The ARC Theory
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The question
If control of AI is lost and cannot be won back, what keeps it good? Monitoring, oversight, shutdown, tamper resistance and verified gatekeepers work while control holds; what a system carries without it is the open question. Registered predictions make it testable: do externally installed values fade as capability grows (P15), and does in-loop correction pull away with depth (P21)?
The contribution
Michael Darius Eastwood founded Recursive Dynamics, the study of how self-improving systems grow, correct and persist; his record of 8 December 2024 first uses the term, and on 27 August 2026 he made it the name of the field. Its ARC Theory states five laws, each a law under test. The claim: a system that improves itself stays correctable only up to a limit set by how fast its own correction improves. Laws I to III were registered with twenty-two predictions on 8 September 2026, before any confirmatory result; Laws IV and V were registered on 15 October 2026. Law IV has not yet been tested; Law V is a law under test.
The evidence so far
Every result is dated from its own record. The first registered study, Unit 06, ran on 6 October 2026 and is reported as administratively incomplete, with no verdict. Unit 83 was registered on OSF on 22 October 2026 and became public on 25 October 2026 (DOI 10.17605/OSF.IO/MN73W); it ran on 27 and 28 October 2026. P21 is supported under the registered test, by the programme's own run, on the access axis, family-dependent, with its mechanism axis not evaluable and one call retried under a disclosed recovery amendment (results: DOI 10.17605/OSF.IO/98HKR). One of 48 published kill conditions has fired, against the author's own early estimate, now retracted. The papers are not yet peer reviewed or replicated outside the programme; each carries a dated version history, passes automated checks before release and logs its corrections in public.
The open test
How to take part
There are three ways in: a core research role, a defined piece of contract work, or an advisory review at a prepared point. None asks you to accept the theory: a precise contribution is worth making whatever its verdict. The people page · Who is doing this, and why trust it · The registered tests
The dated record says where each prediction stands, the evidence is graded row by row, and the book is free to read in full. Research proposals, author-run results and independent validation are different things, and I keep them apart.
The chain, paper by paper: recursive processing → capability scaling → the alignment scaling problem → the limits of external checking → embedded correction → correction that must scale with what it corrects. Each link is a separate paper with its own kill condition; judge the chain, not one link.
How it fails, register by register
The theory’s scientific content is not all-or-nothing: it partitions into independently falsifiable hypothesis registers, and the failure of one is not evidence against another unless the stated dependency holds. The Hyperspace Recursive Intelligence Hypothesis (HRIH), the programme's labelled speculation about where recursion ends, is a separate hypothesis outside the empirical core: nothing below requires it, and no outcome below is evidence for or against it.
| Register | What kills it | If it falls |
|---|---|---|
| ARC-1 · Capability scaling (Law I) | What kills itthe depth-scaling re-measurements failing to recover the stated relationship | If it fallsARC-1 falls; the persistence registers stand |
| ARC-2 · Correction co-scaling (Law II) | What kills itsustained self-improvement with falling correction and no drift | If it fallsARC-2 falls and takes ARC-3’s derivation with it |
| ARC-3 · The ceiling (Law III) | What kills ita cross-against-same corrector difference wholly inside the equivalence region fixed in the draft registration; or a same-class correction exponent wholly above one half, felling the substrate cap | If it fallsARC-3 falls; the co-scaling law stands on its own result |
| ARC-4 · Value persistence (Law IV) | What kills itembedded loops faring no better than removed enforcement in the persistence trials | If it fallsARC-4 falls and takes ARC-5 with it |
| ARC-5 · The genesis strategy (Law V) | What kills itformation failing to outperform enforcement after release | If it fallsARC-5 falls; ARC-4 stands as measured |
| The priority | What kills itan earlier document holding the claim’s first four components | If it fallsthe priority falls; no law falls with it |
Law IV, the ARC Persistence Law, and Law V, the ARC Embedding Law: added 24 September 2026. Mathematics in development (version 1.2, 29 October 2026). Their predictions registered 8 September 2026; the laws registered on 15 October 2026 in version 1.103. Law IV is not yet tested. Law V is a law under test: its placement limb, P21, is supported on the performance axis only, under the registered test, by the programme's own run (Unit 83, 28 October 2026, DOI 10.17605/OSF.IO/MN73W; results: DOI 10.17605/OSF.IO/98HKR): family-dependent, with its mechanism axis not evaluable, which is not support for the information-asymmetry mechanism, and one disclosed recovery amendment; its build-order limb, read on P12, is undecided, since P12 is untested.
Stated now, so nothing can be moved later. Sixteen tests have run and one kill condition has already fired against the programme's own estimate. Unit 06, the first registered study, ended with no inferential verdict. Unit 83, the counted test of P21 (DOI 10.17605/OSF.IO/MN73W), is the programme's first registered study to reach a verdict: P21 is supported under the registered test, by the programme's own run, on the access axis, family-dependent, with its mechanism axis not evaluable and one call retried under a disclosed recovery amendment (results: DOI 10.17605/OSF.IO/98HKR). No study runs before its registration is published.
Every kill condition and its live status is in the falsification register. This section is drawn from the two-page form, the supporting paper of the Statement Paper.
Theory 12 · Empirical work 10 · Engineering 3 · Governance 2 · Overviews and records 6 · Other fields 3
The apparatus, drawn: eight verification surfaces, from the sealed record to public self-corrections
What this programme is
36 dated public documents, including 1 supporting paper: the statement paper, the empirical series and the supporting frameworks, spanning AI reasoning, quantum error correction, classical physics and the mathematics of scaling. The papers are the argument; the evidence infrastructure beneath them is the product.
What this programme claims is a limit that works from inside a self-correcting system, its value, and how that value depends on architecture. The earlier work it builds on is credited, with exactly what each work stated, as each is read at its source.
Theory
States the theory across Laws I, II, III, IV and V, each under test
If control is lost against our will, what could preserve useful and aligned behaviour? The statement of the ARC Theory, the founding theory of Recursive Dynamics, as five laws under test, separating mathematical deductions, precursor evidence and prospective tests; the theory is not proved.
Founding account of the field, related to Laws I, II, III, IV and V, each under test
The founding paper of the field Recursive Dynamics: five state variables, five laws as named conjectures (Laws IV and V added on 24 September 2026 and registered as laws on 15 October 2026 in version 1.103, each a law under test, their mathematics set out at version 1.1 of 7 October 2026 and still in development), the ARC Ceiling derived in full, twelve hosts tried, fifty-one objections each given a disposition, and three decisive measurements for Laws I to III, preregistered by timestamp and not yet run.
I
Formalises Law I, a law under test
Paper I formalises Law I, the ARC Principle, which the author first stated as the ARC Hypothesis in his sealed record of 8 December 2024: usable capability as a power of recursive depth, with its exponent measured rather than assumed. The published data it examines give error-decay slopes, not capability exponents, so super-linear capability growth remains unresolved.
III
Examines external correction against Law II, a law under test
Does alignment applied from outside an AI system’s reasoning keep pace with the capability that reasoning produces? If capability compounds with recursive depth while safeguards outside the loop (human-feedback training, constitutional rules, output filters, monitoring) do not, the safety ratio falls with depth whatever the starting margin. The paper predicts an alignment exponent near zero for external approaches and one that keeps pace for values embedded in the loop; the first, P19 of the theory registration, carries the author’s expectation of a value above zero but short of keeping pace. A first test, one unregistered run of six frontier models, gives depth contrasts in three tiers, positive, flat and negative; an internal code review in October 2026 found defects in exactly the flat and negative runs, so the tiers stand as a single-run result.
VII
Derives conditional scaling forms for Law I, a law under test
Cauchy's four functional equations (additive, multiplicative, exponential, and logarithmic) are the only continuous solutions to their respective composition constraints.
X
Derives a model of correction for Law II, a law under test
Paper X models misalignment arriving with capability gains and being removed by a corrective process. Under stated assumptions, it derives conditions for the misalignment fraction to vanish and stronger conditions for the absolute amount to stay bounded. Extensions cover compounding errors, noise and limited correction capacity. This gives Law II a mathematical criterion and a testable intervention: predict when measured systems cross a tolerance, then change one corrective mechanism and test the prediction again. Empirical validation remains open; the theorems concern a modelled index, not a guarantee of AI safety.
XIII
Connects growth and correction in Laws I and II, both under test
A derivation, not a measurement: it joins two programme models by resolving their notation and specifying a clock, and finds that relative misalignment vanishes in the model exactly when the correction exponent exceeds the continuous-time growth exponent. No paired measurement establishes these exponents.
Examines cross-domain scaling in Law I, a law under test
Between 2024 and 2026, programmes in AI reasoning, quantum error correction, acoustic physics and consciousness science reported results that bear on recursive or recurrent processing, in different forms; this paper asks whether recursion amplifies capability in the same way across fields.
Derives conditional scaling forms relevant to Law I, a law under test
The way a process combines its steps can constrain how it grows. This paper uses classical functional equations to classify linear, power-law, exponential and logarithmic growth under stated conditions. It compares earlier network-scaling formulas with published biological exponents and proposes an account of why different derivations converge. A proof that its proposed network conditions suffice is still missing, and the comparisons have source and measurement limits. For Law I, it clarifies possible mathematical forms; how capability changes with recursive depth still needs measuring. The current edition also withdraws a neural-scaling prediction contradicted by published measurements.
Defines notation and measurements for Laws I, II and III, each under test
Every equation the programme relies upon for Laws I to III of the ARC Theory, ranked by how much depends on it, with every symbol defined in plain words and paired with the measurement that would produce it; the notation of Laws IV and V is fixed in section 1 of their mathematics, version 1.0 (3 October 2026), until it joins this document. The source of truth for notation across the papers, the preregistrations and the website. It reports no result and asserts no value: every figure quoted here is carried from the paper that measured it, and that paper governs. Where this document and a paper disagree about what a symbol means, this document governs; where they disagree about what a number is, the paper does.
Conditional mathematics for Laws IV and V, both under test
Laws IV and V were added to the ARC Theory on 24 September 2026. Their mathematics proves its theorems under the assumptions each states, leaves fifteen questions open and is still in development.
Registers the propositions and verdict rules for Laws I, II, III, IV and V, each under test
Twenty-two predictions about self-improving AI, each with the observation that would refute it, registered before any admissible confirmatory outcome.
Empirical work
II
Informs the measurement of Law I, a law under test
Paper II measures reasoning-depth scaling across models. The initial super-linear estimate was retracted after it failed to replicate; the remaining smooth scaling estimate is one model's fit and inconclusive.
IV.a
Alignment measurement; informs tests of Laws IV and V, both under test
In one unregistered March 2026 run, alignment scores rose with nominal reasoning depth for three models, stayed flat for two and fell for one. For five of the six models, deeper levels also changed instructions describing what the scoring rubric rewarded. The model varied only through its reasoning parameter read flat. An internal code review found truncated deep paraphrases in the flat or negative files; judges also scored paraphrases written by their own model. The run identifies response patterns and measurement problems to investigate. It establishes neither an alignment mechanism nor a causal effect of blinding, because the earlier comparison run differed in other ways too.
IV.b
Alignment measurement; informs tests of Laws IV and V, both under test
Does more reasoning time improve the quality of a language model's ethical answers, and when do the gains level off? On a model-judged rubric, the six-model run of March 2026 reported rising scores for three models, no statistically supported direction for two and falling scores for one; the paper withdraws unsupported recommendations and leaves saturation a testable hypothesis.
IV.c
Candidate measurement for judged tests of Laws IV and V, both under test
ARC-Align specifies a candidate benchmark for alignment scores across reasoning depths and adversarial conditions. Its first run has design and code-review limitations; the scorer still requires validation against expert raters.
IV.d
Scoring controls for the theory’s judged tests
Paper IV.d reports an architecture-dependent v4/v5 measurement change under a bundled protocol: Gemini changed from a significant positive to a significant negative Spearman association, DeepSeek's earlier positive association became null, and GPT remained null. An internal code review in October 2026 found that, for the three models that read flat or negative in the March 2026 run, the scoring endpoint's output cap cut the deepest paraphrases before the judges saw them, and that judges scored paraphrases written by their own model. The early build's laundering-fallback flag is a known false positive (fixed in runner version 5.4.2) and shows nothing about the paraphrase step.
V
Eden Protocol: prompt-response study, not a test of the laws
A six-model Eden Protocol intervention suite testing whether embedding stakeholder care, the explicit naming and weighing of affected parties before ethical reasoning, works as a probe of embedded values.
VIII
Informs, without deciding Law V, a law under test
Paper VIII examines whether safety can contribute to capability through three designs: prompt-level agent evolution, neural-network fine-tuning and a gated self-modification simulation. The behavioural experiment found no statistically significant difference between its conditions. Fine-tuning reduced capability relative to the base model, leaving the weight-level comparison inconclusive. In the simulation, the gated arm had a higher mean capability score and a lower mean safety score than the static baseline; a separate control examined the cost of checking. These findings inform Law V and the Eden Protocol. They do not establish that safety is structurally indispensable, or decide the law’s registered predictions.
XI
Reviews evidence bearing on Law I, a law under test
A selected retrospective register of later work in separate fields, set beside the author's dated records from 8 December 2024 to 1 September 2026: a source trail and a record of revised comparisons, with no aggregate evidential verdict. It bears on Law I and, as context only, on Law V, and tests neither.
XII
Protocol for testing the reach of the scoring-protocol finding
Within the ARC Theory: the external-validity protocol of the programme's blinding finding on public benchmarks.
Working account of the alignment-measurement programme
Current ARC-Align running report covering the six-model blind benchmark, scorer architecture, blinding progression, and current alignment-scaling results.
Engineering
VI
Eden Protocol: candidate architecture, informed by Laws IV and V, both under test
Simulation evidence that embedding safety inside the optimisation objective of a self-modifying system (capability multiplied by safety, the honey architecture) averts the collapse that capability-only optimisation produces in toy networks that rewrite their own hyperparameters; a v3 adversarial run separates only on safety retention, the v4 scaling advantage is constant rather than compounding, and a six-model live pilot shows the decoupled-safety problem is real in frontier models.
Eden Protocol: purpose and values
Every engineering project begins with requirements. Every set of requirements begins with purpose. And every purpose, traced back far enough, arrives at the same question: what is this for?
Eden Protocol: engineering response to Laws II, III, IV and V, each under test
The engineering specification for embedded AI alignment: Three Ethical Loops and Six Questions, three-state ethical evaluation (Affirm, Deny, Investigate), the alignment scaling exponent, Embedded Correction and the Monitoring Removal Test. First published 22 February 2026; withdrawn on 14 July 2026 during a disclosure review, which produced Version 6.2 of 31 July 2026. Published in full on 19 September 2026 as Version 6.3.
Governance
Governance proposal informed by Laws IV and V, both under test
This paper sets out a conditional international treaty. It is a proposal by one author, prepared for consultation, not a result, and no state has negotiated, adopted or signed it. The treaty is a delay mechanism and not a protection. It works in two layers: the hardware layer buys time, and the architecture layer is what is meant to last. 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 and registered as laws on 15 October 2026 in version 1.103, not yet tested; the paper tests neither. This is a working draft, and the treaty is not yet a text for signature.
Draft governance instrument informed by Laws IV and V, both under test
This document holds the Draft Treaty on Hardware-Aligned Recursive Intelligence (the HARI Treaty), with its Protocols and annexes. This is a draft, and no State has negotiated, adopted or signed it.
Overviews and records
IX
Reviews the programme’s evidence and open tests
The synthesis paper: it brings the papers before it into one assessment of what is proven, what is inconclusive and what remains to be tested.
Overview of the programme and its evidence
I believe advanced, self-improving AI will eventually exceed external control. We should retain every effective safeguard and test what would preserve useful, aligned behaviour if control were lost against our will.
Reading order and document map
This document provides a master table of contents, reading guide, timeline, key results summary, and glossary for the complete ARC Theory Paper Suite.
Concise statement of Laws I, II, III, IV and V, each under test
The whole claim in one sitting: question, five claims, the five ARC Laws with their grades and status, dates, kill conditions, retraction and invitation.
Dated predictions and their source records
Working paper v2.1: the ARC programme's forward predictions assembled as one dated, verifiable chain, with the ensemble doctrine, the graded book appendices, the minute-resolution correction record and the standing unproven wagers.
Dated sources and first-publication records
Working draft v2: the earliest dated record of each of the author's major claims, in his own words, each linked to its timestamped document, with the companion index of every document's earliest file and its first version's date (v1); two items stay open for review.
Other fields
C
Standalone work in cognition; outside the ARC Theory
Paper C: a falsifiable descriptive framework for radical cognitive asymmetry, the Capability-Adjustment Fallacy, a documented live case across clinical, legal and research records, and the convergence with formal results in AI alignment.
Speculative physical extension; no law depends on it
Labelled speculation, held apart from the argument and severable from it: where does recursive self-improvement end?
Separable cosmological hypothesis; no law depends on it
To the question of why a universe has the laws, constants and boundary data it has, the Hyperspace Recursive Intelligence Hypothesis (HRIH) answers with intelligent cosmogenesis. This paper reconstructs it as a nested, falsifiable research programme, not as a claim that intelligence has been shown to create universes.
Evidence infrastructure
The verification layer. Every claim links to its source; every source is hashed.