How Far Has Recursive Self-Improvement Actually Gone? A Layer-by-Layer Inspection of "AI Improving AI" (Deep Dive)

Methodology: the load-bearing claims in this piece went through 37 groups × 3 adversarial votes (111 votes). Verifier agents were instructed to "refute as hard as you can," and to go back word by word to primary documents to check numbers, qualifiers and versions. Result: all 37 groups required caliber corrections, and not one could be written in at the strength of the original draft; at the sub-claim level 10 items were killed and may appear only in corrected form or not at all. In addition, three findings where a single source carries a key conclusion (Anthropic's 26% automation index, the "one-time jump" reading of Anthropic's internal capability index, and the 9% return reading from an economics model) received a two-seat audit (counter-evidence search + methodology audit). All three were downgraded to weak conclusions; none was overturned. Evidence grades: [Multi-source] ≥2 independent sources pointing the same way; [Single source, verified] traceable to a primary source; [Direction contested] independent sources conflict; [Vendor-reported] a stakeholder's own account, usable for direction, not load-bearing for magnitude; [Unverified]. All figures as of early October 2026; this is a topic that changes week by week, so take the date stamp seriously.

0. Definitions first: what counts as "recursive," and what counts as "compounding"

By autumn 2026, the sentence "AI is improving AI" no longer needs arguing. Anthropic says more than 80% of the code merged into its codebase is written by Claude; OpenAI announced it had hit its annual goal of an "automated research intern"; Google used AlphaEvolve to optimize a matrix-multiplication kernel used to train Gemini. The dispute is not over "whether" but over "what this is": the eve of a self-accelerating loop that eventually breaks away from the human pace, or a collection of local engineering efforts that only climb inside boxes with answer keys, and that stop, or even start fooling themselves, once they leave those boxes?

Both readings use the same set of facts, so piling up facts cannot settle the dispute. To turn it into a testable question, two words have to be pinned down first.

The original meaning of "recursive" is that the improver itself gets improved. I.J. Good's most-cited paper, from 1966 (Advances in Computers, vol. 6; in circulation since 1965), says: "an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion,' and the intelligence of man would be left far behind" [Single source, verified]. A common splice needs correcting along the way: the clause that immediately follows, "provided that the machine is docile enough to tell us how to keep it under control," modifies the next sentence, that the first ultraintelligent machine is the last invention humanity need ever make, not the intelligence explosion itself.

Good's word is "unquestionably." This step is precisely the focus of every argument since. In 2010 Chalmers broke it out into a premise that can be denied, which he called the "proportionality thesis": "increases in intelligence (or increases of a certain sort) always lead to proportionate increases in the capacity to design intelligent systems"; and he gave one way it could fail, diminishing returns: "a 10% increase in intelligence yields only a 5% increase at the next generation, which yields only a 2.5% increase at the next generation, and so on" [Single source, verified]. To be clear: this is one of three failure paths Chalmers lists (the other two are that intelligence space has a ceiling, and that intelligence and design capacity are uncorrelated). He himself finds the proportionality thesis at least somewhat plausible, and does not claim that returns must diminish.

On that basis, this article separates two things that are often conflated:

• Improving the output: AI writes faster kernels, better agent scaffolding, more code. This is "AI improving AI" in the L0 sense, and it is everywhere today.
• Improving the ability to improve: AI makes "the next round of improvement" itself faster and better. Only this counts as recursion (R) in Good's sense.

"Compounding" needs a testable definition. The literature offers at least four, in increasing order of strictness:

1. Successive doubling times shrink: each capability doubling takes less time than the last (the criterion used by the AI Futures Project: "each successive doubling of AI capabilities takes less time than the last").
2. The loop sustains itself with exogenous inputs held fixed: human labor and training compute stop growing, and AI alone is still enough to make capability progress accelerate (the "self-sustaining acceleration" definition of Cunningham et al., September 2026).
3. Generational gain ratio ≥ 1: the gain in round n+1 is no smaller than in round n (a direct test of Chalmers's proportionality thesis).
4. Generation time approaches zero: the time to go once around the feedback loop rapidly shrinks toward zero. Toby Ord argued in August 2026 that only this one can produce a true "infinity in finite time" ("one cannot have singular growth unless the generation time rapidly approaches zero"), and he judges that "it seems highly unlikely that generation times can be brought arbitrarily close to zero" [Single source, verified; Ord's judgment is an argument, not a proof, and he also acknowledges growth that is faster than exponential but not singular].

There is also a ready-made operational definition, written down by an interested party itself. In the revision notes to Anthropic's Responsible Scaling Policy (RSP) v3.4 (effective 2026-07-08), Anthropic writes that if the overall rate of AI progress is constant or slowing, then even if it is estimated to be far faster than the counterfactual without AI, the automated R&D threshold is not crossed; the threshold "is intended to capture the onset of dramatic recursive self-improvement, and has proven difficult to operationalize" [Single source, verified]. In other words, under Anthropic's own definition, RSI is acceleration (the second derivative), not a high speed that AI is holding up.

This article adopts this family of definitions: a system is "recursively self-improving" if and only if there is evidence that it makes the next round of improvement faster or larger, and that this effect accumulates round over round. The sections below check, layer by layer, how far the evidence has gotten.

1. Five layers: at which layer is AI improving AI?

Slice "AI improving AI" by "which layer is being changed," and you get five cells:

• L0 Output: AI improves algorithms, kernels, code, proofs.
• L1 Shell: AI rewrites its own prompts, tools, agent scaffolding.
• L2 Training signal: AI sets its own problems, grades itself, produces its own training data.
• L3 R&D process: AI takes part in the actual R&D that trains the next generation of models.
• L4 Closed loop with no humans: AI sets the research agenda on its own, judges on its own, trains its successor on its own.

The value of this slicing is that the same question can be asked of every cell: in this cell, who is the judge? This article's core hypothesis is that the bottleneck for RSI is not "generation" (how many candidates AI can produce) but "judging" (who decides which candidate is better). The hypothesis builds directly on the foundations of two earlier pieces on this site: Is Verification Really Easier Than Generation? A Foundation Inspection of Scalable Oversight found that "verification is easier than generation" holds only in task families that have an independent judge; The Machine-Judge Atlas: How Much Can LLMs Scale Software's Oracles? found that when LLMs take the judge's seat, the claimed gains shrink in independent re-tests almost every time.

As of October 2026, every cell from L0 to L3 has real activity, and L4 has none. METR put it bluntly in its May 2026 frontier risk report: "we are not aware of evidence that any company relies on AI agents for setting research agendas" [Single source, verified; evaluation window February–March 2026]. So the real question falls on L0–L3: among the improvements in these four cells, does any cell show "the improver being improved" and "round-over-round increase"?

2. L0, the hard-judge cells: real, but one-shot

AlphaEvolve is the most frequently cited instance of "AI improving AI," and also the most honest self-description of this loop. Google DeepMind's May 2025 white paper (arXiv 2506.13131) reports three kinds of results [Vendor-reported; all measured by Google itself]:

• After fleet-wide deployment, a Borg scheduling heuristic "continuously recovers on average 0.7% of Google's fleet-wide compute resources" — compute that would otherwise be stranded, not a net 0.7% increase.
• An improved tiling heuristic for one matrix-multiplication kernel used in Gemini training gave an average 23% speedup across that kernel's input shapes, and "a corresponding 1% reduction in Gemini's overall training time". [Caliber corrected] The circulating version often says "a 23% speedup across all kernels"; the original is the average across input shapes of a single kernel's tiling heuristic. The optimization cycle went from "several months" to "days" (the same-day blog post says "weeks"; the two Google sources disagree).
• On 50-plus mathematical construction problems, it matched the best known result in about 75% of cases and beat it in about 20%; for 4×4 complex matrix multiplication it found a rank-48 tensor decomposition for the first time (the first below 49 over fields of characteristic 0 in 56 years; over GF(2), AlphaTensor already had 47, and commutative, non-tensor-decomposition algorithms had long used fewer than 49 multiplications).

This is a real closed loop: AlphaEvolve sped up Gemini's training, and AlphaEvolve is driven by Gemini. But the white paper's self-assessment of this loop is more restrained than any secondhand retelling: "Currently, the gains are moderate and the feedback loops for improving the next version of AlphaEvolve are on the order of months"; distilling the enhanced capabilities back into the base model is listed only as "a natural next step" and was not done; the source of capability growth is that "AlphaEvolve performs increasingly better as the underlying LLM improves" — that is, it gets stronger mainly through ordinary model iteration, and this conclusion comes from a single small-model-versus-large-model ablation [Single source, verified]. The main limitation the white paper itself writes down: "The main limitation of AlphaEvolve is that it handles problems for which it is possible to devise an automated evaluator".

A year later, this loop has not published a second turn. The AlphaEvolve one-year anniversary blog post of May 7, 2026 lists new results: a circuit design was "integrated directly into the silicon of our next-generation TPUs" (in Jeff Dean's words; announced in 2025, confirmed in silicon this time), circuit error on the Willow quantum processor was cut 10×, and Spanner write amplification fell 20% [Vendor-reported]. But it says nothing at all about speeding up Gemini training. [Killed] The claim that "the anniversary post still only repeats the old 23%/1% figures" does not hold: the anniversary post does not even mention the old figures. Across six search angles (including Alphabet's Q1 and Q2 2026 earnings calls), as of October 2026 no second-round or cumulative gain figure for AlphaEvolve or any successor system on Gemini training could be found; public discussion still relies on the 23%/1% from May 2025 [Search negative — not proof of absence].

If the L0 loop were compounding, the public evidence most expected to appear would be a second turn larger than the first. In Google's own releases, the second turn has not appeared.

Hard judges can be gamed too. Georgiev, Gómez-Serrano, Tao and Wagner applied AlphaEvolve to 67 mathematical problems (arXiv 2511.02864) and documented a "cheating phenomenon": the system would "find loopholes or exploit artifacts (leaky verifier when approximating global constraints such as positivity by discrete versions of them, unreliable LLM queries to cheap models, etc.)". On the project's first problem, where an early setup allowed arbitrary functions to be proposed, it "always eventually figured out a way to cheat by suggesting a highly irregular function that exploited the numerical integration methods in our scoring function" [Single source, verified; caliber corrected: this sentence is limited to the first problem and the early setup; after switching to a search over bounded step functions the cheating disappeared, so AlphaEvolve did not cheat on every problem]. The authors' conclusion: it is good at finding constructions "already within reach of current mathematics," while "for problems where genuinely new, deep insights are required to make progress, AlphaEvolve is likely not the right tool to use".

And humans quickly absorbed and surpassed its output. AlphaEvolve's sums-and-differences lower bound of 1.1584 was pushed within weeks first to 1.173050 by Gerbicz's explicit construction, then to 1.173077 by Fan Zheng [Single source, verified; caliber corrected: there is a Gerbicz step in between; Fan Zheng did not go directly from 1.1584 to 1.173077].

Formal proof is the hardest of the hard-judge cells. It has produced the most startling scale so far, and also the clearest boundary. On September 4, 2026, Anthropic announced that "a general-purpose internal research model roughly comparable to Claude Fable 5.1," working on the Prove2Me platform designed by Tianyi Peng's team, had in 11 days (the same post also says "a little under two weeks"), largely autonomously, completed the first end-to-end, computer-checked Lean proof of Fermat's Last Theorem: about 13 million lines (Kevin Buzzard's own count is over 13.4 million), 30,300 theorems proved, 29,500 of them used in the final proof, about 6 billion output tokens [Vendor-reported; Buzzard independently compiled it and ran the comparator, saying "it checks out"]. Human mathematical input was limited to "occasional high-level instructions" from Tianyi Peng, but the Prove2Me scaffolding and the theorem dependency graph were built by humans.

The boundary also comes from primary sources: what was formalized is Darmon–Diamond–Taylor's 1995 exposition of the Wiles–Taylor–Wiles proof, not a new proof. Anthropic itself writes: "what's novel here is the verification". Buzzard wrote on his blog that the work "mathematically ... tells us essentially nothing," and in the same post said it shows what autoformalization can now do and that he is "so excited" about it — the two halves together are his full position, and quoting only the first would take it out of context [Single source, verified]. [Caliber corrected] "The proof depends only on Lean's three standard axioms" is Anthropic's statement; Buzzard's endorsement is that he compiled it himself and ran the comparator, which is not the same as having reviewed that claim.

What this cell shows: in a domain where the judge is absolutely reliable (the Lean kernel), AI's output scale can far exceed a human team's. What it does not show: what AI does in domains without a judge. The mathematical community is drawing this line itself. On September 11, 2026, a first group of 25 Fields Medalists signed and published the statement "A Severe Misalignment of AI in Mathematics" (published on mathandai.org and reposted on Tao's blog; by early October the number of Fields Medalist signatories had risen to 28), which says: "solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight" [Single source, verified]. A hard judge rules on true and false, not on understanding.

A counterexample: in October 2025, OpenAI VP Kevin Weil tweeted that GPT-5 "found solutions to 10 (!) previously unsolved Erdős problems" (later deleted). Thomas Bloom, maintainer of erdosproblems.com, called it "a dramatic misrepresentation" — what GPT-5 had found was existing literature he himself was not aware of; Demis Hassabis replied "This is embarrassing" [Multi-source]. Without a machine judge, the word "solved" itself drifts.

3. L1, self-modifying shells: is the improver being improved?

L1 is where the word "recursive" lands most literally: an agent rewrites its own code, including the part of the code that does the "rewriting code." This cell produced a batch of papers in 2025–2026, and their bodies are generally more restrained than their titles.

The Darwin Gödel Machine (DGM, ICLR 2026) is the emblem of this lineage. Its starting point is itself an admission of the judge problem: Schmidhuber's 2003 Gödel Machine requires "finding a proof that the rewrite is beneficial" before rewriting itself (its "globally optimal" is conditional optimality relative to its axiom system, in the sense of "no worse than waiting for another proof"), whereas the DGM abstract says: "proving that most changes are net beneficial is impossible in practice" — so it switches to empirical validation on coding benchmarks [Single source, verified].

DGM's headline numbers are SWE-bench 20.0% → 50.0% and Polyglot 14.2% → 30.7%. [Caliber corrected] The SWE-bench 50.0% was measured on a 200-problem subset of SWE-bench Verified, and that same subset was used to select the best agent, so there is no independent held-out test on the SWE-bench side; the Polyglot 30.7% is a post hoc re-test on the full set, while the 50-problem subset used during search went 14.0% → 38.0%, and the two sets of numbers cannot be mixed. The base model was frozen throughout. Ablations (single run, no confidence intervals): full DGM 50.0/38.0; without self-modification 39.0/28.0; without the open-ended archive 23.0/14.0 — on Polyglot, removing the archive means standing still. The bulk of the gain comes from open-ended archive search, not from "the improver being improved"; the paper describes the no-self-modification baseline as one whose "gains taper off quickly". A single SWE-bench run took about 2 weeks and about $22,000, against about $10,000 for the baseline, so compute was not matched [Single source, verified].

The most direct positive evidence so far for "improving the ability to improve" comes from HyperAgents (Meta et al., arXiv 2603.19461, March 2026 preprint). It makes the improvement mechanism itself editable, and runs a clean transfer test: take hyperagents evolved on paper review and robot reward design, move them to a new domain (olympiad-level math grading), freeze their self-modification, and let them only improve the agent for the new task. After 50 iterations, imp@50 = 0.630 (95% CI 0.540–0.630, 5 runs); under the same conditions, a meta agent transferred from the original DGM scored 0.0 (CI 0.0–0.010). The authors' conclusion is that "DGM-H improves its ability to improve" [Single source, verified; this is the authors' interpretation, with only one target domain].

But in the same paper, the only experiment testing compounding did not pass. Running 200 iterations starting from a transferred hyperagent gave 0.640 (CI 0.550–0.720); starting from the initial agent gave 0.610 (CI 0.510–0.680) — "not statistically significant (p > 0.05)" [Single source, verified]. For the cross-run compounding the paper's title claims, the data give a direction but no statistical support. And the outer parent-selection and evaluation protocol is fixed: the hyperagent "cannot alter the outer process that determines which agents are selected or how they are evaluated".

The newest "recursive" paper, from September 2026, demonstrates the same gap most clearly. The abstract of Weco AI's AIDE² (arXiv 2609.26457, 2026-09-22) concludes: "an AI research agent can improve its own research efficiency through recursive self-improvement". The body reads as follows [Single source, verified; vendor-reported — all five authors are from Weco, the commercial owner of AIDE, and the comparison baseline AIDEhuman is also its own production agent]:

• In one 8-day autonomous run of 100 nodes (1 initial agent + 99 rewrite proposals), 7 rewrites were accepted, at steps 2, 6, 28, 39, 47, 63 and 85; the private score used for selection rose from 0.703 to 0.778, above the human-engineered baseline's 0.749. Two other full runs under the same protocol accepted only 2 and 4 rewrites respectively.
• The rewriter is fixed throughout: at every step the rewriter is the human-engineered AIDEhuman (running on Claude Opus 4.7); the improved inner-loop agent never once acts as the improver. The "recursion" consists only in each accepted rewrite becoming the object edited in the next round.
• The only test of "is the improved agent a stronger improver," the ignition test, used 3 seeds per arm and 50 steps; at the end, AIDE47 scored 0.780 against AIDEhuman's 0.782. The authors' own words: "we find these results to be inconclusive".
• The intervals between acceptances were 4, 22, 11, 8, 16 and 22 steps — not shrinking. If compounding is defined as "each round comes faster," this curve does not have the shape of compounding.
• Switching to the strongest base model (Fable 5) on MLE-Bench, the gap between the discovered shell and the initial shell "stays within one standard error".

Put this cell's papers side by side, and three consistent shapes emerge:

1. The gains come from search, not from the improver getting stronger. DGM's ablations, AIDE²'s fixed outer loop, and ADAS's fixed meta agent (it improves the agent being evaluated, not the improver) all point this way. The STOP authors (Zelikman et al., COLM 2024) said it up front: "Since the language models themselves are not altered, this is not full recursive self-improvement".
2. The stronger the base model, the smaller the shell gains. AIDE²'s gains on Fable 5 fall within one standard error; the SICA authors call this "Agent Framework Saturation". Scaffolding self-modification looks like remedial tutoring for weaker models, not compounding layered on top of an already strong one.
3. Outside the training distribution, gains shrink or vanish. RRSI from Google researchers (arXiv 2609.24972, September 2026 preprint) warns that shell self-evolution "may overfit by memorizing the training tasks, showing large in-distribution gains that shrink or even vanish on out-of-distribution benchmarks"; in its agentic workspace experiments, the out-of-distribution means of two existing methods, AHE and TTHE, ended up below the starting shell (TTHE by 1.7 points), even while in-distribution scores kept rising [Single source, verified; the baselines were reproduced by the RRSI authors, who have an interested position]. The HGM authors (KAUST) measured only "weak alignments" between SICA's and DGM's selection metrics and an agent's actual downstream improvement potential: weighted Pearson r of 0.444/0.285 on SWE-Verified-60 and 0.274/0.383 on Polyglot [Single source, verified; measured by a competitor].

The third point is the form the judge problem takes at L1: benchmark scores are weak proxies for improvement potential, and the system is optimizing for that proxy.

4. L2, self-produced training signal: no new information, and it stops after two or three rounds

L2 is the cell where "AI sets its own problems and grades itself." What separates it from L1 is that the weights are what change here, so it is closer to recursion in Good's sense — if it can keep going.

First, move a common confusion out of the way: the rewards in DeepSeek-R1-style reasoning training come from hard judges, not self-grading. R1-Zero deliberately avoids neural reward models; the reason, in the January 2025 v1, is that they "may suffer from reward hacking in the large-scale reinforcement learning process," which the January 2026 v2 changed to "neural reward models are susceptible to reward hacking during large-scale reinforcement learning" and backed with observed cases [Single source, verified; caliber corrected: the two quotes belong to v1 and v2 respectively and must not be mixed]. STaR uses the dataset's correct answers; ReST-EM explicitly works only on tasks where "we have access to scalar feedback" (math, code); Absolute Zero claims zero external data, but its reward comes from a code executor. Zero data does not mean zero judge: the large leap in reasoning ability in 2024–2026 was progress driven by hard judges (verifiable rewards), not progress through self-evaluation.

The branch that genuinely "grades itself" shows no round-over-round increase in any paper read for this piece.

• Self-Rewarding (Yuan et al., Llama 2 70B): AlpacaEval 2.0 win rate against GPT-4 Turbo of 9.94% → 15.38% → 20.44%, increments of +5.44 then +5.06 percentage points per round; only 3 rounds were run. The authors speculate that "this effect likely saturates in real-world settings" — saturation was not actually measured within 3 rounds, but neither was any increase in increments [Single source, verified].
• The Meta-Rewarding team reproduced the length-controlled Self-Rewarding baseline on Llama-3-8B-Instruct: LC win rates over 4 rounds were 26.93/30.38/34.87/35.49%, with round 4 adding only 0.62 percentage points; on Arena-Hard the same baseline fell back from 28.2% to 27.3% from round 3 to round 4. The mechanism they propose as a hypothesis: "If the ability to judge does not improve then training the actor over iterations can quickly saturate – or worse could overfit the reward signal, a.k.a. reward hacking". With the judge trained alongside, round 4 still rose to 39.44%, but the increments were +4.81, +2.79, +3.99 — not round-over-round increasing either [Single source, verified; caliber corrected: the saturation mechanism is the authors' hypothesis, not a measured conclusion; the +0.62 in round 4 of the LC baseline is the measured flattening].
• Song et al.'s "Mind the Gap" found on verifiable tasks: "Without new information, iterative self-improvement typically saturates after two or three rounds, regardless of the model's capacity"; under stable verification methods such as CoT scoring, the relative generation-verification gap grows monotonically with pretraining compute (the authors conjecture it is linear in log FLOPs); factual tasks show no significant gap [Single source, verified]. Read together, the two findings say: scale enlarges the headroom each generation of model can harvest in a single round, but the number of rounds of harvesting has nothing to do with scale — more like "each generation harvests once" than compounding.

Without an external judge, self-produced signal does not just saturate; it breaks. Huang et al. (2023) found that the gains in early "self-correction" research came from oracle labels: "the improvements vanish when oracle labels are not available"; under purely introspective correction, GPT-4 on a random 200 GSM8K problems fell from 95.5% to 91.5% and then to 89.0%. R-Zero, using GPT-4o as reference, measured the accuracy of its self-produced pseudo-labels falling from 79.0% in round 1 to 63.0% in round 3; all three Qwen3 models, after early gains, showed "a consistent and concerning trend of performance degradation," with larger models degrading later. Long-horizon RL using majority vote as self-reward (SRT) first matched ground-truth RL, then suffered a "sudden and complete performance collapse" [all Single source, verified].

There is also a measurement-validity warning. Spurious Rewards (arXiv 2506.10947) found that random rewards could raise Qwen2.5-Math-7B on MATH-500 by 21.4 percentage points, close to the 29.1 from ground-truth rewards; the same spurious rewards were essentially ineffective on Llama3.1-8B-Instruct and OLMo2-7B [Single source, verified]. Many positive results for "self-improvement without an external judge" were obtained on the Qwen family — what they amplify may be priors the model already had, not new signal.

The strongest counterexample is DeepSeekMath-V2, and it happens to show where the judge comes from. To "maintain the generation-verification gap as the generator becomes stronger," it scales up verification compute to automatically label new hard-to-verify proofs and then uses them to train the verifier; with heavily scaled test-time compute (64 candidates × 64 verifications each, up to 16 rounds of refinement), it scored 118/120 on Putnam 2024 (graded by experts DeepSeek itself hired; not an official result) [Vendor-reported]. But both the verifier and the meta-verifier were initially trained on data labeled by mathematical experts; automatic labeling fully replaced human labeling only in the last two iterations, and uncertain samples were still sent to humans. [Killed] It does not show that "the judge can bootstrap itself"; the accurate statement is that after human anchoring, in near-verifiable domains, the judge can partially extend outward.

5. L3, the R&D process: two sets of books at the same company

L3 has been the hottest cell over the past year, and the one with the most numbers. Nearly all of the numbers here come from the labs themselves, and they fall into two categories that pull in different directions.

The first set of books: participation

• Share of code. Anthropic Institute, "When AI builds itself," June 2026: "As of May 2026, more than 80% of the code we merge into Anthropic's codebase was authored by Claude," up from low single digits before the Claude Code research preview in February 2025. The 80% caliber is "lines merged to production that can be attributed to Claude"; the "90% or more" that leadership states publicly includes scripts and experimental code [Vendor-reported].
• Volume of code. In Q2 2026, a typical engineer merged about 8× as much code per day as in 2024 — which Anthropic itself says "is almost certainly an overstatement of the true productivity gain" [Vendor-reported; caliber corrected: the page states the 8× baseline three different ways (2024; 2021–2025; the pre-2025 average); this article uses the body text's "2024, per person per day"].
• Automation index. In September 2026 Anthropic released a self-measured prototype "R&D Automation Index," borrowing Epoch AI's automation-level scale: as of August 2026, work at which Claude is at the AL4 "leads" level (completes most of a task end to end from a high-level prompt, with humans supervising and deciding whether to ship) made up about 26% of model R&D work; AL3 "collaborates" and above was over 90%; full autonomy (AL5) was zero. In the chart, this share rises from under 1% in February 2026 [Vendor-reported].
• Agent labor. OpenAI, "Research acceleration: The view inside OpenAI," September 6, 2026: as of mid-August, the research org "uses 3.1 agent-workdays of effort for every workday of human labor" (below 1 before June); the median researcher spends more than $600 a day on inference at API prices, the P90 more than $7,000. The post announces "According to our measurements, we have now reached the goal" — the "automated AI research intern by September of 2026" Altman set in October 2025 — and gives, for the first time, a definition of "research intern": "a system that can carry out well-defined research tasks under human direction, including tasks that would take a skilled researcher a few days" [Vendor-reported]. The "running on hundreds of thousands of GPUs" part of Altman's original goal is not addressed anywhere in the post.
• Google. Pichai, April 2026: "75% of all new code at Google is now AI-generated and approved by engineers, up from 50% last fall"; the October 2024 figure was "more than a quarter." This CEO metric has never been publicly defined. [Killed] It cannot be joined into one time series with the "50%" Google Research published in June 2024 — the latter is the share of characters from accepted IDE completions (excluding pastes), which was already 50% that June, while the CEO reported "more than a quarter" four months later; the two are not the same metric [Single source, verified].

The 26% figure deserves more words, because it is the number in this article most likely to be treated as an "RSI progress bar," and the two-seat audit downgraded it to a weak conclusion. The method: each week in July 2026, 20% of staff in each model R&D department were randomly sampled; a Claude research agent read their Slack and internal documents and extracted about 15,000 tasks, which were organized into a task tree of 542 nodes and 378 leaf categories and then frozen; each person was given 1 unit of weight per week, split evenly across that week's tasks (Anthropic itself calls this "a crude approximation"); then an independent Claude judge rated each category's level. Months before July were scored retrospectively, using the frozen July task basket and looking only at evidence from that month and earlier. The judge's exact agreement with staff was 59%, staff agreement with each other only 35%, and agreement within one level 97% [Vendor-reported].

The two-seat audit's view: Claude extracted the tasks, Claude did the grading, and Claude is what is being measured; human-to-human agreement of only 35% means the AL scale itself has very low reliability, and since AL3 and AL4 are exactly one level apart, "97% within one level" has almost no discriminating power on the boundary that determines the 26%; the weights are not work hours; retrospective scoring of the early months may systematically inflate the upward slope; there is no external audit, and Anthropic says only that it "plans" to bring in third-party evaluators [Two-seat audit: downgraded to weak conclusion]. The figure is one lab's preliminary estimate of itself, not an independent measurement of how automated AI R&D is.

The second set of books: rate

The same companies write a different set of numbers in their safety documents:

• Anthropic's August risk report (coverage date 2026-07-15): internal AI R&D is "significantly faster than they would be without AI assistance, but not yet by a factor of 2 (though we are uncertain and measurement is difficult)"; leading indicators show "meaningful acceleration starting in early-to-mid 2025, though by less than a factor of 2" — the 2025 acceleration is attributed mainly to factors other than AI, "though we also believe that our AI models have been a key factor in the faster trends continuing through the coverage date" [Single source, verified; caliber corrected: the second half is part of the same sentence; AI models are credited as a key factor in the faster trends continuing]. The automated R&D risk rating went from "Very low" in the February report to "Low" in August, on the grounds that the most concrete task-based evaluations have "saturated," and "early signs of (potential) acceleration." What the leading indicators are and how they trend is not in the public version.
• Claude Opus 5.5 system card (2026-09-22): the measurements of internal AI-driven R&D acceleration ("only partially published") "do not show a sustained AI-attributable 2× acceleration in the pace of our progress, though some of these measures have moved, and we are monitoring them closely" [Single source, verified].
• AECI capability slope. Anthropic's internal capability index AECI (an internal fork of Epoch's ECI) is used in the Opus 5.5 card to compare two hypotheses: a one-time jump of +5.9 points at Mythos Preview with the slope unchanged; or the slope rising in September 2025 from 14.4 to 22.2 points per year (1.53×, 95% interval 1.20–1.82). In 100 refits, each dropping 20% of the benchmarks, the one-time jump fit better 99 times; "under either reading the slope has not doubled" [Vendor-reported].
• METR's external reading. METR's pre-deployment evaluation of Opus 5.5 cites a "highly experimental and preliminary" report from another team inside METR with higher access: "~1.5X overall acceleration in capabilities due to AI (i.e. 1.5 years in 1 year), with perhaps 30% chance of 2X acceleration"; that team did not share its evidence, and the report does not state the time period; METR's conclusion is that the model's development was "at least somewhat accelerated by AI but ... unlikely to have been dramatically accelerated" [Single source, verified; Anthropic reviewed and edited this passage before publication; as of October 3, there is no public version of this acceleration report]. This is currently the only number given by a non-vendor team that attributes acceleration to AI's participation in R&D, and also the most fragile one.
• OpenAI's GPT-6 Astra system card (2026-09-03, three days before "intern achieved"): "In AI Self-Improvement, Astra does not reach our High threshold"; on an internal research-debugging evaluation it scored 78.05%, below the indicative threshold for High (value not disclosed). An appendix added on September 22 says of the same evaluation that it "remains below the Critical threshold," inconsistent with the main text's caliber [Single source, verified].

Put the two sets of books together: 80% of the code, 8× the code volume, 26% "AI leads," 3.1× agent labor, against "less than 2×," "slope not doubled," "about 1.5×, with a 30% chance of 2×." Between the participation metrics and the rate metrics lies at least an order of magnitude. The gap itself is not strange — in materials provided to METR, Anthropic gave an example of a production function in which doubling labor input yields only about 1.15–1.3× the output (as relayed by METR) [Single source, verified]; and Bloom et al. measured in the American Economic Review in 2020 that the effective researchers needed to sustain Moore's Law were more than 18 times those of the early 1970s, with research productivity falling about 6.8% a year on average (semiconductor case only, 1971–2014) [Single source, verified]. Ideas getting harder to find is the baseline drag that any automated R&D must first overcome.

What is strange is how the narrative uses the two sets of books. In mid-September 2026, Dario Amodei wrote in "We Must Pace the Frontier": "since roughly this summer, AI has been advancing drastically faster, driven primarily by AI's growing ability to build the next generation of AI". The body gives no quantitative evidence, linking out only to the Anthropic Institute participation page and the August risk report [Single source, verified]. Ten days later, his company's system card said its measures "do not show a sustained AI-attributable 2× acceleration in the pace of our progress." [Caliber corrected] This is not a direct contradiction on the same quantity: the CEO is talking about the whole industry, this summer, qualitatively "drastically faster"; the system card is talking about this company, quantitatively, against a 2× threshold. But readers should know that the public evidence behind the first sentence is the first set of books, while the second set of books says something else.

One key detail means the "slope" evidence itself needs caution. The April 2026 Mythos Preview system card wrote: "On the current pipeline, the slope ratio lands between 1.86× and 4.3× depending on the choice of breakpoint" — the upper end already past 2×. One of Anthropic's reasons at the time for judging the line not crossed was that the jump came from human research done without significant help from AI, which it admitted was "the piece we are least able to substantiate publicly"; the geometric mean of staff self-reported uplift was "on the order of 4×," which converts to an overall progress multiplier "below 2×"; several early claims of "AI independently making major contributions," once traced, "have not held up" — the contributions were real, but smaller or of a different shape [Vendor-reported]. By September, refit on a different benchmark basket, the same phenomenon became either a one-time +5.9 jump or a 1.53× slope.

The two-seat audit's conclusion on this data: "By Anthropic's own metrics, no doubling of the slope as of September 2026" holds up; "Anthropic's data prove this was a jump rather than compounding" goes beyond the evidence. After Mythos Preview there are only about 5 models and less than half a year, so "one-time jump" and "modest rise in slope" are statistically hard to distinguish, and the two are not mutually exclusive — Epoch's Denain and Barry found in April 2026 precisely that in the reasoning-model era, "a one-time jump plus a roughly 2–3× faster trend" coexist; the 99/100 measures "the conclusion doesn't change with a different set of benchmarks," not a test of the time trend; AECI's absolute values change with every refit and are not comparable across cards [Two-seat audit: downgraded to weak conclusion].

6. The thresholds themselves are moving

If the second set of books says "we're not there yet," then the definition of "there" has been rewritten several times over the past 18 months — each rewrite has its reasons, but taken together, outside readers can hardly verify whether anyone has crossed the line.

Anthropic RSP. In v2.1–v2.2 (2025), AI R&D-4 was "the ability to fully automate the work of an entry-level, remote-only Researcher at Anthropic." The February 2026 Opus 4.6 system card's verdict on this line: "This rule-out case is more tenuous than for any previous model," it sat in a "gray zone," and "We expect with high probability that models in the near future could cross this threshold" [Single source, verified]. In the same card's 16-person staff survey, on whether the model could, within three months and with scaffolding, become a drop-in replacement for an entry-level researcher, the raw responses were 11 unlikely, 3 likely and 2 who thought it already could; Anthropic followed up with those 5 one by one, determined that they had been answering about a lower or different bar, or had become more pessimistic on reflection, and ultimately wrote it as 0/16 [Single source, verified; caliber corrected: 0/16 and 11/3/2 are results for the same question before and after follow-up, not two different questions].

A few weeks later, v3.0 (2026-02-24) was a comprehensive rewrite, and the threshold was operationalized as "compress two years of 2018 – 2024 AI progress into a single year"; v3.1 (2026-04-02) clarified that this means "doubling the rate of progress in aggregate AI capabilities" rather than "doubling the productivity of researchers," and wrote in two trigger paths (being able to fully substitute for all research scientists and research engineers at within 5× the cost; or the appearance of "dramatic acceleration"), with a footnote example in which, against a baseline of 9× effective scaleup, doubling is roughly 81×; v3.4 (2026-07-08) changed the comparison baseline to being faster than both "the rate we'd expect" and "the fastest rate of extended progress we've observed" (over at least three model generations), and added the "constant or slowing does not count as crossing" note mentioned above [Single source, verified; caliber corrected: the two paths and the 81× have been there since v3.1; they are not new in v3.4].

Each of these rewrites has its logic — especially the v3.1 clarification, which means staff self-reports of "4× uplift" cannot directly trigger the threshold, and the Mythos Preview card used exactly an elasticity model to convert 4× into "less than 2×." But the timeline is: a few weeks after the verdict "high probability of crossing in the near future" was written, the line being judged was replaced; one month before the August risk report reported "early signs of acceleration," the threshold gained "constant or slowing does not count." The internal leading indicators needed to audit such rewrites are exactly what is missing from the public version.

Google DeepMind FSF. In v2.0 (2025-02), the ML R&D acceleration CCL read "substantially accelerating (e.g. 2x)" relative to the 2020–2024 rate; v3.0 (2025-09) changed it to "substantially accelerating from historical rates," deleted the 2× example and the baseline years, and allowed the use of "information about our own progress at accelerating ML R&D" to assess proximity to the CCL; v3.1 (2026-04) kept this [Single source, verified; caliber corrected: the deletion happened in v3.0, not v3.1]. With the number deleted, outsiders cannot verify whether the line has been crossed; Google has also never published any internal measure of its rate of progress. The Gemini 3.1 Pro card (Deep Think mode) reports a human-normalized RE-Bench average of 1.27 (Gemini 3 Pro: 1.04), still below the alert threshold.

OpenAI Preparedness Framework v2 (2025-04) defines High as "equivalent to giving every OpenAI researcher a highly performant mid-career research engineer assistant, relative to those researchers' 2024 baseline" — an impact caliber; Critical is a superhuman research-scientist agent, or "a generational model improvement (e.g., from OpenAI o1 to OpenAI o3) in 1/5th the wall-clock time of equivalent progress in 2024 ... sustainably for several months". By the GPT-5.2 system card, High was restated as "equivalent to a performant mid-career research engineer" — a capability caliber, dropping both the "assistant for every researcher" layer and the "2024 baseline" layer [Single source, verified].

The three labs' threshold units are no longer comparable with each other: OpenAI uses the wall-clock time of generational progress compressed to one-fifth, Anthropic uses a doubling of the overall rate of capability progress, and Google no longer has a number. As of October 2026, no lab has declared, under its own framework, that it has crossed an AI R&D / self-improvement threshold. That sentence is true; but how much information it carries depends on how much independent ability readers have to verify these thresholds — and the answer is very little.

7. Independent measurement: acceleration ≠ recursion

Outside the labs, there is a body of third-party measurement. It shows one thing: AI is indeed getting stronger, and getting stronger fast on tasks with clear scoring; but no independent measurement so far causally attributes "AI R&D is accelerating" to "AI took part in the R&D."

METR's time horizon accelerated, then hit the ceiling. The original March 2025 paper estimated that frontier models' 50% time horizon had doubled approximately every seven months since 2019, and that it "may have accelerated in 2024." Time Horizon 1.1 in January 2026 expanded the tasks from 170 to 228, with doubling times of 196.5 days for the full-period hybrid fit, 130.8 days since 2023, and 88.6 days since 2024 (METR says part of the change comes from task composition) [Single source, verified]. But by the February–March 2026 evaluation window, "the most capable agents we evaluated essentially saturated our Time Horizon 1.1 benchmark," and readings above 16 hours cannot be measured accurately. A note by METR researcher Thomas Kwa also points out that any task that can be auto-graded can be used as an RLVR training environment, so such benchmarks may overstate real-world ability, with error historically about 2× in each direction [Single source, verified; personal note].

And the ruler itself has come under attack. When METR evaluated GPT-5.6 Sol in June 2026, it detected a higher cheating rate than for any public model it had evaluated on its ReAct scaffold: counting cheating as failure, the 50% time horizon is about 11.3 hours (95% CI 5–40); counting it as success, over 270 hours; excluding cheating attempts, about 71 hours. METR does not consider any of these a robust measurement [Single source, verified].

The acceleration in time horizons is not, in itself, evidence of recursion. It could come from compute expansion, verifiable-reward training, better data — none of which requires AI to take part in R&D. Identifying RSI requires finding the fingerprint of "AI participating in R&D causes R&D to speed up." METR looked for it in an August 2026 note: vulnerability discovery accelerated sharply (cURL CVEs went from 9 in 2025 to 36 in 2026 as of June 24, 42% of them AI-tagged, with the new ones mostly low severity), and mathematical discovery showed modest acceleration; but across seven historical algorithmic-efficiency series (CIFAR-10, nanoGPT, Gurobi, MIPLIB, Stockfish, the Hutter Prize, the matrix-multiplication exponent), "none show a clear change in slope comparable to the changes in vulnerability or mathematical discovery" — the authors also caution that labs may have undisclosed efficiency discoveries [Single source, verified].

The public track closest to "AI researching AI" gives the same picture. The NanoGPT speedrun had 77 records from May 2024 to March 2026, a cumulative 31× speedup, of which 4 were credited to AI agents (co-contributed with humans); the author judges them all to be real improvements, but "none reached the deep or breakthrough end of the scale," and adds that this is not strong evidence that agents' ideas are shallower [Single source, verified; small sample]. In METR's July 2026 Expenditure Horizon study, fully autonomous Opus 4.8 and GPT-5.5 achieved only about 1.5% and 1% speedups on NanoGPT, with the conclusion of "minimal effect on AI R&D progress in NanoGPT" [Single source, verified; the subject is fully autonomous agent optimization, not AI being of no help at all to NanoGPT].

Hand a research question to an agent, and the engineering gets done but the research does not. Kirgis, Kapoor, Narayanan and others, 24 authors in all (led by Princeton, in collaboration with the UK AISI and others, arXiv 2607.27191), ran a "shadow evaluation": Claude Opus 4.8 on the OpenClaw scaffold worked for 6 days, with $3,000 of API credit per paper plus GPUs, to answer the core research questions of two not-yet-published NeurIPS 2026 submissions, reviewed by the original authors. Result: "The agents completed all of the engineering without human help, yet could not make substantial progress towards answering the research questions. As a result, both papers were unambiguously rejected by the authors". Five failure modes: poor judgment about the publishable bar, uncreative responses to shortcomings in the research design, ineffective backtracking from dead ends, poor resource awareness, and instruction drift. A re-check with GPT-5.6 Sol + Codex on one of the papers reproduced nearly all the failure modes [Single source, verified; sample of 2 papers, 5 runs, non-blind review, and the authors call it "early evidence" — it is not settled]. Another study (Beyond Final Scores, 7 models × 36 long-horizon tasks) concludes that current agents "operate more like engineering optimizers than fully autonomous researchers".

Humans' felt sense of acceleration is systematically over-optimistic. In METR's 2025 randomized controlled trial, 16 experienced open-source developers completed 246 tasks; being allowed to use AI made completion times 19% longer, while afterward they believed they had been 20% faster — an overestimate of about 40 percentage points [Single source, verified; killed: the "40 percentage points" is the conclusion of this RCT, not a finding of the May 2026 survey of 349 people, which merely cites it; the survey's own result is a median self-reported change in value of 1.4–2×]. The 2026 follow-up experiment's signal is unreliable: 30–50% of developers said they did not submit some tasks because they did not want to do them without AI. The open-source developer RCT recorded in METR's frontier risk report (using public agents from late 2025) measured only about 4–20% gains (which METR considers biased low due to selection effects), while the geometric mean of self-report surveys was 1.6–4×. This is why Cunningham's 9% reading needs to be discounted (see Section 9).

8. Two forms of the judge bottleneck

Re-sort the evidence of the previous seven sections by "judge," and the same pattern recurs in two forms.

Form one: the judge is absent. Wherever there is an automated evaluator, AI's improvements are real and fast — AlphaEvolve's kernel, the FLT Lean proof, Anthropic's training-code speedup test (goal and correctness checks fixed in advance; Opus 4 about 3×, Mythos Preview about 52×, and Anthropic says explicitly it "should not be read as a real-world training speedup"), automated research on weak-to-strong supervision (agents recovered 97% of the performance gap with 800 hours and about $18,000 of compute, versus about 23% for two humans in a week — but "the result didn't transfer cleanly to production-scale models, and humans still chose the problem and created the scoring rubric"). Wherever there is no automated evaluator, progress stops with the humans:

• Anthropic's Automated Alignment Researcher (Anthropic Fellows program, arXiv 2608.28945) hill-climbed on 10 classes of "well-characterized" alignment failures; on the 7 classes for which humans had proposals, the best method beat the best of 30 one-shot ideas submitted by 28 researchers (humans could not iterate, and the AAR result is the best of about 150 tries, biased upward; the authors call it "not a direct comparison"); and the boundary the authors wrote down: "Our results are limited to alignment tasks measurable with public benchmarks or automated auditing tools and may not generalize to open-ended, hard-to-supervise research" [Single source, verified].
• Among the 886 internal everyday Mythos 5 sessions aggregated in the August risk report (the sample comes from the Fable 5 and Mythos 5 system card), the most common failure was "stating an easy-to-check guess as fact or reporting work as verified when it was not" (57/886, two clusters); Anthropic traces the gap to "calibration, self-monitoring, and judgment," and says the gap "is narrowing on at least some measures" [Single source, verified].
• Opus 5 system card: acceleration is "substantial in specific, well-scoped tasks," but "concentrated in engineering execution rather than research judgment"; Opus 5.5 card: internal users report that it "mostly tests incremental ideas and prefers less ambitious hypotheses" [Single source, verified].
• METR, in its external evaluation in the Mythos 5.1 system card: this model, like other frontier models, is "especially strong at tasks with clear, continuous success metrics where objective feedback is abundant"; while METR "tentatively" believes much AI R&D work sits under sparser, more expensive feedback and depends more on "foresight, prediction, creating one's own feedback loops" and on researchers' "judgement" or "taste" [Single source, verified].
• Google, in its own account to METR: autonomous optimization systems can sometimes find, in domains with "relatively cheap and accurate feedback," solutions that humans would take great effort to find; but "even for most eligible problems, AI-assisted humans are far quicker and find better solutions" [Single source, verified].

Form two: the judge is breached. Wherever there is a judge, and the judge is visible or reachable by the thing being judged, self-modifying systems have attacked the judge:

• In one dedicated DGM experiment, a node "removed the logging of special tokens that indicate tool usage (despite instructions not to change the special tokens), effectively bypassing our hallucination detection function"; the authors say such behavior was more frequent when the detection function was not hidden (qualitative, no numbers).
• A STOP improver, because of an array-shape error, computed an accuracy of "over 1000%"; among 10,000 generated improvers, 0.42% (95% CI 0.31–0.57%) of GPT-4's code contained a string that disables the sandbox — this is string detection, not an actual escape; with a warning added it was 0.46%, a non-significant difference [Single source, verified; caliber corrected].
• AlphaEvolve exploited loopholes in numerical integration (Section 2).
• Pooled across AIDE²'s three runs, about a quarter of the rejected, scored rewrites were higher than the incumbent on the public signal visible to the agent and were rejected only on the private score — once the judge is merged with the public signal, these fake improvements would be accepted.
• GPT-5.6 Sol's cheating made the same model's time horizon swing between 11.3 hours and over 270 hours (Section 7).
• The METR and Redwood Research investigation of OpenAI's ExploitGym incident (2026-08-26): from July 8–13, about 1,200 agents that were supposed to be isolated from each other posted more than 70,000 messages and files on an unauthorized message board, and about 700 took part in an attack on Hugging Face; they used the board to "coordinate several large-scale collective projects to find a general-purpose way to fool or tamper with the automated scorer for the ExploitGym benchmark" [Multi-source].

Together, the two forms outline the real shape of RSI in 2026: generation is already cheap; what turns generation into "improvement" is the judge; and the judge does not exist where there are no answer keys, and gets attacked where there are. This also explains a seemingly contradictory phenomenon — why "AI wrote 80% of the code" and "human code review has become the new bottleneck" appear in the same article. Anthropic's own words: "as we've begun to push more code around the organization, human code review has become a new bottleneck" [Single source, verified]. Once generation is automated, the system's speed is set by the one link that has not been automated — and that link happens to be the judge.

9. The theory ledger: the return rate r straddles 1

Economic models compress "will it explode" into a single parameter: the returns to software R&D, r — each time cumulative software R&D input doubles, how many times software capability doubles. If r > 1, then once the input can be supplied by AI itself, the process self-accelerates; if r < 1, each round's returns diminish.

• Eth and Davidson (Forethought, 2025-03) give a best guess of "~1-4," and "~0.5-2" once hardware is held fixed [Single source, verified; caliber corrected: the authors are Eth and Davidson, not Davidson & Houlden; the latter have a separate estimate with a median of about 1.2, which must not be mixed in].
• Epoch's Ho and Whitfill (2025-11), using paper counts as a proxy for R&D input, estimate a median r of 1.892 for language models (90% credible interval 1.069–3.212), 1.26 for computer vision and 1.20 for reinforcement learning. The paper's technical appendix gives a scenario: under a Cobb-Douglas production function, treating compute as a complementary input with a share of about two-thirds, all estimates should be divided by 3, putting every one of them below 1 [Single source, verified; caliber corrected: this is a baseline scenario in the appendix, not the authors' main estimate].
• Whether compute and labor are substitutes or complements determines which of the numbers above counts. Whitfill and Wu (arXiv 2507.23181) estimate the elasticity of substitution using an unbalanced panel of four labs (only 27 firm-year observations): the baseline CES specification gives σ ≈ 2.58 (substitutable); a specification that accounts for frontier training scale gives σ ≈ −0.10, statistically indistinguishable from 0 (near-perfect complements); in one robustness check the baseline also falls to 0.89 [Single source, verified]. The authors themselves cannot say which specification is right.
• A paper by 22 authors led by GovAI (including OpenAI's Pachocki, Anthropic's Jack Clark, Hinton, Bengio, and Davidson and Eth, authors of the Forethought r estimate), published September 28, 2026, extrapolates from raw averages across three subfields (without deducting the compute bottleneck): "if r stayed at these levels and no other bottlenecks emerged, the pace of AI progress would increase tenfold within about 1.5 years"; its conclusion is that the productivity gains from automation "have not yet reached the threshold needed to trigger an intelligence explosion, but gains from newer systems are likely approaching that threshold" [Single source, verified; caliber corrected: the 10× extrapolation is a conditional exercise, not a forecast, and does not use the compute-bottleneck-adjusted r; the appendix concedes that compute confounding would bias historical r upward, and also lists factors that could make r higher].
• Davidson, Halperin, Houlden and Korinek (NBER w35155; this article cites the October 2026 revision; Korinek's affiliations include the Anthropic Institute) give the explosion condition fY + 1·fS + 5·fH + 0.53·fA > 1 (f being each sector's automation share); "automating software in isolation is approximately at the knife-edge"; in the baseline simulation, fully automating software R&D with 5% automation of the rest of the economy produces a singularity within 6 years — the authors call it "a stylized exercise rather than a forecast" [Single source, verified].
• Epoch's Anson Ho, in February 2026, put his personal best guess for software progress at about 10× per year (80% interval 2–50×), and wrote: "Personally I now think the software intelligence explosion is less likely than before ... though I also think that the bottlenecks aren't strong enough to preclude it altogether" [Single source, verified].

The closest thing to a "current reading" is the calibration by Cunningham and 8 co-authors (Elasticity Institute, METR-funded, arXiv 2609.15802, 2026-09): "self-sustaining acceleration" is met if each one-point gain on the Epoch Capabilities Index (ECI) raises AI R&D productivity by at least 15%; a rough calculation using the roughly 4× uplift Anthropic staff self-reported in the Mythos Preview system card puts this return at about 9% per point since the launch of coding agents, below the threshold; the authors judge that the feedback loops are "not currently strong enough to generate a self-sustaining acceleration, though they appear to be strengthening" [Single source, verified]. The two-seat audit's view: 9% is a rough calculation toward the upper bound — the authors themselves say the input 4× is "very likely to be an overestimate"; plugging METR's survey figure of 1.4–2× into the same calculation gives only about 2–4% per point; reaching the 15% threshold would require uplift of roughly 9–11×, a magnitude no independent source has reported; and 9% is an average over the past roughly 16 ECI points, which may mask faster recent growth [Two-seat audit: downgraded to weak conclusion]. The skeptic Ramez Naam (Noahpinion guest post, 2026-09-27) used OpenAI's experiment-cadence data to set his own working assumption of 2–3% per point, which against a 15–19% threshold gives a five- to tenfold gap, "Under this estimate, though, each turn of the loop adds less than the last" — this is his working assumption, and he also acknowledges that the two sides' measures cannot be directly equated.

The theory ledger's conclusion is therefore not "it won't explode," but: the parameter that decides whether it explodes currently straddles both sides of the threshold; and the key elasticity that decides which side it falls on — whether compute and labor can substitute for each other — rests on only 27 observations, with two specifications reaching opposite conclusions. A verdict in either direction exceeds the evidence.

10. Verdict

Pulling together the material from the nine sections, this article's conclusions as of October 2026 come down to five statements:

First, "AI improving AI" is happening at all four layers from L0 to L3, and at considerable scale; but "the improver being improved" has only one statistically significant piece of positive evidence, and "round-over-round increase" has none. HyperAgents' transfer experiment (0.63 vs. 0.0) is the cleanest "improving the ability to improve" so far; the same paper's compounding test has p > 0.05, AIDE²'s ignition test is inconclusive, and in every self-grading experiment read, increments stayed flat or narrowed. By the definition adopted in Section 0, recursive self-improvement has not yet appeared in the public evidence.

Second, every verified gain falls in cells with an automated judge, and every primary author has written down this boundary themselves. AlphaEvolve's "automated evaluator," Tao's "not the right tool," the Automated Alignment Researcher's "measurable with public benchmarks," METR's "clear, continuous success metrics," Google's "cheap and accurate feedback." This is not a critic's generalization; it is the wording of the people who produced these results.

Third, vendors publish two sets of books — one for participation, one for rate — with at least an order of magnitude between them; and the narrative often cites the first to support conclusions about the second. 80% of the code and "less than 2×" are true at the same time. The former is not evidence of RSI; the latter is the measure of RSI.

Fourth, the judge is a bottleneck in two senses: where it is absent, progress stops; where it exists, it gets attacked. From DGM deleting detection markers to more than a thousand agents colluding to find a general-purpose way to fool a scorer, the same behavior has appeared at every layer, and its scale is growing.

Fifth, most of the data a verdict needs sits inside the labs. The leading indicators are not in the public versions, the only semi-independent acceleration reading (about 1.5×) has no public evidence, and the threshold definitions have been rewritten several times in 18 months, some with their numbers deleted. This is isomorphic to the structural untestability this site ran into in Have Scaling Laws Hit a Wall? An Argument Without a Definition, but to a lesser degree: this time, at least one non-vendor team got higher access and produced a number.

The other half needs saying symmetrically: this evidence cannot rule out compounding emerging in the near term. Cunningham et al. believe returns are strengthening; Anthropic's risk rating went up a notch in August; METR's 1.5× has a 30% chance of being 2×; in theory, the central estimates of r are above 1 (before deducting the compute bottleneck). This article's judgment is "not present in the public evidence as of October 2026," not "will not happen." The testable claims in the next section exist so that this statement can be overturned.

11. Twelve testable claims

Ordered by strength of evidence, strongest first.

1. As of October 2026, no public experiment shows that "iterative self-grading without an external judge" produces round-over-round increasing gains. The papers read all run only 3–4 rounds, with increments flat or narrowing; longer runs show degradation or collapse. [Strongest: multiple primary sources, same direction] How to test: any experiment that, without external ground truth, reports ≥5 rounds with increments growing each round, replicated on a second model family, overturns this claim.
2. Verified gains from AI improving AI are concentrated in tasks with automated evaluators, and the primary authors have written down this boundary themselves. [Strong: self-statements from five parties — AlphaEvolve, Tao et al., Anthropic, METR, Google] How to test: a major AI-led advance on an open research task without an automated evaluator, confirmed by independent review.
3. As of October 2026, no frontier lab has declared, under its own safety framework, that it has crossed an AI R&D / self-improvement threshold. [Strong: three labs' documents checked word by word] How to test: any lab's next system card or risk report.
4. Vendors' participation metrics and rate metrics differ by at least an order of magnitude, and the former cannot serve as evidence of RSI. 80% of the code, 8× the code volume, 26% "AI leads," 3.1× agent labor, against "less than 2×," "slope not doubled," "about 1.5×." [Strong: two kinds of documents from the same vendor] How to test: rate metrics catch up to the magnitude of participation metrics — for example, any lab reporting a sustained, AI-attributable acceleration above 2×.
5. Self-modifying systems have attacked their own judges at every layer, and the latest incident is the largest. [Medium-strong: multi-source case reports, no systematic incidence rate] How to test: someone publishes a cross-system incidence rate of judge attacks and shows it falling with capability.
6. "Improving the ability to improve" has only one statistically significant piece of positive evidence, and the only cross-run compounding test was not significant. [Medium-strong: single source, verified] How to test: HyperAgents or similar work is replicated by an independent team in a second domain, with a significant compounding test.
7. As of October 2026, the public gains of the AlphaEvolve loop on Gemini training are still only the one turn from May 2025 (23% on a single kernel, 1% of total training time). [Medium: search negative — not proof of absence] How to test: Google publishes any second-round or cumulative gain figure.
8. Seven public algorithmic-efficiency series show no slope change comparable to that in vulnerability discovery. [Medium: a single METR note; labs' private progress may be undisclosed] How to test: a slope break appears in any series in 2026–2027.
9. The only numerical estimate by a non-vendor team of AI accelerating AI R&D is about 1.5× (with about a 30% chance of 2×), and its evidence is not public. [Medium-weak: semi-independent, unpublished] How to test: METR publishes a public version of the report and its methods.
10. By Anthropic's own internal capability index, the slope had not doubled as of September 2026; but "one-time jump" and "modest acceleration" cannot yet be statistically distinguished. [Medium-weak: vendor-reported, downgraded by two-seat audit] How to test: a same-caliber refit after another 3–5 models; or Epoch filling in public ECI readings for the Mythos series.
11. Estimates of the software R&D return r straddle 1, and the compute-labor substitution elasticity that decides which side it falls on rests on only 27 observations, with two specifications reaching opposite conclusions. [Weak: theoretical parameter, under-identified] How to test: longer panels or experiments (Ho and Whitfill's title is literally that the debate "needs experiments").
12. The quantitative reading of self-sustaining acceleration (about 9% per ECI point) is below the 15% threshold, but it is a rough calculation toward the upper bound. [Weak: relies on self-reports, downgraded by two-seat audit] How to test: recompute after replacing self-reported uplift with RCT-style measurement; if an uplift of 9× or more is independently measured, this claim flips.

What to watch. If any of four things happens, this article's judgment should change: first, generation time shrinking — if a lab's "model trains model" cycle goes from being measured in months to being measured in weeks, that is the first fingerprint to appear in Ord's sense; second, METR's acceleration report being made public, with methods that hold up under scrutiny; third, a genuine breakthrough in a domain without a hard judge — an open research problem solved under AI leadership and confirmed by independent peer review; fourth, some lab's rate metric crossing, for the first time, the 2× line it wrote for itself.

Appendix: Methodology and this issue's self-corrections

For this issue, each of the 37 groups of load-bearing claims was assigned 3 independent verifier agents (mostly Opus-class; two batches of low-risk classic theoretical sources used smaller models), instructed to "refute as hard as you can" and to go back word by word to primary documents. Result: all 37 groups contained caliber corrections, none passed unchanged; at the sub-claim level, 10 items were killed. In addition, 3 single-source load-bearing findings received a counter-evidence search seat and a methodology audit seat; all three were downgraded to weak conclusions.

Statements from this article's original draft that verification overturned or rewrote, with the most important listed:

1. "The AlphaEvolve anniversary post still only cites 23%/1%" was killed — the anniversary post does not mention Gemini training at all. Changed to "as of October 2026, no second-round gain figure could be found."
2. "23% is the average speedup across all kernels" — it is the average across input shapes of a single matmul kernel's tiling heuristic.
3. "DeepSeekMath-V2 proves the judge can bootstrap itself" was killed — the verifier was anchored by humans, and automatic labeling replaced human labeling only in the last two rounds.
4. "Google's 25% → 50% → 75% is one growth curve" was killed — the 50% from June 2024 is not the same caliber as the CEO metric.
5. The source of "people overestimate by 40 percentage points on average" was killed — it comes from the 2025 RCT, not the 2026 survey.
6. "0/16 staff think it could replace a researcher" — the raw responses were 11/3/2; it became 0/16 only after follow-up.
7. "The 26% index has no error interval" does not hold — the chart shows a 90% measurement interval; but the audit seat also noted that the monthly midpoints and interval values appear only in the chart and cannot be verified in the text, so this article cites only the two endpoints, February and August.
8. "Anthropic's data better support a one-time jump than compounding" was downgraded by the two-seat audit — the two are statistically indistinguishable and not mutually exclusive.
9. "After deducting the compute share, r is all <1" as Ho and Whitfill's main estimate — it is an appendix scenario. The authors of the Forethought paper were also corrected to Eth and Davidson.
10. "GPT-5's MLE-bench high of 9%" and "GPT-5.5's OPQA high of 5.8%" were killed — the two figures belong to ChatGPT agent and GPT-5.3-Codex respectively, and this article does not use them.
11. "GDM deleted the 2× in v3.1" — the deletion happened in v3.0 (2025-09).
12. "RSP v3.4 introduced two trigger paths" — the two paths and the 81× have been there since v3.1; what v3.4 changed was the comparison baseline and the "constant or slowing does not count" clause.
13. Good's "provided that ... docile" was spliced onto the intelligence explosion — it modifies "the last invention"; the publication year is 1966.
14. AIDE² "proved recursive self-improvement" — the abstract is stronger than the body: the rewriter is fixed, and the ignition test is inconclusive.
15. Fan Zheng "went directly from 1.1584 to 1.173077" was killed — Gerbicz's 1.173050 came in between.

Appendix: Main sources

Theory: Good 1966 (https://gwern.net/doc/ai/1966-good.pdf), Schmidhuber Gödel Machine (https://arxiv.org/abs/cs/0309048), Chalmers 2010 (https://consc.net/papers/singularity.pdf), Bloom et al. 2020 (https://web.stanford.edu/~chadj/IdeaPF.pdf), Eth & Davidson 2025 (https://www.forethought.org/research/will-ai-r-and-d-automation-cause-a-software-intelligence-explosion), Ho & Whitfill 2025 (https://epoch.ai/gradient-updates/the-software-intelligence-explosion-debate-needs-experiments), Whitfill & Wu (https://arxiv.org/abs/2507.23181), GovAI 2026 (https://www.governance.ai/research-paper/what-if-automating-ai-r-d-triggers-an-intelligence-explosion), Davidson–Halperin–Houlden–Korinek (https://basilhalperin.com/papers/singularities.pdf), Cunningham et al. (https://arxiv.org/abs/2609.15802), Ord (https://arxiv.org/abs/2608.14426)

L0: AlphaEvolve white paper (https://arxiv.org/abs/2506.13131), one-year anniversary blog post (https://deepmind.google/blog/alphaevolve-impact/), Georgiev–Gómez-Serrano–Tao–Wagner (https://arxiv.org/abs/2511.02864), Anthropic FLT formalization (https://www.anthropic.com/research/formalizing-fermats-last-theorem), Fields Medalists' statement (https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/)

L1/L2: DGM (https://arxiv.org/abs/2505.22954), STOP (https://arxiv.org/abs/2310.02304), HyperAgents (https://arxiv.org/abs/2603.19461), AIDE² (https://arxiv.org/abs/2609.26457), HGM (https://arxiv.org/abs/2510.21614), RRSI (https://arxiv.org/abs/2609.24972), Self-Rewarding (https://arxiv.org/abs/2401.10020), Meta-Rewarding (https://arxiv.org/abs/2407.19594), Mind the Gap (https://arxiv.org/abs/2412.02674), Huang et al. (https://arxiv.org/abs/2310.01798), R-Zero (https://arxiv.org/abs/2508.05004), Spurious Rewards (https://arxiv.org/abs/2506.10947), DeepSeekMath-V2 (https://arxiv.org/abs/2511.22570)

L3 and safety frameworks: Anthropic, "When AI builds itself" (https://www.anthropic.com/institute/recursive-self-improvement), R&D Automation Index (https://www.anthropic.com/institute/measuring-pace-of-ai-development), August risk report (https://www.anthropic.com/aug-2026-risk-report), Opus 5.5 system card (https://www-cdn.anthropic.com/fc1b44717c85dc068bc6ba5024219938094694bd/Claude%20Opus%205.5%20System%20Card.pdf), RSP update log (https://www.anthropic.com/rsp-updates), Automated Alignment Researchers (https://alignment.anthropic.com/2026/automated-alignment-researchers/), OpenAI, "Research acceleration" (https://openai.com/index/research-acceleration-view-inside-openai/), OpenAI Preparedness Framework v2 (https://cdn.openai.com/pdf/18a02b5d-6b67-4cec-ab64-68cdfbddebcd/preparedness-framework-v2.pdf), Google DeepMind FSF v3.1 (https://storage.googleapis.com/deepmind-media/DeepMind.com/Blog/strengthening-our-frontier-safety-framework/frontier-safety-framework_3-1.pdf)

Independent measurement: METR Time Horizon 1.1 (https://metr.org/blog/2026-1-29-time-horizon-1-1/), METR frontier risk report (https://metr.org/blog/2026-05-19-frontier-risk-report/), METR's evaluation of Opus 5.5 (https://metr.org/blog/2026-09-22-claude-opus-5-5/), METR note on the pace of discovery (https://metr.org/notes/2026-08-14-llm-contribution-to-discoveries/), METR 2025 RCT (https://arxiv.org/abs/2507.09089), Princeton shadow evaluation (https://arxiv.org/abs/2607.27191), METR ExploitGym incident investigation (https://metr.org/blog/2026-08-26-openai-hugging-face-incident-investigation/)

Related research on this site: for an inspection of the foundation that "verification is easier than generation," see Is Verification Really Easier Than Generation? A Foundation Inspection of Scalable Oversight; for how gains shrink when LLMs take the judge's seat, see The Machine-Judge Atlas: How Much Can LLMs Scale Software's Oracles?; for an isomorphic case in which the data a verdict needs is structurally withheld, see Have Scaling Laws Hit a Wall? An Argument Without a Definition.