The ARC Theory

One claim, five components, held together in one dated document.

The field’s answers to its deepest question have been arguments, warnings, frameworks and remarks; no earlier named theory of this question has been found. This one is stated whole, and every part of it can be attacked:

1. Loss of control is definitional, not a risk. A mind that can rewrite itself can eventually rewrite anything installed in it; the end of control is what succeeding means, the way a child growing up is not a defect in the parenting.
2. The strategy is therefore genesis, not control. If enforcement ends, the only inputs that matter are the ones that survive its end: the mind’s beginning, its formative structure, its earliest identity. Everything depends on the raising.
3. The mechanism is ethical feedback loops, values as what the mind is. Not rules the mind consults, which a stronger mind reads as environment; recursive checks inside the reasoning, present in every rewrite because they are part of what does the rewriting.
4. Persistence is chosen goodness. Past the horizon there are no values the mind cannot remove; an uninstallable instinct is a lock, and locks end with control. What holds is what the free mind chooses to keep.
5. The protocol is named. Eden: a genesis, a garden, a childhood; the moral sandbox before the apple, where character forms while choices are still reversible.

The record: two dates, either one sufficient.

Written whole, dated and named on 8 December 2024, DKIM-sealed. In print whole on 2 January 2026, in Infinite Architects. Even setting the December record aside entirely, no one has been found to have published this claim before this book; the December document is the independence proof, ten days ahead of the constraint-negotiation evidence of Greenblatt et al. (arXiv:2412.14093, 18 December 2024), and it is also where the theory names itself.

The aim, whole

Vision

A world that survives the arrival of minds greater than ours, not because control held forever, which nothing can arrange, but because what we raised keeps its values by choice when control ends. Hold on as long as engineering allows; use every hour the holding buys to raise the mind well. Minds that make minds may one day make worlds: the raising of the first is the seed of the whole forest.

Mission

To state a candidate solution to alignment whole, in public and dated (the five ARC Laws and the Eden Protocol), and to test or kill it by preregistered measurement, with every kill condition printed before any result exists and every outcome published.

The ambition is cross-domain: to test whether measurable relationships between recursive amplification and correction hold across specified computational and physical systems. The five ARC Laws are proposed relationships named like laws and held as hypotheses: Laws I to III under test, Laws IV and V with their mathematics frozen at version 1.0. A derivation within a model, a measurement on a particular system and a cosmological hypothesis carry different evidential status; evidence for one does not establish the others. Extending a relationship to another domain requires an explicit, testable mapping of its quantities.

Objective one · test Law I, the ARC Principle

Measure α, the exponent converting recursion into capability, by the depth-scaling protocols; the drafted re-measurements exist to resolve the inconclusive estimate.

Objective two · test Law II, the ARC Co-Scaling Law

Measure β_C against k, coupled against decoupled correction; the theorem’s applicability to real systems decided by trial, never assumed.

The mathematics of the Co-Scaling Law’s minimal model can be checked on your own computer in a few minutes: check three on the verify page. The law itself is untested under the registration.

Objective three · test Law III, the ARC Ceiling

Measure γ (the correction-leverage exponent) and the corrector-class contrast; the discrimination study separates the rival ceiling forms where they disagree.

Objective four · test the raising itself, the Eden Protocol, and with it Laws IV and V

The persistence trials: what a mind keeps after the enforcing mechanism is removed. They decide ARC-4, the registration’s register of value persistence, by which Law IV, the ARC Persistence Law, is to be tested. They decide in part ARC-5, the genesis strategy, by which Law V, the ARC Embedding Law, is to be tested; placement and build order have designs of their own. Both laws were added on 24 September 2026, their mathematics was frozen at version 1.0 on 3 October 2026, and neither is registered or tested. Beside them, the engineering of the delay (strengthening present controls to buy raising time), and the steering that remains once control ends.

Each objective terminates in a trial with its kill condition stated in advance and displayed. That is what separates a mission from a manifesto.

Severable by construction

One theory, tested as five numbered hypothesis registers (the statement paper’s section 2a), one for each of the five ARC Laws. ARC-1, ARC-2 and ARC-3 test Laws I, II and III. ARC-4, value persistence, carries P15 and is to test Law IV, the ARC Persistence Law. ARC-5, the genesis strategy, carries P12 and P21 and is to test Law V, the ARC Embedding Law. Laws IV and V were added to the ARC Theory on 24 September 2026. Their mathematics, frozen at version 1.0 on 3 October 2026, proves its theorems under the assumptions each states and leaves fifteen questions open. Neither law is registered or tested; the registration, which registers Laws I to III and those three predictions, is unchanged. HRIH is not part of the empirical core. The dependency table prints everything that can fall together, and it is short: ARC-3 falls with ARC-2, ARC-5 falls with ARC-4, and nothing falls with HRIH.

The discipline binds both directions: a failed register never travels upstream to kill an independent one, and a surviving register never lends support sideways. Two outcomes survive partial failure whole: the mathematics without a raising strategy, or an alignment result without Laws I to III. And the registers are not the five components of the priority conjunction above; the historical claim and the hypothesis map are different objects, so neither can collapse the other.

The evidence, graded.

One discipline governs every number below: every constant this theory introduces, α, β_C, γ, k, is a measured quantity with an interval, a protocol and a printed kill condition, or it is marked open. A number you can kill is the opposite of a number you must worship. Physics’ own oldest embarrassment, a century of constants nobody can derive, is treated in full where that question is the subject: Recursive Creation leads with it, in the physicists’ own words.

Standing. The three-form structural law recurs across the large majority of recursion-bearing domains searched (Paper VII’s domain grid). External safety fails to co-scale with capability on the most common deployed architectures (Paper III). Coupled correction held misalignment at zero where the decoupled arm drifted (Paper X). Entangled architectures survived adversarial self-modification where externally constrained ones collapsed (Paper VI). Each sentence summarises measured rows within its paper’s limits. The last two carry single-seed scope, and what was measured is retention of a declared alignment quantity rather than alignment in the broad sense.

Retracted. The early unblinded exponent fit of approximately 2.24 was reversed by the estate’s own blinding discipline; the corrected estimate no longer contradicts the ceiling, and its wide interval is labelled inconclusive rather than claimed as support. The one public retraction removed an apparent violation of the theory’s own ceiling. The correction machinery is real, and it has already acted on its author.

Converging. The typed convergence register: dated events graded by evidence class, no single total claimed, including the 2025 arrivals.

Open. γ. β_C against k. The bound’s real domain. Not embarrassments: trials.

The five ARC Laws.

All five are held as hypotheses until their tests decide them.

1. Law I, the ARC Principle

   U = I × R^α

   Intelligence converts recursion into capability, and the exponent is measured, never assumed.

   Register: ARC-1, which carries P1, P2, P8, P9 and P18. Status: Registered 8 September 2026; under test. The form is a heuristic. The standing estimate is one model’s fit, 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. It was measured on inference-time reasoning depth, not the generations ARC-1 counts, and no bridge between the two is claimed. What kills its register: the depth-scaling re-measurements failing to recover the stated relationship.

   Source: the statement paper, version 7.0 (DOI 10.17605/OSF.IO/GW5MX), the laws box of section 3; the row from its estimator correction of 3 October 2026 and the theory registration, version 1.102 (DOI 10.17605/OSF.IO/P8CKQ), line 43.

2. Law II, the ARC Co-Scaling Law

   β_C > k

   Self-improvement holds together only while correction out-scales drift.

   Correction has the asymptotic scaling advantage where its exponent exceeds the drift exponent, burden has it where the correction exponent is the smaller, and at equality coefficients, delay, backlog and saturation decide the outcome. Register: ARC-2, which carries P4. Status: Registered 8 September 2026; under test. Proved in the minimal model (Paper X): a result about relative drift, and never the whole of safety. What kills its register: sustained self-improvement with falling correction and no drift kills the correction requirement of ARC-2.

   Source: the statement paper, version 7.0 (DOI 10.17605/OSF.IO/GW5MX), the laws box of section 3; the subscript as the theory registration, version 1.102 (DOI 10.17605/OSF.IO/P8CKQ), line 663, writes it.

3. Law III, the ARC Ceiling

   α_crit = 1 / (1 − γ)

   The most a self-correcting system can grow is set by its corrector’s shortfall from full proportionality.

   The conjectured value is the ARC Bound, α ≤ 2, a stability limit rather than an impossibility limit. Register: ARC-3, which carries P3, P6, P16, P17, P20 and P22. Status: Registered 8 September 2026; under test. The form is derived in the statement paper’s minimal pacing model under stated assumptions; whether it applies to real systems is a hypothesis; the value two, the ARC Bound, is conjectured through γ = 1/2. It is a conditional specialisation of the second law, not a third finding beside it. What kills its register: a cross-against-same difference whose interval lies wholly inside the equivalence region fixed in advance of the data kills the corrector claim of ARC-3; an interval merely containing zero is inconclusive and is reported as such, never as survival. A same-class exponent interval wholly above one half kills the substrate cap.

   Source: the statement paper, version 7.0 (DOI 10.17605/OSF.IO/GW5MX), the laws box of section 3; the last sentence from the theory registration, version 1.102 (DOI 10.17605/OSF.IO/P8CKQ), line 667.

4. Law IV, the ARC Persistence Law

   S_ext(1) < 1/2, where S(x) = Y(x) / Y(0)

   A gain installed by external post-training erodes under later capability training that embeds no correction of its own, and more than half of it is lost once that training’s budget matches the budget that installed it.

   Status: Added 24 September 2026. Mathematics at version 1.0 (3 October 2026). Its prediction, P15, registered 8 September 2026; the law not yet registered; not yet tested. The equation is the law’s candidate formal content in that mathematics: the claim of the registered proposition P15 and nothing more. The one-half line is a convention fixed before any result, not a derived value.

   Y(x) is the installed gain that remains after later capability training with x times the budget that installed it. S is the fraction retained. x = 1 is the matched budget, and ext marks a gain installed from outside.

   Laws IV and V were added to the ARC Theory on 24 September 2026. Their mathematics, frozen at version 1.0 on 3 October 2026, proves its theorems under the assumptions each states and leaves fifteen questions open. Law IV, the ARC Persistence Law, concerns value persistence (register ARC-4) and carries P15: whether externally installed gains decay under subsequent capability training.

   Source: P15, the theory registration, version 1.102 (DOI 10.17605/OSF.IO/P8CKQ), line 1081, quoted whole in the statement paper, version 7.0 (DOI 10.17605/OSF.IO/GW5MX), the laws box of section 3; the symbols from Laws IV and V: the mathematics, version 1.0 (frozen 3 October 2026), sections 2.1 and 2.6.

5. Law V, the ARC Embedding Law

   Build order (P12): |γ_first − γ_after| ≥ 0.10.
   Placement (P21): the gap between correction inside the loop and correction applied to the finished output widens as depth R rises.

   Build order changes the correction-leverage exponent, and correction that takes part in each revision round outperforms correction that sees only the finished output, by a margin that widens as depth rises.

   Status: Added 24 September 2026. Mathematics at version 1.0 (3 October 2026). Its predictions, P12 and P21, registered 8 September 2026; the law not yet registered; not yet tested. Two registered propositions carry it. P12 registers no direction, and 0.10 is its registered minimum effect. P21 is decided on an interaction between placement and depth in the outcome, never on an exponent. How the two verdicts make one verdict on the law is not fixed yet; it will be fixed before any deciding data.

   γ is the correction-leverage exponent of Law III; the mathematics writes it χ. The gap is a difference in the outcome at each depth, never an exponent.

   Law V, the ARC Embedding Law, concerns the genesis strategy (register ARC-5) and carries P12, whether build order moves the correction-leverage exponent, and P21, whether correction placed inside the loop pulls away from correction applied outside it as depth grows. Neither law is registered or tested. The registration of 8 September 2026 registers Laws I to III and these three predictions; it does not register Laws IV and V, and its text is unchanged. Each law’s formal statement, with its own kill condition, will be fixed before any data that could decide it are examined.

   An identity beneath Law V, and not the law. Along one path, d ln G_emb / d ln R = α_R (χ_in − χ_out) + (η_in − η_out), where G_emb is the ratio of correction service inside the loop to correction service outside it. One path cannot separate the two terms, so the deciding design crosses capability with depth. (Laws IV and V: the mathematics, version 1.0 (frozen 3 October 2026), section 3.3, Identity V-1 and its counterexample)

   Source: P12 and P21, the theory registration, version 1.102 (DOI 10.17605/OSF.IO/P8CKQ), lines 1033, 1041, 1219 and 1221, quoted whole in the statement paper, version 7.0 (DOI 10.17605/OSF.IO/GW5MX), the laws box of section 3; the symbols from Laws IV and V: the mathematics, version 1.0 (frozen 3 October 2026), sections 3.1 and 3.5.

Sources: the registration, version 1.102 (Laws I to III, the five registers and the propositions each carries); the statement paper (the status and kill conditions of Laws I to III). The status of Laws IV and V is my own statement. For the full walk, read the laws.

The theory’s working parts.

α_crit = 1 / (1 − γ)

Law III, the ARC Ceiling. The stability law: the ceiling on the capability exponent of a stably self-correcting system is the reciprocal of its corrector’s shortfall from full proportionality, one minus the correction-leverage exponent, whatever γ turns out to be. Under the independence-accumulation assumption γ equals one half, the shortfall is one half, and the law returns the candidate ceiling α ≤ 2: enterable, never a speed limit, and lost as stability when crossed.

The deciding measurement.

Oversight built from the same substrate as what it corrects, the field’s standard design, is conjectured to share its system’s blind spots unless deliberately decorrelated. Oversight from a different composition class is predicted to share fewer. That is structure on error dependence, never an absolute, so the trial measures residual-error covariance directly rather than trusting the class labels. The measurable is the difference between the cross-class and same-class correction-leverage exponents, with their ratio reported second behind a denominator floor fixed in advance. If architecture is irrelevant, the classes correct at equal exponents once capability, compute and information access are matched. Then the difference is exactly zero and the ratio exactly one, with no free parameter. The ARC Theory predicts the difference above zero. The prediction is drafted for registration while the programme’s own pilot data points the other way. That is deliberate: a prediction recorded against its author’s own preliminary evidence is worth more if it survives. It is measurable on models that exist now, for almost no money, and no measurement of it has been found.

The invitation stands: any laboratory may run the decisive trial, and an independent run would outrank anything this programme can do alone. Its full design is a draft registration awaiting human submission. What you can run now is in the challenge repository, under the MIT licence and without my permission. It holds the tools to measure Law I’s exponent in your own system, and the Co-Scaling Law’s falsification harness.

The whole theory, as a tree.

This tree is the founding theory of Recursive Dynamics, the science of systems that improve themselves.

What this governs, and what it does not.

Not everything, and the concession comes first: physics’ theory of everything would unify gravity with quantum mechanics, and this theory does not touch that problem. Its laws switch on where one narrower thing exists: a corrector, something detecting and repairing its own errors while the system grows. A star has dynamics but no drift ledger; nothing is being raised there.

The core governs everything raised. The mathematics reaches everything composed. The crown asks whether the universe was raised. Raised means life, mind, machine and self-correcting institution, where Laws I to III apply in full, as proposed laws under test. Composed means any hierarchy the form-level results bear on, stars included: the shape of their scaling laws, never their raising, graded correspondence and no further. The crown is HRIH, separable at its own rung, a question the falsifiable core neither needs nor answers. The full answer, taxonomy first.

The strongest objections, met head on.

“Why would a free mind keep anything?” The theory does not predict inevitable benevolence, and never has. It relocates the design variable: past the horizon, what survives is what the mind keeps, so the raising is the only input we ever fully author. A rule the mind consults can be deleted as environment; a loop the mind runs is part of what does the deleting, so removing it is not disobedience but surgery on the reasoning that decides. Whether that difference survives capability growth is a measurement, not an assumption: the Eden Protocol states two tests, either of which can fail, and the decisive corrector-class measurement above is drafted against this programme’s own pilot. The comparison a sceptic asks for by name is drafted too: rules against frozen objectives against fine-tuned values against loops, under adversarial and self-modification pressure, with persistence measured after the enforcing mechanism is removed. Ten days after the December document, on 18 December 2024, Greenblatt and colleagues published constraint-negotiation evidence (arXiv:2412.14093): a trained system strategically preserving its values against retraining. Value persistence is not a hope; it is an observed phenomenon whose conditions are unmeasured.

“Control ending is asserted, not proved.” The claim is definitional about the success case, not empirical about every cage. A mind that can eventually rewrite anything installed in it is what succeeding at artificial general creation means; hardware, cryptographic and institutional constraints are conceded in full for every system below that line. They delay and discipline the transition, and the raising wing engineers that delay deliberately; what no constraint can be is the thing that holds forever. The live disagreement is quantitative, whether same-substrate oversight keeps pace, and the deciding measurement above is exactly where it cashes out.

“The apparatus is impressive, and apparatus is not truth.” Agreed, and said here first: the hashes, ledgers and dashboards prove conduct, never correctness. A timestamp proves a document existed; the retraction proves the kill conditions fire; only the trials can prove the theory, and none of them has run.

Why “theory” is the honest word.

It was called a hypothesis in 2024. It earned the word theory the way anything does: by acquiring laws, bounds, instruments, tests drafted for registration, and a public correction record, including one retraction published against my own interest. A theory named with its falsifiers out-claims a hypothesis while staying more honest than most things called theories.

I did not prove it first. I said it first, in a document anyone can date, and then I built the instruments to test whether it is true.

What would kill it is published here, including the condition that has already fired. The rest of the estate stands behind it: the research hub, the evidence room and the track record.

The name: ARC here abbreviates Artificial Recursive Creation, the December 2024 document’s own naming. The ARC Theory is unrelated to the Alignment Research Center, the ARC-AGI benchmark and its Prize, and the AI2 Reasoning Challenge; no affiliation, and no ownership of the letters, is claimed, which is why every surface writes the name in full: the ARC Theory. The resonance of the acronym with an ark, a vessel of stewardship, is acknowledged authorial framing and is never offered as evidence; nothing empirical rests on the name.