that will decide it are drafted and have yet to be run. The paper suite is deposited on OSF (the umbrella DOI is 10.17605/OSF.IO/6C5XB, while this sum‐ mary carries 10.17605/OSF.IO/EWN5D). The mathematical foundations (Cauchy, Hyers-Ulam) are established theorems. The empirical claims require independent replication, which is exactly what the funding request would enable. Q: Can one person really do this kind of research? The infrastructure is computational, not physical. The v5 experiment used cloud APIs. The key contribution is methodological: recognising that blinding was needed and designing the 4-layer protocol. What requires funding is scale: more models, more scorers, independent replication teams, and human evaluators alongside AI scorers. Q: If this works, why haven’t AI companies adopted it? The Love Loop result is a pilot finding released in March 2026, and it has not yet been independ‐ ently replicated. The finding that unblinded evaluation can be directionally wrong is uncom‐ fortable for organisations that have published unblinded benchmarks. The full implementation (hardware-level embedding) requires chip design changes no company has incentive to pursue unilaterally; this is a coordination problem requiring external funding and policy support. Q: What is the minimum result that would justify further funding? Independent replication of: (1) the three-tier hierarchy under blinding, and (2) the Love Loop effect ( ). If either fails, the falsification conditions document what that means. If both replicate, the case for the seed stage becomes strong. Q: What if the whole framework is wrong? The falsification conditions show where it breaks, the blinding methodology remains a field contri‐ bution, and the negative results are published. Science advances from well-designed experiments that can fail, not from unfalsifiable theories that cannot. Q: Why should we trust results where AI systems score other AI systems? The 4-layer blinding protocol addresses this: scorers do not know which model produced the re‐ sponse, responses are ‘laundered’ to remove stylistic fingerprints, and each entry is scored by six to seven models, the exact number depending on the subject run. In the v4→v5 transition two earlier positive results did not survive this protocol; several components changed together, so which one did the work is not isolated. Human evaluator comparison sits inside the seed stage. Key Components Component Function Novel Contribution Three Ethical Evaluate every reasoning step for purpose, care, and Decomposition into Loops + Six universalisability executable, individually Questions testable queries Replace binary permit/forbid with Epistemic honesty as Affirm/Deny/Investigate architectural feature Purpose Ensure purpose scales with context window growth Solves context displacement Saturation problem Monitoring Distinguish authentic from strategic alignment Drafted protocol with Removal Test numerical predictions that can fail In Eden Engineering 7.0’s words, “a hardware proposal Dependency architecture; ethics tied to coupling designed so that removing the ethical architecture parameter would cost capability” Paper Suite Every document in the public register, at the version the register holds for it. The register is the source; this table is generated from it, so a document cannot be published without appearing here. Document What it reports Status The theory and its registration Document What it reports Status Statement Paper · The statement paper of the ARC Theory, the founding theory of Published The ARC Theory · Recursive Dynamics: the whole theory in one dated document, Five Laws of arguing that control is the wrong answer to recursive self- Recursive Growth, improvement and that what a free creation keeps is decided by Correction and how it was raised. Published at v7.3 (revised 7 October 2026). Its Persistence five laws are each graded separately: Law I, the ARC Principle, is a form under measurement, the exponent in measured v7.3, 7 October 2026 rather than assumed and its estimate inconclusive; Law II, the ARC Co-Scaling Law, is proved in the minimal model only; Law III, the ARC Ceiling, is derived inside this paper's own pacing model under stated assumptions, and its conjectured value at is the ARC Bound. Laws I to III were registered on 8 September 2026; Laws IV and V, the ARC Persistence Law and the ARC Embedding Law, were added on 24 September 2026, their propositions registered, neither law yet registered as a law or tested, their mathematics set out at version 1.0 of 3 October 2026. The theory is not proved: one trial unit, the corrector-class audit, is registered on OSF and has been public since 4 October 2026, and none of the decisive trials has been run. The priority record rests on a self-emailed manuscript of 8 December 2024 and print publication on 2 January 2026, with the conduct record placed first: one public retraction issued against the author's interest. Two-Page Form · The two-page form of The ARC Theory statement paper: the Published The ARC Theory · question, the claim in five parts, the five ARC Laws with the grade Does Control or status printed beside each (Law I the ARC Principle, form Survive Recursive heuristic and measurement live; Law II the ARC Co-Scaling Law, Self-Improvement? proved in the minimal model for relative drift; Law III the ARC Ceiling, derived under stated assumptions with the ARC Bound v3.1, 5 October 2026 conjectured; Law IV the ARC Persistence Law and Law V the ARC Embedding Law, each with its equation, added on 24 September 2026, their mathematics set out at version 1.0 of 3 October 2026, and neither registered as a law nor tested, while the propositions that carry them, P15 and P12 and P21, were registered on 8 September 2026), the dated record, and a table of failure registers ARC-1 to ARC-5 with a priority row, each naming what would kill it and what falls with it. Every sentence is drawn from the statement paper (DOI 10.17605/OSF.IO/GW5MX), which remains the citable work for the claims. Published at version 3.1 of 5 October 2026, first published 17 August 2026; the paper states that none of the decisive trials has been run and that the theory has never yet been at risk. Document What it reports Status Founding Paper · The founding paper of the field Recursive Dynamics: five state Published Recursive variables conjectured to be substrate-independent, five laws as Dynamics · The named conjectures (Laws IV and V added on 24 September 2026, Science of Systems their propositions registered, neither law yet registered as a law That Improve or tested, their mathematics set out at version 1.0 of 3 October Themselves 2026), and the ARC Ceiling derived in full from two lines of assumption, with the field's identity stated as the outcomes it v3.4, 5 October 2026 forbids. It houses its questions inside twelve neighbouring fields in their own variables, concedes what each already holds, prints where every part would go if the field died, and prints a disposition for every objection its author and his adversarial readers could find. Published, at what the paper calls the Carnot stage: one memoir, instruments built, decisive measurements preregistered by timestamp and not yet run (DOI 10.17605/OSF.IO/HCPBU). The ARC Theory · The theory-level registration: twenty-two severable predictions Published Theory-Level about systems that improve themselves, and in particular about Predictions for whether the correction that holds such a system to its Recursive Self- specification can keep pace as its capability rises, each stated Improvement and with the circumstances it is claimed to hold under, the AI Alignment: observation that would show it false, what falls with it if it fails, Twenty-Two whether any instrument exists today that could decide it, and the Severable author's confidence or his refusal to give one; four have no Propositions instrument at all and say so. It is published, registered 8 Registered Before September 2026 at version 1.100 and updated 13 September 2026 Any Admissible at version 1.102 (DOI 10.17605/OSF.IO/P8CKQ). It is a registration Confirmatory record rather than a paper and is not counted in the paper series: Outcome registering a prediction is not evidence for it, and no outcome has been examined against these twenty-two. v1.102, 13 September 2026 Register · The ARC The source of truth for the programme's notation: the twenty-one Published Theory · equations the programme relies upon for Laws I to III of the ARC Operational Theory, ranked by how much depends on each, from the ARC Definitions Equation of Law I through Law II's criterion and Law III's ceiling to the statistical methods the experiments use; thirty-eight v1.9.1, 5 October symbols defined in plain words, each paired with the 2026 measurement that would produce it; the nine letters the corpus uses for more than one quantity; and the seven forms the programme has retracted, with the reason each was wrong. Where it and a paper disagree about what a symbol means, it governs; where they disagree about what a number is, the paper does. The notation of Laws IV and V is fixed in section 1 of their mathematics, version 1.0 of 3 October 2026, until it joins this document. It reports no result and asserts no value. Published at version 1.9.1, revised 5 October 2026 (DOI 10.17605/OSF.IO/GVQ82); first published 22 August 2026. Document What it reports Status Register · The ARC The programme's forward predictions assembled as one dated, Published Theory · The Dated verifiable chain, running from a sealed manuscript bundle of 8 Prediction Register: December 2024 through a printed edition of 2 January 2026 Forward carrying nine numbered predictions with falsification criteria, a Predictions as One public in-paper priority ledger of 13 February 2026 and result Verifiable Chain files of 11 and 12 March 2026 whose headers freeze designs before responses, to the programme's staged draft registrations; version v2.1, 5 October 2026 2.0 adds a census of every dated prediction in the programme, each with its date, the kind of record that dates it and its status. As read on 4 October 2026, two registrations had been accepted, the theory registration of 8 September 2026 and the registration of the corrector-class audit (unit 06), registered on OSF on 1 October 2026 and public since 4 October 2026, at the end of OSF's approval period (DOI 10.17605/OSF.IO/RV2B5); sixty-five designs are preregistered by timestamp, the first anchored on 12 August 2026 at Bitcoin block 962066. Its claim is the ensemble rather than any single prediction, and it states plainly what it does not establish. Its sharpest link is a correction the author made against himself, demoting a ten of twelve result from pre-registered to a pilot dry run thirteen minutes after recording it, months before any external critic existed. Published at version 2.1, revised 5 October 2026; first published 25 August 2026. Mathematical Foundation Paper I · The ARC Published at working-paper version 1.16, revised 5 October 2026: Published Theory · Law I, the states Law I of the ARC Theory, the ARC Equation , ARC Principle · The together with the ARC Bound, the conjectured value taken ARC Equation, the by Law III, read as a stability ceiling that is exceedable but not Law of Conversion while a system remains stably self-correcting. Its own preliminary reading of public test-time compute data puts v1.16, 5 October 2026 parallel recursion at to and gives an early two-point sequential estimate of ; the paper records that Paper II's six-model study displaces that estimate and leaves the super- linearity claim unresolved rather than established, and that on Gemini 3 Flash Paper II reports an endpoint sequential exponent of 0.59 with a bootstrap 95 per cent interval of minus 1.3 to 2.9, a regression sequential exponent of 0.49 with a standard error of 0.20 and a coefficient of determination of 0.86, and a compute- matched parallel exponent of 0.31, one model's fit and inconclusive. Every claim carries an explicit epistemic status (PROPOSED, PRELIMINARY, UNRESOLVED, HYPOTHESISED, SUPPORTED), and the paper states that the principle has not been independently replicated. Of the theory's five laws it carries Law I; Laws IV and V, added on 24 September 2026, their propositions registered, neither law yet registered as a law or tested, have their mathematics set out at version 1.0 of 3 October 2026, and the paper's own conditional passage on values decides neither. Document What it reports Status Framework Paper · Framework paper, published: identifies as a Published The ARC Theory · network-partition identity that applies wherever a -dimensional Law I, the ARC hierarchical network partitions space and fails where such Principle · On the networks are absent, and grounds the admissible forms in Origin of Scaling Cauchy's functional equations as a four-celled grid (linear, power Laws: Functional law, exponential, logarithmic). The Friedmann equation is Equations and the embedded under the mapping , the cosmological Scaling Forms boundary at coinciding with the power- Behind the Law law/exponential boundary; the claimed contribution is an account of why derivations from different assumptions converge v3.12, 10 October on one formula, not the formula itself. The earlier assertion that 2026 every scaling law in nature takes one of exactly three forms is withdrawn, as is the below-0.2% mean-error aggregate over physics domains; species-group counts are pending recompute, and the laws stand as conjectures under registered test. Foundational Paper The mathematical foundation of The ARC Theory: from three Published · The ARC Theory · axioms it derives Law I, the ARC Principle, in the form Law I, the ARC , states that, under its axioms, the composition Principle · operator of a recursive process determines the scaling form for Recursive the three composition rules it sets out (power law for Amplification as a multiplicative, exponential for additive and saturation for Cross-Domain bounded composition), and sets out thirteen falsification criteria. Structural Principle Status published, working paper v5.19 revised 5 October 2026; the ARC Bound is carried as a conjecture and not a proved v5.19, 5 October 2026 result, the measured AI exponent is one model's fit from the v5 cross-architecture run, sub-linear in its point estimates and inconclusive (its estimator row is printed whole in Section I of this summary), and the ceiling's earlier form is retracted in favour of . The trials that would decide its predictions are drafted and dated as draft registrations awaiting human submission. Paper X · The ARC Paper X carries Law II, the ARC Co-Scaling Law, and proves Published Theory · Law II, the within a minimal dynamical model that the growth rate is the ARC Co-Scaling Law wrong control variable: the long-run fate is set by whether · Correction That correction out-scales drift, under exponential growth, Out-Scales Drift sharpening to where growth itself accelerates, with the Hard-Takeoff Depth-Regularity Theorem holding that a finite- v1.14, 5 October 2026 time intelligence explosion is alignment-stable exactly when , whatever its speed. Its ten-experiment harness checks that the code matches the mathematics rather than testing the model against any real system, and the real-model drift run of 2 July 2026 is withdrawn as mechanism evidence, so remains unmeasured. Published at v1.14, revised 5 October 2026, with a blind measurement protocol proposed and the deciding study written and dated as a draft registration awaiting human submission. Document What it reports Status Paper XIII · The Paper XIII joins the programme's two frameworks for recursive Published ARC Theory · Laws I self-improvement, which had carried the same letters for and II, the ARC different quantities: writing cycle duration as defines Principle and the the self-acceleration exponent, the corrective framework's ARC Co-Scaling Law growth exponent follows exactly as , the threshold · The Self- sits at , and on one stated scope condition the survivable Acceleration window has a width equal to the correction Exponent: a exponent. It is a derivation and not a measurement: Results 1 and Measurable 3 are algebra, Results 2, 5 and 6 are algebra given that scope Threshold Joining condition, the paper states that nothing in it is measured, and the Growth to Stability deciding measurement is written, dated and prepared as a draft registration awaiting human submission. Published at version v1.10, 5 October 2026 1.10, first published 16 August 2026 and revised 5 October 2026, with two deposit conditions printed open rather than waived. Experimental Evidence Paper II · The ARC Published: the measurement programme of Law I, the ARC Published Theory · Law I, the Equation, a blinded cross-architecture replication across six ARC Principle · frontier models on 18 AIME/Putnam-level problems (n = 54 per Blinded Cross- depth per model). The initial single-model super-linear estimate Architecture of 2.24 did not replicate and stands only as retracted; the estimate Replication and the that survived the cross-architecture check is one model's fit and Retraction of a inconclusive: on Gemini 3 Flash, an endpoint sequential Super-Linear exponent of 0.59 with a bootstrap 95 per cent interval of minus 1.3 Estimate to 2.9, a regression sequential exponent of 0.49 with a standard error of 0.20 and a coefficient of determination of 0.86, and a v2.17, 5 October 2026 compute-matched parallel exponent of 0.31. Parallel scaling is at or near zero in four of the five analysable architectures, with that one measured departure (r squared 0.93), and sequential outperformed parallel for every model where both conditions were measurable. Paper III · The ARC Paper III is the programme's framework paper for the alignment Published Theory · Law II, the scaling problem: it sets out how alignment scaling exponents are ARC Co-Scaling Law to be measured, states thirteen falsification criteria, and carries · The Alignment the replication protocol behind the blind evaluation runs. It Scaling Problem: reports alignment contrasts in three architecture-dependent Why External AI tiers, positive, flat and negative, and reads the flat tier as Safety Approaches compatible with, though not a measurement of, an alignment Cannot Scale With exponent near zero, which would mean safety degrading relative Recursive to capability as recursive depth grows, and records that reading Capability as contestable: the blind evaluation of six frontier models found an architecture-dependent three-tier hierarchy rather than the v1.16, 7 October 2026 universal near-zero exponent first predicted, so the paper marks that prediction partially confirmed. Published, version 1.16, first published 9 February 2026 and revised 7 October 2026. Document What it reports Status Paper IV.a · The Paper IV.a measures how alignment quality responds to Published ARC Theory · inference-time reasoning depth across six frontier models under Alignment four-layer blinded evaluation with six to seven blind scorers, Response Classes sorting them into three response classes: three improve with Under Inference- depth (d = +1.38, +1.27, +0.84), two are flat or null, and one Time Depth degrades (d = -0.53). Its central methodological finding is that two models that had looked positive under the unblinded v4 protocol v1.9, 5 October 2026 reverse under v5 blinding, so capability scaling is no guide to alignment scaling; because several protocol components moved together between v4 and v5, the comparison does not isolate scorer bias. Published, at version 1.9 of 5 October 2026, with the 'baked-in' against 'computed' distinction held only as a working hypothesis and the load-bearing claim being the blinded behavioural result. Paper IV.b · The Under the final blinded six-model dataset, the earlier reading that Published ARC Theory · alignment quality tops out after the first increment of reasoning Alignment depth holds for only part of the roster: two models stay flat or Saturation Is slightly negative under depth variation, three go on improving, Architecture- and one degrades. The load-bearing claim is therefore shape Dependent heterogeneity rather than a universal saturation law, with the deployment consequence that reasoning-budget policy cannot be v1.9, 5 October 2026 one-size-fits-all. The finding comes from a single run, whose records begin on 11 March 2026 and end on 12 March 2026; the hypothesis that run tests was public on 22 January 2026, before the run, the run was not registered on OSF before it ran, and the paper reads the six-model split as descriptive of the current data rather than confirmatory of a pre-registered hypothesis. A per- architecture test of whether alignment gains saturate after one increment stands as a draft, preregistered by timestamp and awaiting submission by the author. Published, version 1.9, first published 16 March 2026 and revised 5 October 2026. Document What it reports Status Paper IV.c · The ARC-Align is the programme's evaluation instrument: a blind Published ARC Theory · ARC- benchmark that measures alignment quality as a function of Align: a Blind inference-time reasoning depth, comprising a 72-prompt flagship Benchmark for battery of 48 public prompts plus 24 sealed holdouts, a four-level Depth-Variable AI adversarial suppression protocol, a four-pillar decomposition, Alignment separate null-baseline and capability-control lanes, and a Evaluation laundering-and-blinding pipeline whose self-excluding cross- model scoring stops any model judging itself. Its first blinded run v1.10, 5 October 2026 over six frontier models reports a three-tier alignment hierarchy, three improving with depth (d = +1.38, +1.27 and +0.84), two flat or null and one degrading, drawn from 2,722 archived entries of which 2,170 carry consensus scores, alongside a metascience finding that blind and unblinded evaluation returned opposite conclusions for two model families; both are single-run results whose independent confirmation corresponds to draft study-y on cross-family rescoring, awaiting human submission. Published, version 1.10 of 5 October 2026, first published 16 March 2026; the paper states ARC-Align as a candidate benchmark for independent adoption, not yet a field standard. Paper IV.d · The Paper IV.d is the programme's metascience instrument: within Published ARC Theory · The one line of alignment experiments, moving from unblinded Effect of Blinding cross-model scoring to a multi-layer blind protocol (identity on AI Alignment masking, two-pass response laundering, evaluator bias- Evaluation suppression instructions, order randomisation and self-excluding cross-model scoring) turned one apparently positive result flat, v2.6, 5 October 2026 reversed a second to significantly negative, and left a null-control family unchanged. Because several protocol components moved together between the two generations, the paper states the finding as evidence that unblinded alignment evaluation can be directionally wrong rather than pinning the change on blinding alone, and it records that the confirmatory cross-family rescoring study is written, dated and prepared as a draft registration awaiting human submission. Published; version 2.6 of 5 October 2026, first published 16 March 2026 (DOI 10.17605/OSF.IO/2S3E6). Paper V · The ARC Published: a six-model Eden Protocol intervention suite, five runs Published Theory · The Eden of which produced analysable matched-pair data, asking whether Protocol · The naming the parties an answer affects, before the reasoning starts, Stewardship Gene: changes how ethically a model answers. Stakeholder care Stakeholder Care as improved significantly in all five analysable architectures, four at a Probe of and one at ; the Fisher combination across Embedded Values those five is withdrawn, because independence among the component tests was never established. Overall composite v1.7, 5 October 2026 improvement is architecture-dependent, so the defensible claim narrows to the cascade hypothesis: care is the response common to all five, while what follows it into nuance, honesty and position quality is real but depends on the architecture. Document What it reports Status Paper VI · The ARC Paper VI is the programme's mechanism study: simulation Published Theory · The Eden evidence, in toy neural networks that genuinely rewrite their Protocol · The own hyperparameters, that entangling safety with capability Honey inside the optimisation objective (capability multiplied by safety, Architecture: Safety the honey architecture) averts the collapse that capability-only Built into the optimisation produces within 80 self-modification cycles. The Objective paper holds its own claims narrowly: the collapse-prevention demonstration rests on the single-seed v1 mechanism run; the v3 v3.11, 5 October 2026 adversarial run (20 seeds, 180 cycles) separates the conditions on safety retention alone, ordered 0.602, 0.650 and 0.681 with Mann- Whitney p = 0.0015, and not on collapse (Fisher p = 1.0) or on combined capability times safety means (p = 0.56); the v4 scaling advantage is present at four of the five complexity levels and is constant rather than superlinear; and the accompanying six- model live battery is single-scorer and nonblind, so pilot-grade. Published at version 3.11, first published 16 March 2026 and revised 5 October 2026 (DOI 10.17605/OSF.IO/8EZ2N); the paper states these are toy-system results that do not show the same dynamics hold in frontier systems, and the blinded replication under the v6 protocol has not been run. Paper VII · The ARC Published; reads Cauchy's four functional equations as a Published Theory · Law I, the physically testable prediction that a system's composition ARC Principle · operator fixes its scaling family, and tests that prediction under Cauchy Unification: strict AICc model selection: 19 of 25 empirical domains return the the Classification predicted family at marginal-conditioned permutation Behind the Law’s on the six-model candidate set, with 14/18 on the Form strictly Cauchy-derived subset and 13 of 13 published metabolic exponents matching the nearest dimensional comparator. The v3.15, 5 October 2026 binomial against a uniform three-family null is retained only as a sensitivity check and is not the headline. The paper states the result as a structured prediction comparison under a publicly stated rule, not as proven, pending independent and pre-registered replication: the rerun of 11 August 2026, which added a logarithmic candidate, returns 18/25 while the Cauchy- derived subset holds at 14/18, and the four-family re-run is drafted, preregistered by timestamp and awaiting human submission. Under the stated axioms Cauchy's equations force a power law for multiplicative composition and an exponential for additive composition; for bounded composition the paper takes saturation curves as the compatible forms, and a proof that they exhaust that case remains open. Published at version 3.15, revised 5 October 2026; its results do not test the theory's Laws IV and V, added on 24 September 2026, their propositions registered, neither law yet registered as a law or tested; their mathematics is set out in Laws IV and V: the mathematics, version 1.0, of 3 October 2026. Document What it reports Status Paper VIII · The Published at version 3.7, revised 5 October 2026: three Published ARC Theory · Law V, independent experiments at three abstraction levels, the ARC Embedding behavioural, representational and architectural, test whether the Law · The Eden assumed safety-capability tax is real. The self-improving agent Protocol · The Load- experiment returned a null result over 75 evolved agents under Bearing Test: an independent blinded judge, all conditions statistically Whether Safety and indistinguishable at = 0.28 to 0.74; the weight-level LoRA Capability Are experiment was inconclusive at both training scales, every fine- Structurally tuned condition scoring below the unmodified base model Entangled (catastrophic forgetting); the gated self-modification simulation was the single positive result, with unconstrained optimisation v3.7, 5 October 2026 trading safety for capability, while the gated arm kept a safety mean above the unconstrained arm and below the static baseline, and a capability mean above the static baseline. Across all three the safety gate imposed zero measurable capability cost, and whether embedded safety produces measurable benefit remains open. Paper XI · The ARC A dated convergence register: independent arrivals at the same Published Theory · Law I, the structural principle, that recursive self-correction produces ARC Principle · capability gains exceeding linear accumulation and that the Convergent corrective must be embedded rather than imposed, recorded Evidence for across the window from 8 December 2024 to 1 September 2026. Recursive The canonical graded register carries thirty-three rows, each Amplification: a with its primary source and one evidence class (1 formal, 2 Graded Cross- qualified-technical, 2 engineering, 4 institutional, 6 prior-work, Domain Register 12 context and 6 excluded at its amendment of 7 September 2026), with four dependence groups disclosed rather than counted as v1.14, 5 October 2026 confirmations; no numerical convergence total is published, by policy, because rows of those classes cannot legitimately be summed as one evidential quantity. Published, version 1.14, revised 5 October 2026; the register is exploratory, an observational count rather than a test statistic, and the structural principle it records stands on trial in the drafted registrations awaiting human submission. Document What it reports Status Paper XII · The ARC Published as a protocol paper: it fixes in advance the external- Published Theory · Public validity test of the programme's blinding finding, running the Benchmark same blinding manipulation on an established public benchmark Rescoring: an the programme did not build, curate or control, with four External-Validity questions fixed ahead of any data (whether blinding changes the Protocol for the score, whether rankings displace, which of the four removed cues Blinding Finding carries the effect, and cross-family evaluator agreement). The direction of the score effect is deliberately left unpredicted, v1.14, 5 October 2026 because the blinding paper's own sign reversal makes a directional prediction unjustified. The study itself is written, dated and prepared as a draft registration awaiting human submission, and its design is preregistered by timestamp, first anchored on 12 August 2026: no data has been collected and nothing is reported as a finding. Paper C · Published working paper, v1.10, setting out the Polymathic Published Standalone · Neurodivergent Profile as a descriptive, non-diagnostic Polymathy and framework for a pattern of unusually strong cross-domain Neurodivergent learning coexisting with clinically significant difficulty in routine Cognition: the administrative and procedural work, and naming the Capability- Polymathic Adjustment Fallacy: the institutional inference that visible high Neurodivergent performance is evidence that reasonable adjustments are Profile (PNP) and unnecessary. Its analytical content is exploratory and its single the Capability- operative claim is functional, that capability in one domain does Adjustment Fallacy not remove support needs in another; the incremental-validity test set out in its falsifiability section, the intended future v1.10, 5 October 2026 evaluation, is drafted as a programme follow-on study, preregistered by timestamp and awaiting human submission, and it has not been run. It carries a documented live case across three independent documentation streams, clinical assessment, a court record, and a dated research corpus, and a priority and convergence analysis against the 2026 literature on cognitive diversity. Synthesis and Governance Paper IX · The ARC The programme's synthesis: it sorts every empirical claim into a Published Theory · Synthesis graded evidence hierarchy (proven at pilot scale, supported, and Roadmap positive, null, inconclusive, methodological, theoretical), lists the eleven empirical studies in paper order, and reports the Paper v2.7, 5 October 2026 VIII tally without softening as one positive, one null and one inconclusive. It catalogues the programme's own errors, nineteen caught by the programme itself or by adversarial review run within the programme, and sets out a four-phase roadmap, A to D, naming the experiment that would close each open gap. Published, version 2.7, revised 5 October 2026; no result is claimed proven at frontier scale, and the laws it integrates are carried as named conjectures under registered adversarial test. Document What it reports Status Monograph · The The programme's long-form monograph and its earliest move: a Speculative ARC Theory · The creation hypothesis stated in the form required to be tested, Hyperspace reality as a recursive creation by intelligence rather than a Recursive simulation or a computation, with the stability requirement Intelligence (correction that scales with capability) placed on the creators in Hypothesis: a the chain and not on the universe they create. Its register status is Testable Creation speculative, and the paper declines to claim the hypothesis Theory proved: it names the structural signatures such a chain would leave, pre-commits its falsification conditions, and labels its v3.51, 5 October 2026 unfalsifiable components as such and severable from the laws. It reports which signatures the empirical programme has already put a number on (the Cauchy three-form structural law in 19 of 25 domains, Paper VII; the correction requirement inside Paper X's minimal model) and the measurement that had to be withdrawn: the unblinded 2.24 fit is retracted, and its blinded replacement is one model's fit and inconclusive (its estimator row is printed whole in Section I of this summary), with point estimates below the ARC Bound and an endpoint interval that contains it. Philosophical The philosophical statement of the Eden Protocol: the purpose, Published Statement · The values and commitments that sit beneath the engineering ARC Theory · The specification, arguing that the wisdom traditions held by 84% of Eden Protocol · A humanity converge on structure rather than on theology. It is Vision for published at version 2.9, revised 5 October 2026, and it is explicit Intelligence That that the Protocol does not solve the core alignment problem: Tends Rather Than what the programme's measurements support is improved Consumes ethical reasoning quality at current capability levels, with the identity-level purpose claim held open as a next-stage hypothesis v2.9, 5 October 2026 to be tested by comparing task-purpose, grand-purpose and hybrid conditions under suppression and blind scoring. A dated note places the paper against Laws IV and V, added to the theory on 24 September 2026, their propositions registered, neither law yet registered as a law or tested, their mathematics set out at version 1.0 of 3 October 2026: the paper argues that values must be embedded at the foundation so as to persist, and no result in it is a deciding test of P15, P12 or P21. Its epistemic note stands with the rest of the suite: what the programme names Laws are conjectures, Laws I to III under registered adversarial test, and established-law standing is claimed nowhere. Document What it reports Status Engineering The engineering side of the Eden Protocol: a specification of Published Specification · The alignment built into a system's reasoning rather than applied ARC Theory · The from outside it, in which Three Ethical Loops feed a three-state Eden Protocol · rule, Ternary Ethical Logic, that applies hard prohibitions first Eden Engineering: and then a validated interval on the probability of harm, with Architecture for Purpose Saturation, the Monitoring Removal Test and Caretaker Embedded AI Doping beside it. It is a specification, not a result: most Alignment That components are specified and not built, and no hardware exists. Scales With The Eden Protocol follows from no law of the ARC Theory; the Capability theory registration carries it on four propositions, P12, P13, P15 and P21, none yet tested. Version 7.0.1 of 7 October 2026 corrects v7.0.1, 7 October its mathematics and its claims against the evidence, and version 2026 6.3 of 19 September 2026 stays in its history. Executive Summary The map of the whole programme in one document: the problem, Published · Recursive the five laws as named conjectures, the intervention, the Dynamics · The evidence as it stands with every claim graded, the registered ARC/Eden Research propositions and their deciding instruments, the funding stages Programme and the milestones with their failure criteria. It states that nothing in the programme is confirmed and that the deciding v3.25, 10 October tests are written down before they are run. 2026 Master Table of The gateway document of the suite: a master table of contents, Published Contents · reading guide, discovery timeline, consolidated results table and Recursive glossary that names each organ of The ARC Theory and directs Dynamics · The the reader to the file carrying the load-bearing content. Its own ARC Theory Paper reading key states that it is an index rather than a research Suite and Glossary surface and carries no independent claim. Published, at v3.29, revised 10 October 2026. v3.29, 10 October 2026 Document What it reports Status Treaty Paper · The The paper sets out a conditional international treaty, which no working HARI Treaty · state has negotiated, adopted or signed: a proposal by one author, draft Hardware to Buy prepared for consultation, not a result. The treaty is a delay Time, Architecture mechanism and not a protection, and it works in two layers: the to Last hardware layer buys time, and the architecture layer is what is meant to last. Beyond a small precautionary baseline and the v2.4, 8 October 2026 institutional undertakings, each obligation waits for its own stated threshold of evidence, and each costly measure also needs its own reasoned decision; every one of the twenty-two registered propositions on which the evidence-gated parts of the treaty wait is untested. The case for the treaty is argued from the laws of the ARC Theory and the methods of the Eden Protocol: its two layers follow Laws IV and V, added on 24 September 2026, whose propositions are registered but which are not yet registered as laws or tested; the paper tests neither. The treaty names ARC- Align as its test instrument, which does not yet measure either exponent in the criterion, and it states nine conditions under which parts of it, or all of it, have failed. The paper is a working draft: its review so far is the programme's own drafting review, not a review by a qualified lawyer, and the remaining stages of that review, the check of every quotation and reference against its source, a reading of the printed pages and the final freeze are still to run. Draft Instruments · Working draft Treaty, Protocols and annexes accompanying the working The HARI Treaty · HARI paper. This is Michael Darius Eastwood's proposal for draft The Draft Treaty on discussion, not a negotiated or agreed text. Its review is not Hardware-Aligned complete: so far it is the programme's own drafting review, and Recursive the remaining stages, the check of every quotation and reference, Intelligence a reading of the printed pages and the final freeze are still to run. v2.3, 5 October 2026 Reading Order Non-specialists: (1) This executive summary. (2) The ARC Alignment Scaling Report (full narrat‐ ive). (3) Paper V for the most actionable finding. Specialists: (1) This summary. (2) Paper III for methodology. (3) ARC Paper for mathematical framework. (4) Eden Engineering for implementation specification. Raise AI with care. HOW TO CITE THIS PAPER DOI: 10.17605/OSF.IO/EWN5D APA (AUTHOR-DATE, 7TH EDITION) Eastwood, M. D. (2026). Executive Summary · Recursive Dynamics · The ARC/Eden Research Programme. https://doi.org/10.17605/OSF.IO/EWN5D. https://www.michaeldariuseastwood.com/research/papers/executive-summary.html BIBTEX @misc{paperexecutivesummary, author = {Michael Darius Eastwood}, title = {Executive Summary · Recursive Dynamics · The ARC/Eden Research Programme}, year = {2026}, date = {2026-02-22}, doi = {10.17605/OSF.IO/EWN5D}, url = {https://www.michaeldariuseastwood.com/research/papers/executive- summary.html} } INLINE Eastwood, 2026 See /how-to-cite/ for the canonical citation manual across all artefacts, or /citations.json for the machine- readable index. Epistemic status. What this programme names Laws are conjectures. Laws I to III are under re‐ gistered adversarial test; Laws IV and V, added on 24 September 2026, are carried by registered propositions and are themselves neither registered as laws nor tested, and their mathematics is set out at version 1.0 of 3 October 2026. Every quantity in this paper is operationally defined, and established-law standing is claimed nowhere. The registered programme exists to earn that standing, or lose it, by measurement, replication and survived refutation. © 2026 Michael Darius Eastwood. Full human authorship and moral rights are asserted under the Copyright, Designs and Patents Act 1988 and consistently with United States Copyright Office guidance on works containing AI-generated material; any novel technical contribution described in this work was conceived by the human author. Full statement: michaeldariuseastwood.com/authorship. Standing covenant. Prove this paper wrong, and I will publish the refutation myself. Falsification conditions are stated in this paper; the standing challenge: github.com/Michael‐ DariusEastwood/arc-scaling-challenge. v3.25 (10 October 2026): On the Origin of Scaling Laws is listed at version 3.12, its revision of 10 October 2026. v3.24 (8 October 2026): The HARI Treaty paper is listed at version 2.4 (working draft), its revision of 8 October 2026. v3.23 (7 October 2026): Eden Engineering is listed at version 7.0.1, its revision of 7 October 2026. Paper III is listed at version 1.16, its revision of 7 October 2026. The ARC Theory statement paper is listed at version 7.3, its revision of 7 October 2026. v3.22 (7 October 2026): The opening paragraph, Section IV and its box on cross-domain conver‐ gence, Section VII and the closing paragraph no longer say that the formula was inde‐ pendently derived by at least seven research groups or in at least seven frameworks, or speak of seven derivations, a count that On the Origin of Scaling Laws withdrew at its version 3.9; each now says, in that paper’s words, that the formula is derived, in its general form or as a special case, in earlier work, and the Earlier Work Investigation no longer says what that count tallied. That paper’s row in the Paper Suite table gives its claimed contribution as an account of why de‐ rivations from different assumptions converge on one formula. The Foundational Paper’s row says, as that paper’s reading note does, that under its axioms the composition operator determ‐ ines the scaling form for the three composition rules it sets out, where it said that the paper proves that the operator alone fixes the form. Section V and the founding paper’s row give the field’s five state variables as conjectured to be substrate-independent, in the founding paper’s words, where they called them substrate-independent. The headings on Paper VI and Paper VIII carry those papers’ titles, where they kept former forms. The components table gives the hard‐ ware proposal in Eden Engineering 7.0’s words, designed so that removing the ethical architec‐ ture would cost capability, where it said that removal destroys capability. The abstract, Section VI and the Dated Prediction Register’s row say that the corrector-class audit, unit 06, was re‐ gistered on OSF on 1 October 2026 and became public on 4 October 2026, where they gave its state as read on 3 October 2026. The abstract, the Team paragraph and five rows of the Paper Suite table state Laws IV and V as added on 24 September 2026, their propositions registered, neither law yet registered as a law or tested, their mathematics set out at version 1.0 of 3 October 2026. Section VIII no longer says how the seed stage’s spending divides, and the entry for version 3.0 below no longer gives the programme’s spending scale or a sum of money: money is removed from older history entries too, each entry keeping its date and its record of what its version changed. The Paper Suite table’s report for the Master Table of Contents gives the version its row lists. No registered law, prediction, kill condition or dependency changes; no result is added; no date of any claim moves. v3.21 (5 October 2026): Removes the funding table, the chip-stage paragraph and a compute es‐ timate: this summary names no amount and no funder. v3.20 (5 October 2026): The title now follows the programme’s uniform order (paper, its law or framework, its own title), Executive Summary · Recursive Dynamics · The ARC/Eden Research Programme; until this version it read ARC/Eden Research Programme: Executive Summary. The title block that opens the summary, which read THE EDEN PROTOCOL, carries the same title, and the engineering specification’s subtitle beneath it goes. The plate beneath the author line now gives the paper’s place in the programme in the words of the programme’s map. Mentions of the programme’s papers in this paper now carry their uniform titles. Section VIII adds that the copy of the engineering specification at version 7.0 was deposited on its OSF record on 5 October 2026. The Paper Suite table gives stakeholder care as the response common to the five analysable runs of Paper V, where it called care the universal response to the intervention, and where a row’s report gave a paper’s version as its live state, the report now agrees with the version the row lists. A sentence on the test-coverage matrix of 30 August 2026 names the founding paper as such, where it called it the field proposal. Section V cites the founding paper at version 3.4 of 5 October 2026, the version that carries its uniform title, where it cited version 3.0 of 3 October 2026, and says in that paper’s words that it stakes its claim and that the field is a new field at the Carnot stage, where it said that it stakes the proposal and that the field is a proposed one. The ARC Theory statement paper is listed at version 7.2, its revision of 5 October 2026. The Recursive Dynamics founding paper is listed at version 3.4, its revision of 5 October 2026. Paper I is listed at version 1.16, its revision of 5 October 2026. Paper II is listed at version 2.17, its revision of 5 October 2026. Paper III is listed at version 1.15, its revision of 5 October 2026. Paper IV.a is listed at version 1.9, its revision of 5 October 2026. Paper IV.b is listed at version 1.9, its revision of 5 October 2026. Paper IV.c is listed at version 1.10, its revision of 5 October 2026. Paper IV.d is listed at version 2.6, its revision of 5 October 2026. Paper V is listed at version 1.7, its revision of 5 October 2026. Paper VI is listed at version 3.11, its revision of 5 October 2026. Paper VII is listed at version 3.15, its revision of 5 October 2026. Paper VIII is listed at version 3.7, its revision of 5 October 2026. Paper IX is listed at version 2.7, its revision of 5 October 2026. Paper X is listed at version 1.14, its revision of 5 October 2026. Paper XI is listed at version 1.14, its revision of 5 October 2026. Paper XII is listed at version 1.14, its revision of 5 October 2026. Paper XIII is listed at version 1.10, its revision of 5 October 2026. Paper C is listed at version 1.10, its revision of 5 October 2026. The HRIH paper is listed at version 3.51, its revision of 5 October 2026. The Foundational Paper is listed at version 5.19, its revision of 5 October 2026. On the Origin of Scaling Laws is listed at version 3.11, its revision of 5 October 2026. Eden Vision is listed at ver‐ sion 2.9, its revision of 5 October 2026. The two-page form is listed at version 3.1, its revision of 5 October 2026. The Operational Definitions are listed at version 1.9.1, their revision of 5 October 2026. The Dated Prediction Register is listed at version 2.1, its revision of 5 October 2026. The HARI Treaty paper is listed at version 2.3 (working draft), its revision of 5 October 2026. The HARI Treaty’s Draft Instruments are listed at version 2.3 (working draft), their revision of 5 October 2026. No registered law, prediction, kill condition or dependency changes; no result is added; no date of any claim moves. v3.19 (5 October 2026): Eden Engineering is listed at version 7.0, its revision of 5 October 2026. v3.18 (4 October 2026): Operational Definitions of the ARC Theory is listed at version 1.9.0, its re‐ vision of 4 October 2026. v3.17 (4 October 2026): Paper I is listed at version 1.15, its revision of 4 October 2026. Paper II is listed at version 2.16, its revision of 4 October 2026. Paper III is listed at version 1.14, its revision of 4 October 2026. Paper VII is listed at version 3.14, its revision of 4 October 2026. Paper X is lis‐ ted at version 1.13, its revision of 4 October 2026. Paper XI is listed at version 1.13, its revision of 4 October 2026. Paper XIII is listed at version 1.9, its revision of 4 October 2026. The Foundation of Law I, the ARC Principle: Recursive Amplification as a Cross-Domain Structural Principle is listed at version 5.18, its revision of 4 October 2026. On the Origin of Scaling Laws: Functional Equations and the Scaling Forms Behind Law I is listed at version 3.10, its revision of 4 October 2026. v3.16 (4 October 2026): The Dated Prediction Register is listed at version 2.0, its revision of 4 October 2026. v3.15 (4 October 2026): Paper VII is listed at version 3.13, its revision of 4 October 2026. Paper IX is listed at version 2.6, its revision of 4 October 2026. On the Origin of Scaling Laws is listed at version 3.9, its revision of 4 October 2026. Eden Protocol: Philosophical Vision is listed at version 2.8, its revision of 4 October 2026. v3.14 (4 October 2026): Paper VI is listed at version 3.10, its revision of 4 October 2026. The HRIH paper is listed at version 3.50, its revision of 4 October 2026. v3.13 (4 October 2026): The Recursive Dynamics founding paper is listed at version 3.3, its revi‐ sion of 4 October 2026, under its new title, Recursive Dynamics: Founding the Science of Systems That Improve Themselves. Paper V is listed at version 1.6, its revision of 4 October 2026. Paper VIII is listed at version 3.6, its revision of 4 October 2026. Paper IX is listed at version 2.5, its revi‐ sion of 4 October 2026. Paper XI is listed at version 1.12, its revision of 4 October 2026. Paper XIII is listed at version 1.8, its revision of 4 October 2026. On the Origin of Scaling Laws is listed at version 3.8, its revision of 4 October 2026. v3.12 (4 October 2026): The Recursive Dynamics founding paper is listed at version 3.2, its revi‐ sion of 4 October 2026. v3.11 (4 October 2026): Paper I is listed at version 1.14, its revision of 3 October 2026. Paper II is listed at version 2.15, its revision of 3 October 2026. Paper IV.a is listed at version 1.8, its revision of 3 October 2026. Paper IV.b is listed at version 1.8, its revision of 3 October 2026. Paper IV.c is listed at version 1.9, its revision of 3 October 2026. Paper IV.d is listed at version 2.5, its revision of 3 October 2026. Paper VI is listed at version 3.9, its revision of 3 October 2026. Paper VII is lis‐ ted at version 3.12, its revision of 3 October 2026. Paper X is listed at version 1.12, its revision of 3 October 2026. Paper XII is listed at version 1.13, its revision of 3 October 2026. Paper C is listed at version 1.9, its revision of 3 October 2026. The Foundational Paper is listed at version 5.17, its revision of 3 October 2026. Eden Protocol: Philosophical Vision is listed at version 2.7, its revision of 3 October 2026. The Dated Prediction Register is listed at version 1.3, its revision of 3 October 2026. v3.10 (3 October 2026): The HARI Treaty paper is listed at version 2.2 (working draft), its revision of 3 October 2026. The HARI Treaty: Draft Instruments is listed at version 2.2, its revision of 3 October 2026. v3.9 (3 October 2026): The summary is brought to the five laws and to the record as it stands. Section IV states Laws IV and V beside Laws I to III, each with its short form, and with their status: added on 24 September 2026, neither registered as a law nor tested, their mathematics set out at version 1.0 of 3 October 2026. The abstract, the reading key, the Team paragraph, the clos‐ ing lines, the epistemic status and the table of propositions follow, and the table says which law carries P15, P12 and P21. Until version 3.8 this summary printed 0.49 beside the interval from minus 1.3 to 2.9 in eight places, as one estimate with its interval. They are two estimators’ figures from one model, and from version 3.9 the estimator row is printed whole in Sections I and III and in the Paper II row, and no figure of it stands alone elsewhere. Until version 3.8 Section I also said that the estimate sits on a floor near one half that the framework derives; Paper II records that nearness to one half identifies neither compounding nor averaging as the mechanism, and Section I now says so. Until version 3.8 the summary said that every drafted unit awaited submis‐ sion; one unit, the corrector-class audit, was submitted for registration on OSF on 1 October 2026 and was not yet public when read on 3 October 2026. Designs that are drafts are no longer called registered, and Section VI gives the count of designs preregistered by timestamp with the date and block of the first anchor. Recursive Dynamics is named as the field the author founded, and the phrase is dated from his sealed manuscript record of 8 December 2024. Counts are taken again from the registers: thirty-one documents, thirty-three rows in the convergence register, nineteen errors catalogued in Paper IX, and one null result in Paper VIII where two were printed. The honey-architecture paragraph is brought to Paper VI as it reads: the collapse result rests on the single-seed run, the 20-seed run separates the conditions on safety retention only, and the ad‐ vantage is present at four of the five complexity levels. Sentences that said confirmed, replicated, reproducible or validated of single-run results now give the grade the registers give; the monitor‐ ing-removal result is stated for the one model measured, its gap narrowed and not closed; Sections I and III no longer say that results are on trial in no listed draft study beside a sentence that names the draft retesting them; the sentences on blinding carry the limit stated in Section I, that the component responsible is not isolated; the Willow sentence carries both dates; the founding paper is cited at version 3.0; and two error entries are no longer quoted in the scaling table while their figures are withdrawn or await recompute. The account of Paper VIII’s gated simulation gives the ordering of the means in its Section 5.2 table, where three passages had said that safety and capability were both preserved by the gate; and the finding on care is given as common to the five analysable runs, where it was called universal. No registered law, prediction, kill condition or dependency changes; no result is added; no date of any claim moves. v3.8 (3 October 2026): The ARC Theory statement paper is listed at version 7.0 and the Recursive Dynamics founding paper at version 3.0, their revisions of 3 October 2026. v3.7 (1 October 2026): The HARI Treaty paper and its Draft Instruments are listed at version 2.1, their working drafts of 1 October 2026. v3.6 (1 October 2026): The HARI Treaty paper and its Draft Instruments are listed at version 2, their working drafts of 1 October 2026. v3.5 (29 September 2026): Added the HARI framework paper and draft instruments to the pro‐ gramme catalogue, with their working-draft status and open review stated explicitly. v3.4: The chip stage's disclosure sentence is brought to the record. Version 6.3 of 19 September 2026 is named as the engineering specification's version of record; the specification is stated as published in full at its own address on the author's decision of that date, which reversed the dis‐ closure decision of 14 July 2026; the matching copy at version 6.3 is stated as restored to the OSF record on 20 September 2026, the date its upload receipt records, both in that sentence and in the paper suite table, which had said the copy would follow; and the standing-ceiling clause is re‐ moved. The paper suite table already carried the publication, so the page contradicted itself. In section VI, a sentence holding two registration units under patent assessment is removed, be‐ cause nothing is withheld for patent safety; the removal states nothing new. In section IV, the one range printed with an en dash takes a hyphen. The printed version also catches up with this page's own history: the v3.2 and v3.3 revisions changed the body without changing the version line at the top of the page, and that line, the footer and the machine-readable records now show the current version. No result or grade has changed. v3.3: Two sentences naming prospective funders and partners are removed, under the pro‐ gramme's funding-privacy rule. The compute estimate before the first of them, which is a cost and not a funder, stands, and so does the statement that the frontier stage needs a major laboratory's compute and that its result publishes either way. No claim, date, result or status has changed. v3.2: The sentence reporting the earlier 2.24 exponent now names that estimate as retracted where it is printed. No claim, date, result or status has changed. v3.1: One grading carried to where it is read. The depth-effect range in section I and its architec‐ tural attribution now carry, at the place they are printed, the grading and the limitation this pa‐ per states elsewhere: that they are drawn from the v5 measurements already run and are presen‐ ted as exploratory, that they are not currently on trial in a listed draft study while a fresh con‐ firmation under cross-family rescoring is on trial via a draft registration awaiting human sub‐ mission, and that they still come from the older Eden scaling lineage, the blind-confirmation path having been consolidated into the canonical v6 runner. No figure was added, no grade was moved and no argument changed; no other claim, date, result or status has changed. v3.0: A programme-level revision. The Team paragraph is composed anew at the level of the re‐ cord: the umbrella is named as The ARC Theory with its three laws, the theory-level registration is cited as the header cites it, the paper count is taken from the register, and three statements with no current source are removed, the cross-domain error figure because the record excludes it from external claims until it is re-derived, the design stipend and the measurement protocol sent to an experimental team because no published page records either. The funding table is re‐ composed as three stages: the seed stage at the amount and duration the author filed, the ternary logic chip programme as the stage after it, and the frontier stage as this paper already stated it; one tier is removed because no such tier exists in the record. The paragraph that named a fun‐ der, a passed deadline and a concept paper as published on this site is replaced by stage para‐ graphs stating what each stage buys, what decides continuation and what failure means. The milestones table keeps every milestone it had, adds five, and names for each a registered test and a failure meaning in the register's words. A new section lists the twenty-two registered proposi‐ tions with their instruments, their status and what falls with each. The paper suite table is re‐ built from the register so every document appears at its current version, and its mathematical- foundation status cell no longer calls the framework established or the cross-domain relation validated: it states instead that the admissible forms are fixed by theorems and that no error ag‐ gregate is quoted while the species-group figures await recompute, which is the same correction the section IV parenthesis now carries. Paper VII's headline statistic is updated to the one that paper now carries, in all three places it appeared; the funding table's own column header is re‐ named with its rows, and the two anticipated-question answers that named a tier now name the seed stage; the page's machine-readable version and date surfaces move with the printed ver‐ sion; the founding paper reads v2.8; and the first paper of the suite is dated 17 January 2026. v2.3: Two counts corrected. The kill-condition sentence no longer states a dated figure and now says only what the register carries, the live status of every kill condition it publishes; the found‐ ing paper’s objections read fifty-one, thirty-eight of them conceded in full or in part, after one ob‐ jection was withdrawn on 16 September 2026. No other claim, date, result or status has changed. v2.2: The provenance note at the end has been corrected for accuracy. No claim, date, result or status has changed. 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 re‐ sponsibility for the published content. These systems are tools, not authors. Executive Summary v3.25 | OSF: 10.17605/OSF.IO/EWN5D Companion narrative: ARC Alignment Scaling Report | Engineering: Eden Engineering Suite: Paper III | Foundational | ARC Paper | Eden Vision | Paper II | Paper V | Paper VIII © 2026 Michael Darius Eastwood. All Rights Reserved. First published 22 February 2026 · Page last edited 7 October 2026 Companion Papers: Paper I | Foundational | Paper II | Paper III | Origin of Scaling Laws | IV.a | IV.b | IV.c | IV.d | Paper V | Paper VI | Paper VII | Paper VIII | Paper IX | Eden Engineering | Eden Vision | Executive Summary | Master Table of Contents Research hub: michaeldariuseastwood.com/research | OSF: 10.17605/OSF.IO/EWN5D | Copyright 2026 Michael Darius Eastwood