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MetaRSI / RSI2: A Meta-Recursive Self-Improving System for Recursive Self-Improving Systems Themselves

Zihan Tan, Leixin Sun, Zitong Shi, Yitao Liu, Jiajun Wu, Nathaniel Brooks, Jiaru Qian, Xiaoran Shang, Suyuan Huang, Yi Ding, Yangxu Liao, Mukai Li, Qiushi Sun, Shudong Liu, Xuankun Rong, Xiaohang Yu, Zhuo Chen, Hejia Geng, Chenxin Li, Aozhou Wang, Zengji Tu, Robert Tang, Yuxin Zhan, Eric Jiang, Yuxin Wu, Jianqing Zhang, Xiao Liang, Fang Wu, Haochi Zhang, Alexander Marlow, Guancheng Wan

arXiv:2609.06396v2cs.LG

TL;DR

RSI has been validated mostly on machine-checkable benchmarks, leaving open how it applies where disciplinary correctness is established through argument, replication, or measurement. MetaRSI-v1 composes data, scaffold, and model operators under joint scheduling and proposal-policy optimization; the paper formulates refutable relations about where loops exist and what they can improve.

  • Problem

    RSI has been validated mostly on coding and formal benchmarks, while open-ended disciplinary work settles correctness through argument, replication, or measurement.

    Source: §1 · p. 2, §2.3 · p. 6

  • Method

    MetaRSI-v1 composes Data-RSI, Harness-RSI, and Model-RSI under shared scheduling and proposal-policy optimization across data, scaffold, and model changes.

    Source: §1 · p. 3, §7 · p. 33

  • Results

    The paper states five refutable relations about verification frontiers, system re-description, capability relocation, trust, and imported capability, framing the loop as the unit of progress.

    Source: §7 · p. 33

  • Takeaways & Limitations

    The paper identifies the cost of closing a new loop where none has existed as the productive question for recursive self-improvement.

    Source: §7 · p. 33

    The three-operator system is a closed amplifier: it can redistribute demonstrated capability but cannot bootstrap knowledge it does not contain.

    Source: §6.2 · p. 26

Abstract

from arXiv · show

Recursive self-improvement (RSI) lets a system improve the model-building machinery from its own failures, so every later model inherits the gain. Yet RSI has been validated almost exclusively on coding and formal benchmarks such as science QA and mathematics. This format bound limits RSI to improvement within a machine-checkable slice, not general capability where questions are open and correctness is settled by argument, replication, or measurement. We argue RSI must next operate across real, diverse scientific, engineering, and meta-scientific domains, not where formal evaluation is merely tractable. To that end we present MetaRSI-v1, where improvement is the scheduled composition of three typed operators over one unified paradigm. Data-RSI amplifies existing competence and marks its boundary; Harness-RSI edits a five-slot scaffold without touching weights; Model-RSI internalizes capability into parameters through bounded training. Sharing one loop kernel and artifact vocabulary, they make data, scaffold, and model changes composable rather than exclusive. A two-axis optimizer jointly decides operator order and each operator's proposal policy, while a meta-level policy revises the schedule across terms. We validate MetaRSI-v1 under the field's standard evaluations, on code and closed-form science, with no external teacher: the target model plays every role in its own loop. MetaRSI-v1 reframes self-improvement from a single-surface edit to a composition across the full model-production pipeline, opening two paths: a model route internalizing capability through training, and a harness route leaving weights untouched and thus extending self-improvement to any model reachable through an interface, with Data-RSI redefined as the shared substrate feeding both. The framework further yields refutable laws on where loops exist, how operators compose, and what supervision buys.

1. Introduction

Recursive self-improvement uses a system’s failures to improve the machinery that builds later models, but it has been validated mostly on machine-checkable coding and formal benchmarks. MetaRSI-v1 composes data, harness, and model changes under shared scheduling and proposal-policy optimization.

1. Introduction

  • RSI has been validated almost exclusively on coding and formal benchmarks, where machine-checkable correctness does not establish general disciplinary capability settled by argument, replication, or measurement.The survey reports that 69% of 45 systems close their loops against machine-checkable targets, including scientific benchmark systems.Source: §1 · p. 2
  • System behavior depends jointly on data, weights, and execution scaffold, so changes to any surface alter what the others describe.MetaRSI-v1 uses a unified paradigm and a meta-level policy to choose which change comes next.Source: §1 · p. 3
  • MetaRSI-v1 combines three typed operators over one loop kernel: Data-RSI amplifies demonstrated competence, Harness-RSI edits a five-slot scaffold, and Model-RSI internalizes capability through bounded training.Transition adapters pass signals and outputs between operators; the RSI2 Agent jointly optimizes operator order and proposal policies, while the MetaRSI2 Agent revises schedules across terms.Source: §1 · p. 3
  • MetaRSI-v1 is validated on code execution and closed-form scientific reasoning with the target model playing every model-driven role and no external model proposing, judging, or scheduling.The stated validation isolates the mechanism from assistance by a stronger teacher.Source: §1 · pp. 3–4
  • The framework redefines Data-RSI as verified records from execution experience that mark competence boundaries and feed both Harness-RSI and Model-RSI, with their changes generating fresh evidence.It also proposes local loops at individual stages of scientific and engineering work, whose records can accumulate and transfer across domains.Source: §1 · p. 4

2. Related Work

Prior work has expanded capability through scale, alignment, inference-time computation, and execution scaffolds, while RSI systems span output, scaffold, data, and cross-component changes. The reviewed evidence also shows a concentration in closed verification and a gap between recall-style benchmarks and open-ended or practice-based capability.

2.1. Foundation Models

  • Capability engineering has shifted from parameters through alignment data and inference procedure to execution scaffolds, motivating treatment of data, scaffold, and model as jointly writable surfaces.Scaling, alignment, inference-time computation, and tool-, memory-, and agent-based scaffolds are described as successive regimes.Source: §2.1 · p. 4

2.2. Recursive Self-Improvement

  • Prior RSI work spans self-refinement, scaffold rewriting, data generation, and a smaller set of cross-component systems, including systems that change harnesses and weights together.The surveyed work includes reflection, scaffold search and rewriting, self-generated training data, and multi-component optimization.Source: §2.2 · pp. 4–5
  • In 69% of surveyed systems, verification uses a key or test, and scientific benchmarks fall within this closed-target majority rather than outside it.The review identifies two gaps: cross-substrate systems hard-wire operator order, and improvement operators are usually fixed programs rather than objects of optimization.Source: §2.2 · p. 5, Figure 4 · p. 5

2.3. Capability Boundaries

  • Of 55 closed loops, 53 are at verifier rungs 1–3; the five rung-5 domains above the capability threshold are not simply the domains where models perform worst.Loop count falls with verifier rung (Spearman ρ = −0.75, p < 0.001), while capability’s association is not significant after controlling for rung; every domain scores lower on practice than recall.Source: Figure 5 · p. 6
  • Open-ended and practice-based tasks remain far from expert performance even as closed-form science scores have risen from 38.8% to the low nineties on GPQA-Diamond.Benchmarks for research replication, paper reproduction, and laboratory protocols remain difficult for systems that saturate multiple-choice science; paired practice scores are 35 to 83 points below recall scores.Source: §2.3 · p. 6
  • The capability threshold separates domains where amplification and external structure can help from those where new knowledge must enter; the verifier rung is assigned from each domain’s practice benchmark.The census includes 33 loops added in August 2026, none above rung 2, and eight domains still without a closed loop.Source: §2.3 · p. 7

3. Preliminaries

MetaRSI treats the deployed system as data, model, and harness together, and defines improvement around evidence compiled from its executions. Procedures act under fixed measurement and resource constraints, with an objective that accounts for gain, cost, regression, and signal mismatch.

3. Preliminaries

  • A deployed system combines data state D, model state θ, and harness state H; changing any one changes system behavior.D includes training data, θ includes parameters and bounded architectural choices, and H is the scaffold mediating model interactions.Source: §3 · p. 7
  • The learning signal Σ compiles evidence from current-system attempts, including outcomes, trajectories, admitted knowledge, and decision records.Its typing is fixed while evidence sources may vary; the signal is perishable because a system change invalidates evidence compiled by the earlier system.Source: §3 · pp. 7–8
  • The sealed evaluator, held-out task set, release rule, and resource ledger remain outside every improvement procedure’s write surface.Keeping measurement protected distinguishes capability improvement from changing the definition of success.Source: §3 · p. 8
  • Improvement episodes begin from a clean system, use adaptation tasks to observe failures, score the final system once on a sealed set, and operate within a total budget.An episode can apply a sequence of procedures, producing a chain of systems.Source: §3 · p. 8

3.1. Objective Formulation

  • The objective optimizes deployed improvement productivity while penalizing cost, regression on prior capability, and divergence between working signal and sealed measurement.Procedures produce candidates rather than promoting them, and composition order can matter because one procedure changes what the next reads.Source: §3.1 · pp. 8–9, §3 · p. 8

4. Methodology

MetaRSI-v1 combines three operators under a shared loop kernel and artifact vocabulary, with a scheduler that chooses operator order and revises proposal policies. Its operators write data, harness, or model state, using a common learning signal and protected evaluation.

4. Methodology

  • MetaRSI-v1 composes Data-RSI, Harness-RSI, and Model-RSI through a shared kernel and artifact vocabulary, then schedules their order and proposal-policy changes.A meta agent revises the scheduler’s policy once an improvement term completes.Source: §4 · p. 9

4.1. The Loop Kernel: One Paradigm for Heterogeneous Operators

  • The loop kernel gives operators one authority boundary: models propose changes, while deterministic code validates, evaluates, and adjudicates them.The kernel consumes a typed learning signal, and its cycle recompiles evidence after re-evaluation; the seven-stage refinement is not unique.Source: §4.1 · pp. 9–10, Figure 6 · p. 10

4.2. Three Base Operators

  • The three operators have disjoint write surfaces for data, scaffold, and model state, making each promoted change attributable to one operator.Their differing costs and complementary effects support scheduling and transitions among operators.Source: §4.2 · p. 11, Table 1 · p. 15, §4.2.3 · p. 15

4.2.1. Data-RSI: Verified Synthesis from Execution Experience

  • Data-RSI amplifies competence evidenced by execution and marks its boundary, producing verified records that feed the other operators.Its pipeline distills experience into directives, generates records adversarially, and verifies them; blind re-derivation certifies self-consistency but not correctness beyond the model’s knowledge.Source: §4.2 · p. 11, §4.2.1 · pp. 11–13

4.2.2. Harness-RSI: Editing the Execution Scaffold

  • Harness-RSI edits typed patches over five scaffold slots without changing model weights, with changes taking effect immediately and requiring no training.Patches state a repair hypothesis, expected effect, and risk; edits outside declared slots are rejected mechanically.Source: §4.2.2 · p. 13

4.2.3. Model-RSI: Internalizing Capability into the Model

  • Model-RSI trains bounded parameter and architecture choices on Data-RSI records, trading a one-time training cost for capability that persists across scaffolds without per-inference context cost.Each round starts from the same fixed base checkpoint and cumulative dataset; candidates that fail to improve the historical best are discarded.Source: §4.2.3 · p. 14

4.3. Operator Composition: Five Admissible Transitions

The section constrains operator sequences by signal freshness, then separates planning the operator sequence from revising each operator’s policy. A meta-level agent updates the scheduler across completed terms, with human participation possible at decision points.

4.3. Operator Composition: Five Admissible Transitions

  • Freshness permits five cross-operator transitions and the D→D and H→H self-transitions, but excludes H→M and M→M because they would consume stale data.A harness change alters system behavior without producing a new dataset; Model-RSI likewise requires a dataset produced since the latest capability-altering step.Source: §4.3 · p. 15
  • Each admissible edge uses a typed adapter to convert the producer’s artifact into the consumer’s input, while checking freshness and type compatibility.Adapters reformat, distill, or reject artifacts; they have no authority over the target system.Source: §4.3 · pp. 15–16

4.4. Two-Axis Scheduling

  • Horizontal orchestration draws a budgeted, evidence-backed operator program whose order follows the admissible transition graph and whose evaluation, release criteria, and stopping conditions are specified in advance.The runtime executes the declared order after planning.Source: §4.4 · p. 16
  • Vertical optimization revises an operator’s proposal policy within its mutable contract surfaces, while protecting its evaluator, sandbox, schemas, evidence chain, identity, and declared types.Acceptance requires the actual diff to match the declared modification, making the change auditable.Source: §4.4 · p. 17
  • The two axes use the same evidence but change different objects: orchestration changes the target sequence, while vertical optimization changes operator policies.This separation supports attribution to the sequence, operator, and their interaction.Source: §4.4 · p. 17

4.5. MetaRSI: Improving the Scheduler

  • After each term, the meta-agent uses whole-term evidence about released gains, unselected candidates, and budget use to revise scheduler instructions without changing what the scheduler may decide.Its fixed parameters revise the scheduler policy, while the decision space, evaluator, and release gate remain protected.Source: §4.5 · pp. 17–18
  • Separate write surfaces keep each agent within its level: the meta-agent revises scheduler instructions, while operator sub-agents revise only their assigned policy surfaces.The paper presents these boundaries as what makes the improvement levels compositional.Source: §4.5 · p. 18
  • Human participation can focus on the framework’s few judgment-heavy decisions while the high-volume operators run automatically, with human guidance intended to decrease as evidence accumulates.The paper describes a spectrum from fully automatic operation to a human at every decision point, and treats human involvement as a waypoint toward autonomy.Source: §4.5 · p. 18

4.6. Overall Operation: The Lifecycle of an Improvement Term

An improvement term routes a system through horizontal operator programs and vertical policy updates until a stop intent, then uses the completed trace to revise the scheduler. Evaluation and release remain separated from proposal, making improvements auditable.

4.6. Overall Operation: The Lifecycle of an Improvement Term

  • Each term begins with an evaluation signal, alternates budgeted horizontal programs and accepted vertical policy updates, recompiles the signal after capability-altering steps, and closes at a stop intent.The meta-agent reads the completed trace and proposes scheduler updates; the returned state includes the released successor and updated policies.Source: §4.6 · pp. 18–20
  • In the worked sequence, Harness-RSI addresses a verification habit; after that change, refreshed data supports Model-RSI training on a remaining knowledge deficit, followed by removing a redundant scaffold entry.The harness change makes the earlier dataset stale, so Data-RSI must rebuild a fresh dataset before Model-RSI is admissible.Source: §4.6 · p. 19
  • At any decision point, the scheduler may replace the next operator step with vertical optimization when an operator’s directives have not produced an evaluation delta.The example rewrites data.policy’s diagnosis priorities and directive construction within its contract.Source: §4.6 · p. 19

4.7. What the Framework Protects

  • Operators propose, an independent evaluator scores, and a protected release gate promotes at most one successor; no component evaluates its own output.The sealed measurement is outside every agent’s write surface, including the meta layer.Source: §4.7 · p. 20, §4.6 · p. 20
  • Artifact lineage and these separations make in-term improvements auditable after the fact, which the paper identifies as a prerequisite for domains with weaker verifiers than test suites.The three improvement levels have distinct agents, objects, and cadences, from each operator step to once per term.Source: Table 2 · p. 19, §4.7 · p. 20

5. Experiments

The experiments test scheduled composition on a self-hosted open-weight model and interface-only frontier models, with target models playing every model-driven role. Results show gains from composition and continued improvement when the improver itself is meta-updated.

5.1. Experimental Setup

  • The setup uses a self-hosted Qwen3.5-35B-A3B target for all three operators and interface-only frontier targets for Data-RSI and Harness-RSI.Every model-driven role is played by the target itself; external input is limited to the environment verifier, and conditions use equal budgets, sealed splits, and five outer seeds.Source: §5.1 · pp. 21–22, §5 · p. 21

5.2. Main Results

  • MetaRSI-v1 is best on all four benchmarks, gaining +10.9 average points over the frozen system and +3.6 over the strongest fixed-order composition.The comparison uses the same budget; Table 3 reports the released successor on sealed splits.Source: Table 3 · p. 22, §5.2 · p. 22
  • Scheduling beats the level +7.3 composition baselines by 3.6 points, while the full system exceeds the best single operator on every benchmark by 2.5 to 5.0 points.Operator rankings vary by benchmark; Harness-RSI leads on closed-form suites, and gains average +8.8 on executable versus +13.0 on closed-form suites.Source: §5.2 · pp. 22–23, Figure 9 · p. 23

5.3. Frontier Models Under the Harness Route

  • All six frontier models improve on Terminal-Bench 2.1 under the harness route, gaining +5.6 to +9.2 points, with a +7.3-point mean.The comparison uses the reference execution harness; AIME is saturated, while SWE-bench Pro does not support a clean cross-model comparison because resolve rates are scaffold-sensitive.Source: Figure 10 · p. 23, §5.3 · p. 24

5.4. Improving the Improver

  • Over five terms, the meta path reaches +26.2 average points against +20.7, while both paths decay in per-term gains.The meta path averages +3.8 per term over terms 2–5 versus +2.5 without the meta-update, and reaches the defined plateau one term later.Source: Figure 11 · p. 24, §5.4 · p. 25
  • With equal budgets and the same released S1, the meta-updated improver gains 7.2 average points against 4.9 for the original improver.Its advantage scales with benchmark headroom, while both improvers rank the four benchmarks in the same order.Source: §5.4 · p. 24
  • Across three terms, all six frontier models gain in every term, for a mean cumulative gain of +11.3 points.Mean gains are +7.3, +2.8, and +1.2 by term; retention tracks headroom, with the two lowest-baseline models retaining 43% and 63% of term-1 gain in term 2 versus 26% to 39% for the other four.Source: Figure 12 · p. 25, §5.4 · p. 25
  • The meta path carries 68% of accepted operator-policy edits forward versus 38%, and leaves 8.2% of attainable gain on the table versus 16.5%.It also retains previously acquired capability where the other path loses 0.2 points on GPQA-D-hard100 at term 5.Source: §5.4 · p. 25, Table 4 · p. 25

6. Discussion

The discussion frames MetaRSI’s scope as expanding self-improvement through composable routes across domains, while recognizing constraints in physical settings and the need for information from outside the loop. It develops falsifiable claims about loop closure, checkability, and where RSI effort is likely to pay.

6.1. What Composition Buys

  • The shared evidence-based diagnosis routes procedural failures to the harness and missing knowledge to data or weights, while typed adapters make operator sequences schedulable and replayable.A weak verifier requires separations that keep the loop from changing its own success definition; partial verification is a harder case of the same problem.Source: §6.1 · p. 26

6.2. An Amplifier Is Not a Source

  • Data-RSI, Harness-RSI, and Model-RSI redistribute competence already present, so the composed loop is a closed amplifier, not a source of new capability.Genuine gains require information from outside the loop; Data-RSI measures the deficit and bounds the request for external supervision, whose volume is reported.Source: §6.2 · p. 26

6.3. Two Routes Through the Loop

  • Data-RSI remeasures the changed system, enabling either a scaffold route that leaves weights untouched or a model route that internalizes capability into weights.The scaffold route suits API-accessible or training-budget-constrained models; the model route makes capability available outside a particular scaffold and free at inference. Their composition deletes redundant scaffold entries after internalization, returning context budget.Source: §6.3 · pp. 26–27, §6.3.1 · p. 27, §6.3.2 · p. 27

6.4. Loops Across Domains

  • A new domain can instantiate the framework with an observable task family, a verifier of available fidelity, and a seed scaffold, rather than designing a new loop.At stronger verification rungs the framework applies unchanged; at weaker rungs, Data-RSI bounds which residual questions require human, instrument, or corpus supervision. Loops can begin at one pipeline stage, and existing reports and artifacts can reduce later probing costs; whether many such loops yield broad expert competence remains open.Source: §6.4 · p. 28, §6.4.1 · p. 28, §6.4.2 · p. 29

6.5. Toward Loops That Touch the Physical World

  • Physical loops retain the learning signal and budget ledger, but irreversible actions require recoverability checks, staged fidelity, and protected human authorization.In open physical settings, failures outside the environment model require a fourth operator that revises that model and triggers downstream re-probing. Agent-to-instrument protocols [62] and instrument routines [63] illustrate a path in which automated laboratories precede open-world embodiment.Source: §6.5 · pp. 29–30

6.6. The Reusable Artifact

  • RSI-Harness packages task-specific, inspectable genomes as a standalone runtime, enabling shared narrow scaffolds and a test of whether unrelated domains reuse entries.Its public library can reveal whether scaffold entries are shared across task families.Source: §6.6 · pp. 30–31

6.7. Five Laws of Recursive Self-Improvement

  • After the census more than doubled in August 2026 to 55 loops, 53 of 55 closed at verification rungs 1–3; the rung remained significant controlling for capability, while capability did not remain significant controlling for the rung.The eight domains that had never had a loop still had none; the passage says loops form where closing is cheap, where verification is free.Source: §6.7 · p. 31
  • The remaining proposed laws say that self-knowledge expires and must be refreshed, competence can move between substrates with different costs, trust requires unwritable success criteria, and gains import capability.The paper presents these as falsifiable claims: description costs govern loop speed, multiple writable substrates enable cost retirement, and results should distinguish amplified competence from imported information.Source: §6.7 · pp. 31–32
  • The five laws govern loops rather than specific models, benchmarks, or parameter counts; unwritable scope and measurable external boundaries define Laws 4 and 5.The passage presents these laws as the ground for the position that progress should be understood in terms of loops.Source: §6.7 · p. 32

6.8. Position: The Unit of Progress Is the Loop, Not the Model

  • The proposed unit of progress is the loop: expand where loops can be closed rather than optimizing model capability alone.The paper argues that the productive question is how cheaply a new loop can be closed in a previously unserved area.Source: §6.8 · p. 32
  • More than two thirds of surveyed systems verify against closed, machine-checkable targets, and across 22 domains loop availability tracks checkability rather than model competence.The standing loss is concentrated in five domains where capability exists but no machine-checkable target is available.Source: §6.8 · p. 32
  • Likely avenues include first-order loops, harness changes where weights cannot be touched, and using diagnostic boundaries to allocate effort.The paper considers synthesizing data for absent capabilities, scaling a fixed verifier, and mistaking an unmodeled situation for a capability gap unlikely to pay.Source: §6.8 · p. 32
  • The position covers settings with situations enumerable in advance, while its extension to open worlds is projected from other sections; the machinery to try is buildable from existing parts.The open-world extension treats the space of situations itself as an operand.Source: §6.8 · p. 32

7. Conclusion

MetaRSI-v1 composes changes to data, scaffold, and model to address RSI’s concentration on machine-checkable targets. The conclusion reports a measured gain and proposes five refutable relations about recursive self-improvement.

7. Conclusion

  • The surveyed field’s concentration reflects evaluation format: better than two thirds of systems close loops against machine-checkable targets, certifying benchmark-bound rather than general disciplinary capability.The conclusion frames the paper’s aim as moving RSI from a single editable surface to the production line for deployed models.Source: §7 · p. 33
  • 3.6 points over the strongest fixed pipeline: MetaRSI-v1 improves the released successor under a fixed budget, sealed measurement, and no external teacher.The authors also state that the target system performs the loop’s roles without an external model proposing, judging, or scheduling.Source: §7 · p. 33
  • MetaRSI-v1 schedules three typed operators over one execution paradigm, composing data, scaffold, and model changes across the model-production pipeline.Data-RSI amplifies existing competence and marks its boundary; Harness-RSI edits a five-slot scaffold without touching weights; Model-RSI internalizes capability through training.Source: §7 · p. 33
  • The conclusion identifies five refutable relations, including that self-improvement’s reachable frontier follows verification rather than capability and that genuine capability additions are imported.It also reports releasing RSI-Harness and the run genomes to seed a community library of task-specific scaffolds.Source: §7 · p. 33

A. Evaluation-Domain Census

The evaluation-domain census counts self-improving systems that meet four closed-loop benchmark criteria and classifies them by the format that closes their loop. Its 45 systems include 31 with machine-checkable targets and 14 with open targets.

A. Evaluation-Domain Census

  • A system enters the census only if it reads its own execution evidence, modifies its own data, harness, or weights, uses the modified system in the next round, and reports a quantitative named-benchmark result.Architecture proposals without closed-loop benchmark results and training-time techniques rather than deployed self-improving agents are excluded.Source: A. Evaluation-Domain Census · p. 39
  • The census contains 45 systems: 31 close against machine-checkable targets and 14 against open targets.The pool was drawn from three surveys and three curated community indexes, covering papers from 2022 through August 2026.Source: A. Evaluation-Domain Census · p. 39
  • Thirty-one of the 45 systems fall in verification class x, where a closed, machine-checkable target closes the loop.The census labels each system by both its main benchmark domain and the verification object that closes its loop; it counts measured loop closure, not claimed generalization.Source: A. Evaluation-Domain Census · p. 39
  • Verification classes comprise 14 executable-test, 16 exact-match or choice-key, and one numeric-key system as closed formats; open formats comprise 10 environment-reward, one learned-judge, and three domain-outcome systems.Systems using several formats are assigned the format of their primary closed-loop benchmark.Source: A. Evaluation-Domain Census · p. 39

A.1. The Twenty-Two-Domain Audit

The audit assigns domains verification rungs from practice benchmarks and compares those rungs with closed-loop counts and reported capability. Across the larger census, loops remain concentrated at low rungs, while capability does not rise monotonically with verification difficulty.

A.1. The Twenty-Two-Domain Audit

  • The audit uses all 22 domains for loop-count and rung panels but only 17 subject domains for capability panels, excluding testbed families whose success rates are not comparable to subject-matter accuracy.Classical languages are also excluded from the capability axis because their only published score is a practice benchmark, not a recall score.Source: §A.1 · p. 39
  • The four testbed families added for newer systems use rung-1 or rung-2 verification, including exact-match QA and simulator-scored environments.Ten of the 21 systems added in August 2026 close loops on testbeds absent from the earlier taxonomy.Source: §A.1 · pp. 39–41
  • No mathematics or closed-form science system in the census is classified as open verification; subject matter alone does not determine whether a target is open.The census classifies systems by subject, verification class, and the benchmark used.Source: Table 7 · p. 40
  • The five rungs run from executable tests and exact match through simulation, reproduction, and instrumented protocols to expert rubrics without ground truth.Each domain takes the rung of its practice benchmark, not its recall benchmark or loop count.Source: §A.1 · p. 41
  • A loop’s own verifier does not set its domain’s rung: MOSS’s rubric-scored software-engineering loop remains in a rung-1 domain because software engineering’s practice benchmark is SWE-bench.The rung is read from domain practice, not from the target a system selected for its loop.Source: §A.1 · p. 41
  • Spearman was −0.75 across 22 domains versus −0.79 across 18 in the smaller sample; 53 of 55 loops (96.4%) were at rungs 1 to 3.None of the 33 later loops was at rung 4 or 5.Source: §A.1 · p. 41
  • All five rung-5 domains above the capability threshold remained in the same region, with no loops except law’s one narrow slice.Their capability scores were economics 80.8, health and clinical 72.1, philosophy and history 70.1 each, and law 67.8.Source: §A.1 · p. 41
  • Mean capability by rung is non-monotonic at 91.6, 55.0, 58.6, 32.6, and 72.2; economics at rung 5 scores 80.8 against engineering design’s 55.0 at rung 2.The comparisons show the standing loss is about verification rather than a simple ordering of competence.Source: §A.1 · pp. 41–42

A.2. Recall and Practice Pairs in Figure 5(e)

Figure 5(e) pairs recall or exam benchmarks with benchmarks of domain practice, spanning six domains. The comparisons require qualification because most are between separate benchmark frontiers, and the gaps combine task difficulty with verification strictness.

A.2. Recall and Practice Pairs in Figure 5(e)

  • 35 to 83 points is the span across six recall-or-exam versus practice-benchmark pairs, whose endpoints are listed in Table 8.The panel alone does not show what the span represents; the endpoint provenance qualifies its interpretation.Source: §A.2 · p. 42
  • 38.1 points is the within-system MLE-bench Lite–High delta; the other five pairs compare independently selected benchmark frontiers, not necessarily the same models.Those five gaps are indicative of the format gap, not causal estimates.Source: §A.2 · p. 42
  • The MLE-bench pair uses High as its practice end, while Table 9 reports All at 64.4 as domain capability.The pair contrasts the easiest and hardest splits; the two tables use different splits of the same benchmark.Source: §A.2 · p. 42
  • The humanities practice endpoint is 5.2 from an older o3-mini result; newer HLE scores make its plotted 64.9-point frontier gap materially smaller.No per-category humanities score is available to replace that endpoint; the research-mathematics ∼0 endpoint is a community observation, not a leaderboard score, and the wet-lab pair compares different benchmarks.Source: §A.2 · p. 42
  • The span measures task difficulty and verification strictness together, so it does not separate their contributions.Recall endpoints are machine-checkable, while practice endpoints use several forms of evaluation, including expert rubrics, soft metrics, review, and harder executable tests.Source: §A.2 · p. 42

B. Operator Cards and Optimization Contracts

Operator cards guide the RSI2 Agent-v1 in choosing operators, while fixed-structure optimization contracts delimit what the RSI2 Sub-Agent-v1 may change. Updates are accepted only after deterministic checks confirm that the requested and actual edits comply with the contract.

B. Operator Cards and Optimization Contracts

  • Each operator card tells the RSI2 Agent-v1 what the operator does and when to choose it, and is partly mutable.The optimization contract is a separate artifact read by the vertical RSI2 Sub-Agent-v1.Source: B. Operator Cards and Optimization… · p. 42
  • The optimization contract fixes the structure of what may be changed, while its mutable surfaces define which policy portions can be rewritten.Table 10 distinguishes mutable, action, and protected surfaces for each operator.Source: B. Operator Cards and Optimization… · p. 42, Table 8 · p. 43
  • An update passes only if its contract identifier, declared edits, requested surfaces, mutable surfaces, and actual text diff satisfy four deterministic checks.Matching the declared changes to the actual diff prevents undeclared edits from being smuggled into a policy update.Source: B. Operator Cards and Optimization… · p. 43

C. Transition Adapter Specifications

Transition adapters implement admissible edges among data, harness, and model operators using fixed input and output types and bounded model calls. They transform artifacts and recompile learning signals, but may not modify the target system directly.

C. Transition Adapter Specifications

  • D→H extracts failure-signature clusters into bounded, deduplicated memory entries or skill descriptors; D→M materializes curriculum shards and validates the training recipe against backend and budget constraints.The first emits an Experience artifact; the second emits materialized shards and a validated recipe request.Source: C. Transition Adapter Specifications · p. 43
  • H→D reruns the fixed evaluator under a promoted genome and recompiles the learning signal with harness-attributed changes, marking failures as persistent, new, or resolved.This makes subsequent synthesis reflect the system under its updated harness.Source: C. Transition Adapter Specifications · p. 43
  • M→D reruns the fixed evaluator after a checkpoint release and recompiles the learning signal with per-dimension movement, including regressions.The adapter also reports learning signatures and a regression list.Source: C. Transition Adapter Specifications · p. 44
  • M→H proposes scaffold deletions when training removes their associated failure and additions when new capability makes tools or skills useful; proposed deletions are replayed before promotion.A deletion that reduces accuracy is reverted.Source: C. Transition Adapter Specifications · p. 45

D. Failure Signature Taxonomies

Failure labels are assigned by task-specific rules with shared priority ordering, while reusable-mechanism attribution is model-assigned and must agree with the deterministic cause.

D. Failure Signature Taxonomies

  • The first two failure fields are rule-assigned by task family, and the shared priority order attributes multi-symptom failures to the earliest cause.Environment errors are excluded from improvement targeting because they are not properties of the system.Source: D. Failure Signature Taxonomies · p. 45
  • Closed-form failures are ordered from output-protocol violations and abstentions through reasoning-answer mismatch, arithmetic error, distractor confusion, and none.Source: D. Failure Signature Taxonomies · p. 45
  • Executable failures use ordered turn-level causes and task-level causes, including validation, exploration, artifact, scope, completion, and environment errors.Source: D. Failure Signature Taxonomies · p. 45
  • Only the reusable mechanism field is model-attributed, and validation rejects mechanisms that contradict the assigned terminal cause.Source: D. Failure Signature Taxonomies · p. 45

E. The Three Record Gates

Data-RSI admits records only through fail-closed gates that check verification, novelty, and provenance before returning records with lineage.

E. The Three Record Gates

  • Every Data-RSI candidate record passes fail-closed gates; records that cannot be positively verified are rejected.The procedure receives a candidate record, capability slot, released checkpoint, and sealed corpus.Source: E. The Three Record Gates · p. 46
  • For closed-form records, an independent solver re-derives the answer and a separate verifier checks its label, format, and derivation consistency.Source: E. The Three Record Gates · p. 46
  • For executable records, the environment and tests must run, tests must pass on the reference solution and fail on a no-op, and a clean-state solver must solve within bounds.Source: E. The Three Record Gates · p. 46
  • The novelty gate routes already-held records to consolidation without value attribution and rejects exact, high-overlap, or semantic near-duplicates, failing closed on uncertainty.Source: E. The Three Record Gates · p. 46
  • The provenance gate requires a failure signature or external source, excludes records derived from diagnostic evaluation artifacts, and returns admitted records with lineage.Source: E. The Three Record Gates · p. 46

F. Run Layout and Accounting Conventions

The run conventions preserve inspectability and resumability, isolate training comparisons, and fix evaluation and accounting rules in advance.

F. Run Layout and Accounting Conventions

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