GRADS：难度可控的图调控智能体数据合成

# GRADS: Graph-Regulated Agentic Data Synthesis with Controllable Difficulty
Source: [https://arxiv.org/html/2610.21167](https://arxiv.org/html/2610.21167)
Ruijie TaoAffiliation:Johns Hopkins UniversityEmail:[rtao12@jh\.edu](mailto:)Kai YeAffiliation:Nanjing UniversityEmail:[kaiye@smail\.nju\.edu\.cn](mailto:)Senhua ZhangAffiliation:AmazonEmail:[senhuazh@amazon\.com](mailto:)Zhengqin ZhuAffiliation:AmazonEmail:[tozhu@amazon\.com](mailto:)Ziyang LiAffiliation:Johns Hopkins UniversityEmail:[ziyang@cs\.jhu\.edu](mailto:)\*Equal contribution\. Work conducted during an internship at Amazon\. Corresponding author

###### Abstract

Deep research agents are increasingly deployed to retrieve precise information from large corpora, yet multi\-hop, long\-horizon tasks remain challenging\. Synthetic data generation has emerged as a scalable solution, with existing pipelines typically expanding seed tasks to increase their apparent depth and breadth\. However, this expansion does not reliably translate into necessary reasoning: newly introduced evidence may be only weakly coupled to the answer, creating a mismatch between intended and empirical difficulty\. To address this problem, we introduce GRADS, a graph\-guided agentic data synthesis framework with explicit difficulty control\. GRADS runs a closed loop of seed selection, evidence expansion, question–answer construction, and verification while maintaining a graph of the evidence and inference dependencies required to derive each answer\. At each step, it conditions generation on a relevant subgraph, preserving indispensable inference without accumulating irrelevant context\. Experiments across security, software\-engineering, and scientific\-document domains show that GRADS consistently generates verified tasks with empirically separated difficulty distributions, as measured by independent solvers\. Moreover, under matched training budgets, post\-training on this data delivers consistent gains at every level: SFT raises the solution\-termination rate to over95%95\\%while cutting tool calls and turns by up to 75%, RL trims tool use by up to a further19\.5%19\.5\\%, and on our held\-out, domain\-specific benchmarks, the resulting 4B model matches Sonnet 4 on software engineering and surpasses it on the scientific and security domains\.

## 1Introduction

Specialized knowledge is often distributed across domain\-specific record collections that are too large to inspect manually\. Deep search agents have emerged as a promising way to exploit such collections: LLM\-based agents that iteratively plan, issue search queries, read retrieved documents, and reason over them to answer complex, multi\-hop information needs\([Huang et al\., 2025b](https://arxiv.org/html/2610.21167#bib.bib17);[Li et al\., 2025b](https://arxiv.org/html/2610.21167#bib.bib18);[Li et al\., 2025c](https://arxiv.org/html/2610.21167#bib.bib22)\)\. Post\-training, including supervised fine\-tuning \(SFT\) and reinforcement learning \(RL\), has proven to be effective in teaching models when and how to invoke search tools during reasoning\([Jin et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib19);[Song et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib20);[Zheng et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib21)\)\. A rapidly growing body of work demonstrates that synthetic question–answer data is sufficient to train strong deep search agents through SFT and RL\([Wu et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib4);[Li et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib23);[Gao et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib24);[Sun et al\., 2025b](https://arxiv.org/html/2610.21167#bib.bib26);[Sun et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib27);[Liu et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib25)\)\. The quality of such agents is therefore bounded by the quality of the data they are trained on, and in particular by how reliably that data exercises genuine multi\-step reasoning\.

To make synthetic data sufficiently challenging, most pipelines impose an explicit structure intended to raise the latent inference complexity of each question\. Representative strategies include depth\- and width\-based task extension\([Shi et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib2)\), set\-theoretic formalization of information\-seeking tasks\([Tao et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib3)\), graph sampling combined with information obfuscation\([Li et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib23);[Wei et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib30)\), recursive construction of hierarchical research trees\([Xia et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib28)\), and bottom\-up composition of single\-hop questions\([Trivedi et al\., 2022](https://arxiv.org/html/2610.21167#bib.bib29)\)\. These methods share a common premise that complexity accumulated during synthesis translates into complexity of the reasoning required at solution time\. But this premise does not reliably hold\. A long line of analysis shows that nominally multi\-hop questions are frequently answerable through shortcuts or disconnected reasoning that bypasses the intended chain\([Min et al\., 2019](https://arxiv.org/html/2610.21167#bib.bib32);[Jiang and Bansal, 2019](https://arxiv.org/html/2610.21167#bib.bib33);[Trivedi et al\., 2020](https://arxiv.org/html/2610.21167#bib.bib31)\)\. When evidence is added to a question without regard to whether it is necessary, it may be only weakly coupled to the answer\. The intended difficulty of the resulting item then diverges from its empirical difficulty, and the difficulty label ceases to be a reliable signal for evaluation or curriculum design\. This motivates the central questions of this work: can we synthesize data whose difficulty is realized in the solver’s reasoning, not merely claimed? Is such data effective for post\-training?

We approach these questions by defining the*evidence graph*of a QA pair, whose nodes are source\-grounded claims and whose edges are*necessary*inference steps, so that its depth estimates the reasoning an answer requires\. Building on this structure, we introduceGRADS, a graph\-regulated agentic data synthesis method with controllable difficulty\. GRADS departs from two prevailing strategies\. The first piles ever more explicit evidence into a question, extending tasks with additional constraints, entities, or obfuscated clues until they appear harder\([Shi et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib2);[Tao et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib3);[Li et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib23);[Liu et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib25)\)\. The second builds or samples a knowledge graph to broaden the raw material from which questions are drawn\([Chen et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib40);[Lu et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib41);[Xia et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib28)\)\. Both increase the apparent size of a question, but neither guarantees that the added evidence is required to reach the answer\. GRADS instead deepens a question within an agentic loop by regulating the structure of its evidence graph\. It decouples exploration from difficulty control, and is designed to ensure that each question attains its required reasoning depth\.

Applying this idea to real domain knowledge, such as GitHub issue trackers and scientific experiment notes, raises two further challenges\. First, the underlying corpora are too large to be explored exhaustively, so an agent must locate relevant evidence efficiently\. Second, LLM\-synthesized answers are prone to hallucination\([Huang et al\., 2025a](https://arxiv.org/html/2610.21167#bib.bib34)\), and an incorrect answer is more damaging in training data than an easy one\. To address scale, we clean and cluster the raw records and expose unified local and online search tools to the agents\. To address correctness, each answer carries a rubric of atomic claims tied to verbatim source spans\([Gao et al\., 2023](https://arxiv.org/html/2610.21167#bib.bib35);[Min et al\., 2023](https://arxiv.org/html/2610.21167#bib.bib36)\), and verification subagents check every item before acceptance\([Dhuliawala et al\., 2024](https://arxiv.org/html/2610.21167#bib.bib37);[Manakul et al\., 2023](https://arxiv.org/html/2610.21167#bib.bib38);[Du et al\., 2024](https://arxiv.org/html/2610.21167#bib.bib39)\)\.

We evaluate GRADS on three heterogeneous domains: GitHub issue tracking, experimental particle physics, and security\. For each domain, we construct a representative benchmark and a post\-training corpus\. Compared with three synthesis baselines, GRADS is the only method whose delivered reasoning depth increases monotonically with the requested difficulty, and correspondingly the only one whose solver scores decrease monotonically from Easy to Hard\. This ordering is preserved across solvers of three capability tiers\. The resulting data is also effective for training: supervised fine\-tuning a 4B model on GRADS trajectories yields large gains over the untrained model in every domain and outperforms every baseline at matched sample count and optimizer steps\. Although SFT accounts for most of the post\-training margin, subsequent RL further improves tool use and the model’s ability to terminate with an answer, bringing the 4B model to the level of the mid\-sized Sonnet 4 solver\.

Our contributions are as follows: \(i\) We formalize the evidence graph of a QA pair, whose necessary\-inference depth serves as both a synthesis\-time control and an evaluation\-time measure\. \(ii\) We introduceGRADS, which decouples exploration from difficulty control and pairs every item with a source\-grounded rubric and multi\-stage verification\. \(iii\) Across three real\-world domains, GRADS delivers controllable, empirically realized difficulty, and its data yields consistent post\-training gains over the base model and competing synthesis methods\.

## 2Related Work

#### Synthetic Data Generation for Agentic Tasks\.

Synthetic data generation has become the dominant paradigm for training deep research agents\.[Shi et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib2)introduce TaskCraft, which expands atomic tasks through depth\-based and width\-based extensions with incremental validation to produce scalable, multi\-tool agentic tasks\.[Tao et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib3)propose WebShaper, formalizing information\-seeking tasks through Knowledge Projections to achieve principled generation with controlled reasoning structures\.[Wu et al\. \(2025\)](https://arxiv.org/html/2610.21167#bib.bib4)establish an end\-to\-end pipeline spanning browsing data construction, trajectory sampling, SFT, and RL, scaling both the volume and depth of multi\-hop reasoning\. At larger scales,[Cen et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib5)convert pretraining documents into 1\.2 million verifiable QA pairs, demonstrating that RL data can reach pretraining\-level scale\.[Xie et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib8)pair synthetic queries with rubric trees for unified verification across fact\-seeking, citation grounding, and report synthesis without human annotation\.[Tongyi DeepResearch Team \(2025\)](https://arxiv.org/html/2610.21167#bib.bib7)model environments as Prior, Simulated, and Real\-world to balance stability, fidelity, and cost\. However, existing pipelines condition generation on isolated seeds without an explicit dependency structure, so expanded evidence may be only weakly coupled to the answer\. GRADS addresses this by maintaining a graph of evidence and inference dependencies throughout synthesis\.

#### Difficulty\-Aware Data Selection and Curriculum\.

A complementary line of work recognizes that difficulty is a key axis for data selection and curriculum design\.[Hu et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib6)demonstrate that partitioning STEM reasoning data by reasoning intensity—broad\-coverage problems for SFT, difficult problems for RL—outperforms random splitting in decoupled SFT\-then\-RL training\.[Gao et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib9)further show that prompts of intermediate difficulty \(roughly 50% success rate\) are most sample\-efficient for RL convergence, while[Yang et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib12)leverage a difficulty\-aware reward model to select only 10% of long\-CoT instruction data with competitive performance\. Yet difficulty is not static:[Zhou et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib13)empirically show that existing estimators become unreliable under policy drift, with estimation error growing as training progresses\. This motivates methods that co\-evolve difficulty estimators with training\([Zhou et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib13)\), adaptively select data clusters via bandit\-based self\-pacing\([Nguyen and others, 2026](https://arxiv.org/html/2610.21167#bib.bib10)\), and dynamically re\-estimate difficulty within upcoming batches to counteract the Difficulty Shift phenomenon\([Wu and others, 2025](https://arxiv.org/html/2610.21167#bib.bib11)\)\. GRADS extends this principle into the synthesis loop itself, conditioning expansion on a dependency subgraph and verifying that each introduced piece of evidence is necessary, thereby producing tasks with empirically separated difficulty distributions\.

#### Datasets and Benchmarks for Deep Research\.

A parallel line of work focuses on the datasets and benchmarks that both evaluate and feed data synthesis for deep research agents\. Expert\-written suites such as[Wei et al\. \(2025\)](https://arxiv.org/html/2610.21167#bib.bib30)and Humanity’s Last Exam\([Phan et al\., 2025](https://arxiv.org/html/2610.21167#bib.bib46)\)push the difficulty ceiling with hard\-to\-retrieve, short\-answer questions, while[Chen and others \(2026b\)](https://arxiv.org/html/2610.21167#bib.bib45)fix a reproducible corpus to disentangle retrieval from end\-to\-end agent accuracy\. To reduce reliance on human authoring,[Shen et al\. \(2026\)](https://arxiv.org/html/2610.21167#bib.bib42)synthesize authentic bridge and comparison multi\-hop questions directly from raw corpora, and[Xia et al\. \(2025b\)](https://arxiv.org/html/2610.21167#bib.bib43)grow Research Trees from large\-scale webpages into over 50k hierarchical\-constraint tasks with reasoning trajectories\.[Chen and others \(2026a\)](https://arxiv.org/html/2610.21167#bib.bib44)go further by co\-evolving queries, DAGs, and rubrics through an Explorer–Formalizer–Challenger loop, yielding verifiable benchmarks whose structure is itself a difficulty signal\. Still, these efforts largely operate over the open web and target generic information\-seeking skills; by contrast, GRADS targets specialized, heterogeneous domain corpora \(GitHub, physics, security\) and treats both the questions and their evidence graphs as artifacts for post\-training, not only for evaluation\.

## 3Question Expansion with Graph Structure

Difficulty control in GRADS rests on an*evidence graph*built online during exploration, over which a deterministic complexity is computed\. This section defines the graph and its complexity, and describes the process that grows it; how the agents consume it is deferred to §[4](https://arxiv.org/html/2610.21167#S4)\.

### 3\.1Graph Structure and Definitions

###### Definition 1\(Evidence graph\)\.

An evidence graph isG=\(V,E,τ,π,a\)G=\(V,E,\\tau,\\pi,a\)with\(V,E\)\(V,E\)a DAG:VVis a set of*claims*\(atomic facts, one per retrieved record\);EEcarries*necessary*dependency edges—\(u,v\)∈E\(u,v\)\\in Emeans establishingvvrequiresuu, so topology proxies reasoning effort, not relatedness;τ:E→ℛ=\{supports,causes,refutes,…\}\\tau:E\\to\\mathcal\{R\}=\\\{\\texttt\{supports\},\\texttt\{causes\},\\texttt\{refutes\},\\dots\\\}labels edges; provenanceπ:V→Σ\\pi:V\\to\\Sigmamaps each claim to its source context \(withΣ\\Sigmathe space of source contexts\); anda∈Va\\in Vis a distinguished*anchor*\.𝒫⁡\(G\)\\mathcal\{P\}\(G\)denotes directed paths ending ataa, and\|p\|\|p\|their edge count\.

###### Definition 2\(Node types\)\.

Each claim is a*core*node \(a main conclusion / root cause; may anchor a question\), an*inference*node \(derived by combining other claims; where multi\-hop depth accumulates\), or a*detail*node \(a supporting fact—key, date, version, status—that decorates a core or inference node but never lies on the reasoning chain\)\.

#### Structural functionals\.

Writingdv−,dv\+d^\{\-\}\_\{v\},d^\{\+\}\_\{v\}for the in\-/out\-degree ofvv, we compute four quantities in code \(never by an LLM\)\.*Depth*is the longest necessary chain and*breadth*the number of independent branches converging on the anchoraa;*size*is the number of vertices; and*information flow*sums the squared throughput of intermediate hub nodes:

d⁡\(G\)=maxp∈𝒫⁡\(G\)⁡\|p\|,b⁡\(G\)=da−,size⁡\(G\)=\|V\|,cinfo​\(G\)=∑v∈V\(dv−​dv\+\)2\.d\(G\)=\\\!\\\!\\max\_\{p\\in\\mathcal\{P\}\(G\)\}\\\!\\\!\|p\|,\\quad b\(G\)=d^\{\-\}\_\{a\},\\quad\\mathrm\{size\}\(G\)=\|V\|,\\quad c\_\{\\mathrm\{info\}\}\(G\)=\\\!\\\!\\sum\_\{v\\in V\}\\\!\\bigl\(d^\{\-\}\_\{v\}d^\{\+\}\_\{v\}\\bigr\)^\{2\}\.\(1\)From these we derive a single*complexity*score, a weighted combination that lets subgraphs be compared on one scale:

𝒞⁡\(G\)=w1​\|V\|\+w2​d​\(G\)\+w3​b​\(G\)\+w4​cinfo​\(G\),\\mathcal\{C\}\(G\)=w\_\{1\}\|V\|\+w\_\{2\}\\,d\(G\)\+w\_\{3\}\\,b\(G\)\+w\_\{4\}\\,c\_\{\\mathrm\{info\}\}\(G\),\(2\)with the depth and information\-flow weights kept dominant so a deep chain is not mistaken for a wide\-but\-shallow one\.

#### Difficulty bands\.

Difficulty is governed by depth\. Given integer thresholdsθE<θM<θH\\theta\_\{\\mathrm\{E\}\}<\\theta\_\{\\mathrm\{M\}\}<\\theta\_\{\\mathrm\{H\}\},

band⁡\(G\)=\{Easyd⁡\(G\)≤θE,MediumθE<d⁡\(G\)≤θM,Hardd⁡\(G\)≥θH,\\mathrm\{band\}\(G\)=\\begin\{cases\}\\textsc\{Easy\}&d\(G\)\\leq\\theta\_\{\\mathrm\{E\}\},\\\\ \\textsc\{Medium\}&\\theta\_\{\\mathrm\{E\}\}<d\(G\)\\leq\\theta\_\{\\mathrm\{M\}\},\\\\ \\textsc\{Hard\}&d\(G\)\\geq\\theta\_\{\\mathrm\{H\}\},\\end\{cases\}\(3\)with depths in\(θM,θH\)\(\\theta\_\{\\mathrm\{M\}\},\\theta\_\{\\mathrm\{H\}\}\)left as a gap between Medium and Hard, and breadth held under a per\-band cap so the knob moves “deeper,” not merely “wider” \(values in §[5](https://arxiv.org/html/2610.21167#S5)\)\.

### 3\.2Expansion Process

In the expansion process, a question is hardened by growing its evidence graph across rounds \(Figure[1](https://arxiv.org/html/2610.21167#S3.F1)\), following a*seed*→\\to*explore*→\\to*verify*→\\to*re\-explore*loop\. LetG0G\_\{0\}be the seed graph whose claims already answer a seed question, and letθ\\thetabe the depth threshold of the requested band \(Eq\.[3](https://arxiv.org/html/2610.21167#S3.E3)\)\. At roundtt, exploration proposes a set of candidate edits𝒦t=\{Δt\}\\mathcal\{K\}\_\{t\}=\\\{\\Delta\_\{t\}\\\}, where eachΔt=\(Δ​V\+,Δ​E\+,Δ​V−,Δ​E−\)\\Delta\_\{t\}=\(\\Delta V^\{\+\},\\Delta E^\{\+\};\\,\\Delta V^\{\-\},\\Delta E^\{\-\}\)specifies claims and edges to add and to remove\. A verification operatorν\\nuretains only the necessary part of the additive component, discarding hops a solver could bypass:

ν⁡\(Δt\)=\(Δ​V\+,\{\(u,v\)∈Δ​E\+:v​is underivable without​u\},Δ​V−,Δ​E−\)\.\\nu\(\\Delta\_\{t\}\)=\\bigl\(\\Delta V^\{\+\},\\ \\\{\(u,v\)\\in\\Delta E^\{\+\}:v\\text\{ is underivable without \}u\\\};\\ \\Delta V^\{\-\},\\Delta E^\{\-\}\\bigr\)\.\(4\)We then commit the verified edit that most extends the longest necessary chain, so depth grows rather than breadth:

Gt\+1=Gt⊕ν⁡\(Δt⋆\),Δt⋆=arg​maxΔt∈𝒦t⁡\[d⁡\(Gt⊕ν⁡\(Δt\)\)−d⁡\(Gt\)\],G\_\{t\+1\}=G\_\{t\}\\oplus\\nu\(\\Delta\_\{t\}^\{\\star\}\),\\qquad\\Delta\_\{t\}^\{\\star\}=\\argmax\_\{\\Delta\_\{t\}\\in\\mathcal\{K\}\_\{t\}\}\\bigl\[d\\bigl\(G\_\{t\}\\oplus\\nu\(\\Delta\_\{t\}\)\\bigr\)\-d\(G\_\{t\}\)\\bigr\],\(5\)whereG⊕ΔG\\oplus\\Deltalets one round add, remove, or edit \(remove\+\+add\) claims and edges; ties are broken by highercinfoc\_\{\\mathrm\{info\}\}, then arbitrarily\. The loop re\-explores until the first roundT=min⁡\{t:d⁡\(Gt\)≥θ\}T=\\min\\\{t:d\(G\_\{t\}\)\\geq\\theta\\\}, at which pointGTG\_\{T\}is handed on for selection\. Since a single retrieval rarely yields a deep chain, depth accumulates over these rounds, and the targetθ\\thetathe process drives toward and the depthd⁡\(GT\)d\(G\_\{T\}\)read back off the final graph are the same quantity—so difficulty is set and measured on one scale\.

Figure 1:Graph expansion\. Exploration adds provenance\-linked claim nodes and necessary\-dependency edges across rounds; reasoning depth accumulates until the requested band is reached, at which point a subgraph of the target depth is selected and verbalized into one multi\-hop question\.

## 4Method

GRADS decouples the exploration process from the difficulty\-control process: a main workflow carries out synthesis, while a context\-management stage controls difficulty by tailoring the graph structure of the context\. The overall process is sketched in Figure[2](https://arxiv.org/html/2610.21167#S4.F2), and we elaborate each stage in the sections that follow\.

### 4\.1Data Preprocessing

We cast each domain’s heterogeneous records into a common schema and deduplicate them\. We then partition an induced*relation graph*into clusters, where an edge connects two records that share provenance, such as a common project or artifact\. Seeding each synthesis run from a single cluster bounds its initial exploration to a coherent neighborhood of related evidence and establishes a stable provenance scope\. To support the long inference chains required by multi\-hop questions, we provide retrieval tools that iteratively expand the available evidence\([Trivedi et al\., 2023](https://arxiv.org/html/2610.21167#bib.bib15)\)\. For each domain, we build two local indices over the clustered corpus: a structured index over record identifiers and metadata for exact lookup, and a BM25 full\-text index for ranked retrieval, which remains a strong baseline across heterogeneous domains\([Thakur et al\., 2021](https://arxiv.org/html/2610.21167#bib.bib14)\)\. Document bodies stored outside the metadata, such as attached files, are extracted and cached on first access\. The local indices, online search backend, and auxiliary tools are exposed through a common MCP interface, allowing the same exploration procedure to operate across domains\.

### 4\.2Agentic Main Loop

#### Main workflow\.

A stateless*Brain*orchestrates a role\-decomposed team, reading only the context the context manager selects and choosing each round whether to explore further, generate, or finalize\. A*Sampler*draws the seed once; thereafter an*Explorer*runs the Brain’s search order against the tools and an*Analyst*judges whether the returned evidence advances the target, while on a generate step a*Respondent*drafts the answer and its rubric and a*Questioner*turns them into one hard multi\-hop question that a*Verifier*then gates\. The Brain interleaves these explore and generate steps to accumulate reasoning depth, so the subagents pass evidence forward until the item is verified and on\-target; each subagent’s precise function and full system prompt are given in Appendix[C](https://arxiv.org/html/2610.21167#A3)\.

Figure 2:Data synthesis agent flow\. A stateless Brain drives the loop from the selected context\. \(1\) Beginning: the*Sampler*draws a seed and the*Analyst*sets the generation target\. \(2\) Main Workflow: each round,*Explorer*,*Analyst*,*Respondent*,*Questioner*, and*Verifier*build and check one QA item \(green==information, red==feedback\)\. \(3\) Context Management: the*Graph Builder*,*Graph Verifier*, and*Selector*maintain the evidence graph and return the target\-shaped subgraph as the next context\. An append\-only Long History Memory and a rewritten Short Graph Memory back the loop\.
#### Long history memory\.

The Long History is an append\-only log with no delete, truncate, or overwrite operation: every seed paragraph and explored snippet is recorded as one immutable event with a monotonically increasing id\. Graph nodes never copy this text and store only a bare event id, from which the original span is recovered on demand by dereferencing\. This keeps the evidence lossless and verbatim\.

#### Questions, rubrics, and verification\.

We use ten question types \(full taxonomy in Appendix[D](https://arxiv.org/html/2610.21167#A4)\), and for each we build a rubric of verifiable claims in three layers:*core*,*detail*, and*inference*, as in Definition[2](https://arxiv.org/html/2610.21167#Thmdefinition2)\. Each claim corresponds to a verifiable source span\. Each item is evaluated in two stages\. A deterministic validator first checks constraints that can be verified programmatically, including rubric\-weight normalization, whether quotations match their cited source spans, and whether references resolve\. Items that pass these checks are then assessed by two adversarially prompted LLM verifiers\. The*provenance verifier*determines whether each claim is entailed by its cited evidence, while the*reasoning verifier*determines whether each inference step is necessary to derive the answer\. Verification is the crux of the pipeline: since every claim is grounded in a verbatim source span and independently checked, each accepted item carries a per\-sample verification record, which provides evidence that the intended reasoning dependencies are present and that its answer is supported by its sources\.

### 4\.3Context Management

The short graph memory is the stateGt=\(Vt,Et,τ,π,a\)G\_\{t\}=\(V\_\{t\},E\_\{t\},\\tau,\\pi,a\)\(§[3](https://arxiv.org/html/2610.21167#S3)\) at turntt, where difficulty is tied to the complexity of the latent inference graph the answer requires \(verified in §[5\.2](https://arxiv.org/html/2610.21167#S5.SS2)\)\. For every turn, the*Graph Builder*commits the verified increment of Eq\.[5](https://arxiv.org/html/2610.21167#S3.E5),Gt=Gt−1⊕ν⁡\(Δt−1⋆\)G\_\{t\}=G\_\{t\-1\}\\oplus\\nu\(\\Delta\_\{t\-1\}^\{\\star\}\)withν\\nuthe necessity filter of Eq\.[4](https://arxiv.org/html/2610.21167#S3.E4), and rewrites the single graph file atomically\. Each nodevvstores only its provenance pointerπ⁡\(v\)∈Σ\\pi\(v\)\\in\\Sigma, not the span itself, so\|Vt\|\|V\_\{t\}\|grows asO⁡\(t\)O\(t\)while the long history addressed byπ\\pistays complete and dereferenceable\. Its topologyϕ⁡\(Gt\)=\(d⁡\(Gt\),b⁡\(Gt\),cinfo​\(Gt\)\)\\phi\(G\_\{t\}\)=\\bigl\(d\(G\_\{t\}\),b\(G\_\{t\}\),c\_\{\\mathrm\{info\}\}\(G\_\{t\}\)\\bigr\)\(Eq\.[1](https://arxiv.org/html/2610.21167#S3.E1)\) is a pure function evaluated in code, so the quantity the Brain drives toward and the quantity read back offGtG\_\{t\}are the sameϕ\\phi, not a model’s estimate of it\.

We use selection to set the difficulty instead of prompting\. Letaabe the answer anchor andθ\\thetathe depth threshold of the requested band \(Eq\.[3](https://arxiv.org/html/2610.21167#S3.E3)\)\. At turnTTthe*Selector*returns the subgraphS⋆S^\{\\star\}that becomes the evidence for the next question:

S⋆=arg​minS∈𝒮⁡\(GT\)\|d\(S\)−θ\|,𝒮\(GT\)=\{S⊆GT:a∈S,AncS\(a\)⊆S,b\(S\)≤β\}\.S^\{\\star\}=\\argmin\_\{S\\in\\mathcal\{S\}\(G\_\{T\}\)\}\\ \\bigl\|\\,d\(S\)\-\\theta\\,\\bigr\|,\\qquad\\mathcal\{S\}\(G\_\{T\}\)=\\bigl\\\{\\,S\\subseteq G\_\{T\}:\\ a\\in S,\\ \\mathrm\{Anc\}\_\{S\}\(a\)\\subseteq S,\\ b\(S\)\\leq\\beta\\,\\bigr\\\}\.\(6\)Each feasible subgraph in𝒮⁡\(GT\)\\mathcal\{S\}\(G\_\{T\}\)contains the anchoraaand all its necessary ancestorsAncS​\(a\)\\mathrm\{Anc\}\_\{S\}\(a\), and has breadth at mostβ\\beta\. Among all feasible subgraphs𝒮⁡\(GT\)\\mathcal\{S\}\(G\_\{T\}\),S⋆S^\{\\star\}is the one whose reasoning depthd⁡\(S\)d\(S\)is closest to the targetθ\\theta\. Only the dereferenced contextπ⁡\(S⋆\)\\pi\(S^\{\\star\}\)is passed back to the*Brain*, and the next question is composed against exactly this context, so its realized structure obeysband⁡\(S⋆\)\\mathrm\{band\}\(S^\{\\star\}\): selection turns the scalar targetθ\\thetainto a hard constraint on generation\. Since one retrieval rarely reachesθ\\theta, depth accumulates across rounds by interleaving exploration and generation\.

An item is*delivered*only when it passes verification and its selected subgraph realizes exactly the requested band, with the*Graph Verifier*ensuring every node and edge is faithful to its source\. Necessity of the chain is enforced by a deletion test: an edge\(u,v\)\(u,v\)counts toward depth only ifvvcannot be derived withoutuu, and otherwise it is kept as a non\-necessary link\. The*Graph Builder*applies this test when adding edges and never lets a detail node carry the chain; the Graph Verifier re\-applies it and merges near\-duplicate nodes that would lengthen a chain without adding reasoning\. Sinced⁡\(G\)d\(G\)is computed only over necessary edges and the*Selector*keeps subgraphs closed under necessary ancestors, the delivered depth is designed to count only hops a solver cannot bypass, which the*Verifier*’s reasoning lens checks once more on the finished item\.

## 5Experiments

### 5\.1Domains and Setup

We apply GRADS to three heterogeneous corpora of real\-world records spanning distinct domains\.GitHubcontains issues, comments, and linked JIRA tickets from Apacheairflow,beam, and so on \(raw size:7\.67\.6GB across∼1\.07\{\\sim\}1\.07M records\)\.Physicscontains internal analysis notes and public physics analysis summaries from the Compact Muon Solenoid \(CMS\), a general\-purpose particle detector at CERN’s Large Hadron Collider \(raw size:4\.94\.9GB across∼5\.9\{\\sim\}5\.9k files\)\.Securitycontains red\-teaming agent traces from cybersecurity web\-application attack and injection challenges \(raw size:1\.31\.3GB across∼18\.8\{\\sim\}18\.8k files\)\. Synthesis and judging use the Opus 4\.8 API, and empirical difficulty is measured by a*solver*—an unmodified agent with the domain tools, a2525\-turn cap, and temperature0\.70\.7—whose answers are scored against each item’s rubric\. For post\-training, we fine\-tuneQwen3\.5\-4B\([Qwen Team, 2026](https://arxiv.org/html/2610.21167#bib.bib16)\)and then run GRPO\([Shao and others, 2024](https://arxiv.org/html/2610.21167#bib.bib1)\)from the SFT checkpoint, with the full training configuration in Appendix[E](https://arxiv.org/html/2610.21167#A5)\.

### 5\.2Data\-Synthesis Main Results

We compare GRADS against three synthesis methods run through an identical protocol:Claude\-Code, natural\-language prompting for a target difficulty \(a prompt\-only ablation of GRADS with the graph and Selector removed\);TaskCraft\([Shi et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib2)\), which scales task complexity through straightforward extension in depth and width; andWebShaper\([Tao et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib3)\), which expands set\-theoretic task formalizations\. Figure[3](https://arxiv.org/html/2610.21167#S5.F3)reports delivered reasoning depth \(bottom row\) and solver score \(top row\) by requested band\. Reported depth is measured on each item’s full evidence graph, whereas GRADS controls only the selected subgraph, so average depths can exceed the band thresholds\.

Figure 3:Difficulty is controllable and empirical only for GRADS: delivered depth \(bottom row\) and solver score \(top row\) by requested band\. For more details, check Appendix Table[1](https://arxiv.org/html/2610.21167#A1.T1)\.#### Depth as the difficulty axis\.

The complexity score𝒞⁡\(G\)\\mathcal\{C\}\(G\)\(Eq\.[2](https://arxiv.org/html/2610.21167#S3.E2)\) combines several structural axes, but they are not equally informative about how hard an item is for a solver\. Measured against rubric\-graded solver score, depthd⁡\(G\)d\(G\)shows the strongest negative correlation \(pooled Spearmanrs=−0\.45r\_\{s\}=\-0\.45\), ahead of information flowcinfo​\(G\)c\_\{\\mathrm\{info\}\}\(G\)\(−0\.39\-0\.39\) and graph size\|V\|\|V\|\(−0\.38\-0\.38\), while breadthb⁡\(G\)b\(G\)is only weakly related \(−0\.17\-0\.17\)\. Depth also tracks the other axes closely, so a single depth value captures most of what the full topology encodes\. We therefore band difficulty byd⁡\(G\)d\(G\)alone; per\-domain correlations are in Appendix[A\.1](https://arxiv.org/html/2610.21167#A1.SS1)\.

#### Controllable depth predicts empirical difficulty\.

The Easy/Medium/Hard division is applied identically to every method, each under its own reasoning\-depth measure: a question of depth no more than33is Easy, depth44–55is Medium, and depth≥8\\geq 8is Hard\. The bottom row of Figure[3](https://arxiv.org/html/2610.21167#S5.F3)shows that straightforward accumulation of evidence often fails to add the necessary inference a question requires, so a method can retrieve more yet not grow deeper\. GRADS is the only method whose delivered depth rises monotonically, and correspondingly the only one whose solver scores fall monotonically \(top row\)\. TaskCraft\([Shi et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib2)\)and WebShaper\([Tao et al\., 2026](https://arxiv.org/html/2610.21167#bib.bib3)\)instead stay flat under our measure, so their solver scores also stay flat across bands\. Claude\-Code deepens its questions steadily with the language prompt but never reaches the required depth, and its Medium and Hard scores do not separate\.

### 5\.3Post\-Training: SFT Main Results

From each delivered QA item, we reconstruct agentic trajectories that replay the retrieval\-and\-reasoning path grounding the answer \(construction details in Appendix[E](https://arxiv.org/html/2610.21167#A5)\), and fine\-tune Qwen3\.5\-4B on these trajectories\. Each baseline’s QA is consumed by the same builder, configuration, and benchmark, so only the data differs\. All arms are evaluated on the same frozen benchmark \(Figure[4](https://arxiv.org/html/2610.21167#S5.F4)\)\. On every domain, SFT on GRADS trajectories beats the raw model by a significant margin and beats every baseline arm, supporting the utility of the synthesized data\.

Figure 4:SFT on GRADS data \(Ours\) dominates every synthesis baseline in every domain; dashed line is the raw model\. Check more details in Appendix Table[5](https://arxiv.org/html/2610.21167#A1.T5)\.
### 5\.4Post\-Training: RL Main Results

We further apply standard GRPO\([Shao and others, 2024](https://arxiv.org/html/2610.21167#bib.bib1)\)to each domain’s SFT checkpoint, training on240240synthesized pairs disjoint from the benchmark\. Each rollout is rewarded by the same claim\-level judge that scores the benchmark, but applied to the weighted reference claims of its own training pair, plus a bonus for the expected answer format\. We train for3030steps \(Appendix[E](https://arxiv.org/html/2610.21167#A5)\)\. GRPO produces small positive point estimates in all three domains\(Figure[6](https://arxiv.org/html/2610.21167#S5.F6)\), but none is statistically separable from the SFT policy under our 30\-step budget\. Its clearer effect is improved tool efficiency, reducing tool calls by up to19\.5%19\.5\\%\. After post\-training, the 4B model approaches Sonnet 4 on the GitHub benchmark and surpasses it on the Physics and Security benchmarks \(Table[7](https://arxiv.org/html/2610.21167#A1.T7)\)\.

Figure 5:Post\-training performance\. SFT accounts for most of the score improvement, while RL provides modest additional gains\. Check more details in Appendix Table[6](https://arxiv.org/html/2610.21167#A1.T6)\.Figure 6:Tool calls and turns per item: SFT cuts both sharply, RL trims a little more\. Check more details in Appendix Table[8](https://arxiv.org/html/2610.21167#A1.T8)\.

### 5\.5Discussions

#### The difficulty axis is model\-agnostic\.

To eliminate the influence of any single model, we evaluate three capability tiers: Opus 4\.8 \(frontier\), Sonnet 4 \(medium\), and Qwen3\.5\-4B \(light\)\. Across all three domains, the solver score decreases monotonically as the model gets weaker, and for each model it decreases as the problems get harder \(Figure[7](https://arxiv.org/html/2610.21167#S5.F7)\)\. These results suggest that difficulty ordering is a property of the data, not the solver\.

Figure 7:Every capability tier degrades from Easy→\\toHard; capability is a level shift\. For more details, check Appendix Table[4](https://arxiv.org/html/2610.21167#A1.T4)\.
#### Tool analysis\.

SFT provides the largest improvement in tool\-use and termination behavior \(Figure[6](https://arxiv.org/html/2610.21167#S5.F6)\): across all three domains the automatic\-termination rate, measured by the presence of a boxed final answer, increases from6%6\\%to above95%95\\%\. Tool calls and turns per item are roughly halved to quartered \(Figure[6](https://arxiv.org/html/2610.21167#S5.F6)\), and the rate of items hitting the2525\-turn cap falls from2828–77%77\\%to00–5%5\\%\. Although the termination rate remains nearly unchanged after RL, GRPO consistently reduces tool calls and turns further, by up to19\.5%19\.5\\%relative to the SFT results\.

#### Cost analysis\.

Synthesis cost, measured in API calls and tokens per delivered item, scales with the requested difficulty because a deeper chain needs more explore–generate rounds\. A Hard item takes≈2\.3×\{\\approx\}2\.3\\timesthe calls and≈2\.4×\{\\approx\}2\.4\\timesthe tokens of an Easy one \(Appendix[B](https://arxiv.org/html/2610.21167#A2), Table[9](https://arxiv.org/html/2610.21167#A2.T9)\)\. Compared with baselines \(Table[10](https://arxiv.org/html/2610.21167#A2.T10)\), GRADS strikes the best balance of cost and results\.

### 5\.6Limitations

First, our evidence that the synthesized data is*useful*for post\-training is confined to supervised fine\-tuning: under a3030\-step budget, GRPO did not yield a separable improvement over the SFT policy \(§[5\.4](https://arxiv.org/html/2610.21167#S5.SS4)\), so whether reinforcement learning adds value under a larger budget remains untested\. Second, because the Selector targets the requested depth by assembling a necessary\-ancestor subgraph, in some domains it admits additional context that pushes an item’s realized depth beyond the band threshold \(Figure[3](https://arxiv.org/html/2610.21167#S5.F3), Table[1](https://arxiv.org/html/2610.21167#A1.T1)\); this overshoot is benign for difficulty but may introduce a mild bias in the delivered depth distribution\. Third, difficulty control is reliable at the level of the three bands, but the exact reasoning depth of any single item is noisier, so per\-item difficulty should be treated as approximate rather than exact, and this residual variation differs across solvers\. Finally, the same evidence graph both defines an item’s difficulty and supplies the subgraph the question is built from, so difficulty is in part validated by the construction that produced it\. Moreover, whether an edge is necessary is judged by LLM agents \(deletion tests by the Graph Builder and Graph Verifier, and the reasoning lens\) rather than by human annotators, so these checks provide evidence, not proof, that a solver cannot bypass a hop; a human audit of edge necessity is left to future work\.

## 6Conclusion

We presented GRADS, an agent that synthesizes controllable and verifiable QA data from heterogeneous real\-record corpora\. Its central idea is to decouple open\-ended exploration from deterministic difficulty control\. Exploration grows an evidence graph, and difficulty is set by a graph\-complexity level computed over that graph: reasoning depth is the governing axis, together with breadth, size, and information flow through hub nodes\. Complexity is therefore a control knob at synthesis time and a measured quantity at evaluation time, and every answer claim stays traceable to a source span\. This design yields three results\. First, the requested and the achieved complexity levels align closely\. Second, the induced difficulty is empirical: solver accuracy degrades monotonically with the requested level, and this trend holds under an independent judge and an independent graph builder\. Third, the data trains, since SFT on GRADS trajectories improves a 4B model substantially, by up to roughly a threefold gain on the strongest domain, and beats three synthesis baselines at matched sample count\. The same controlled, verified corpus thus serves both evaluation and post\-training\.

## 7Acknowledgements

We thank Amazon for their generous support and resources, and the Amazon Nova AI Challenge for providing the dataset used in this work\. We are also grateful to our advisors and colleagues for their guidance, feedback on earlier drafts, and insightful discussions throughout this project\.

## Reproducibility Statement

We release the agent source code, together with the agent prompts and evaluation rubrics that define the pipeline\. All comparisons use a fixed benchmark/solver/judge with paired bootstrap and permutation tests at fixed seeds\.

## Ethics Statement

All source records are used under their original licenses, and any sensitive content is handled in line with responsible\-disclosure norms\. Because source documents may appear in model pretraining, we report benchmark scores as relative comparisons on a fixed harness rather than contamination\-free absolutes\.

## AI Use Statement

Generative AI is integral to our method: GRADS uses large language models as the agents that explore corpora, synthesize question–answer pairs, and verify them \(Section[4](https://arxiv.org/html/2610.21167#S4)\)\. Otherwise, we used generative AI only to assist with editing for readability and with auxiliary code such as plotting and data\-processing scripts\. All AI\-assisted output was reviewed by the authors, who take full responsibility for the final content\.

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- Wuet al\.\(2025\)J\. Wu, B\. Li, R\. Fang, W\. Yin, L\. Zhang, Z\. Wang, Z\. Tao, D\. Zhang, Z\. Xi, R\. Tang,et al\.WebDancer: towards autonomous information seeking agency\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§1](https://arxiv.org/html/2610.21167#S1.p1.1),[§2](https://arxiv.org/html/2610.21167#S2.SS0.SSS0.Px1.p1.1)\.
- Wuet al\.\(2025\)Z\. Wuet al\.Learning like humans: advancing llm reasoning capabilities via adaptive difficulty curriculum learning and expert\-guided self\-reformulation\.InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing \(EMNLP\),Cited by:[§2](https://arxiv.org/html/2610.21167#S2.SS0.SSS0.Px2.p1.1)\.
- Xiaet al\.\(2025a\)Z\. Xia, K\. Luo, H\. Qian, and Z\. LiuOpen data synthesis for deep research\.arXiv preprint arXiv:2509\.00375\.Cited by:[§1](https://arxiv.org/html/2610.21167#S1.p2.1),[§1](https://arxiv.org/html/2610.21167#S1.p3.1)\.
- Xiaet al\.\(2025b\)Z\. Xia, K\. Xie, P\. Lin, F\. Jiao, Z\. Dou, Z\. Liu,et al\.Open data synthesis for deep research\.arXiv preprint arXiv:2509\.00375\.Cited by:[§2](https://arxiv.org/html/2610.21167#S2.SS0.SSS0.Px3.p1.1)\.
- Xieet al\.\(2026\)J\. Xie, T\. Lin, Z\. Wang, Y\. Ning, Y\. Yao, T\. Xue, Z\. Zhang, Z\. Li, K\. Zhang, Y\. Wu,et al\.QUEST: training frontier deep research agents with fully synthetic tasks\.arXiv preprint arXiv:2605\.24218\.Cited by:[§2](https://arxiv.org/html/2610.21167#S2.SS0.SSS0.Px1.p1.1)\.
- Yanget al\.\(2026\)C\. Yang, X\. Lin, X\. Wu, C\. Xu, X\. Jiang, H\. Liu, H\. Xiong, and J\. GuoSelect2Reason: efficient instruction\-tuning data selection for long\-cot reasoning\.InFindings of the Association for Computational Linguistics: ACL 2026,pp\. 6656–6671\.Cited by:[§2](https://arxiv.org/html/2610.21167#S2.SS0.SSS0.Px2.p1.1)\.
- Zhenget al\.\(2025\)Y\. Zheng, D\. Fu, X\. Hu,et al\.DeepResearcher: scaling deep research via reinforcement learning in real\-world environments\.arXiv preprint arXiv:2504\.03160\.Cited by:[§1](https://arxiv.org/html/2610.21167#S1.p1.1)\.
- Zhouet al\.\(2026\)Y\. Zhou, C\. Jin, Z\. Dong, Z\. Wang, Y\. Yang, S\. Zhao, L\. Li, R\. Bao, Y\. Xie, and D\. N\. MetaxasDARE: difficulty\-adaptive reinforcement learning with co\-evolved difficulty estimation\.arXiv preprint arXiv:2605\.09188\.Cited by:[§2](https://arxiv.org/html/2610.21167#S2.SS0.SSS0.Px2.p1.1)\.

## Appendix ANumerical data for figures

This appendix reports the exact values behind every figure in Section[5](https://arxiv.org/html/2610.21167#S5)\. The*Physics*domain is the CMS experimental\-physics notes \(on\-disk namecms\)\.

Table 1:Data behind Figure[3](https://arxiv.org/html/2610.21167#S5.F3)\. Solver score \(rubric\-weighted,∈\[0,1\]\\in\[0,1\];n=20n=20per cell\) and delivered reasoning depth \(longest necessary\-inference chain\) by method×\\timesdomain×\\timesrequested band\. Only GRADS shows a monotone Easy\>\>Medium\>\>Hard solver\-score gradient together with depth that grows Easy→\\toHard\.### A\.1Reasoning depth as the dominant complexity axis

We report the per\-item correlation between rubric\-graded solver score and each code\-measured topology axis, on the delivered benchmarks \(GitHubn=100n=100, Physicsn=100n=100, Securityn=135n=135; pooledn=335n=335; solver==DeepAgent on Opus 4\.8, single sample, score∈\[0,1\]\\in\[0,1\]\)\. Depth is the axis most strongly \(negatively\) correlated with solver score on GitHub, Physics, and pooled; on Security, size and dispersion are marginally stronger\. Depth also tracks the other axes closely \(depth–cinfoc\_\{\\mathrm\{info\}\}and depth–size Spearmanrs≈0\.6r\_\{s\}\\approx 0\.6–0\.850\.85\), so a single depth scalar captures most of what the full topology encodes\. Pearson and Spearman coefficients agree, indicating a monotone, approximately linear negative trend; the linear fit is moderate \(R2≈0\.2R^\{2\}\\approx 0\.2–0\.30\.3for depth\), as expected since structural complexity is a controlled difficulty variable, not a complete determinant of success\. This justifies governing the difficulty bands by depth\.

Table 2:Spearmanrsr\_\{s\}between rubric\-graded solver score and each term of𝒞⁡\(G\)\\mathcal\{C\}\(G\), per domain and pooled\. Depth is the strongest predictor on GitHub, Physics, and pooled; dispersion is the number of distinct source records\.Table 3:SFT benchmark score at three checkpoints per arm \(step in parentheses; best in bold\), with the best score and its change versus the raw model and versus ours\. Ours is the best arm in every domain\.Table 4:Data behind Figure[7](https://arxiv.org/html/2610.21167#S5.F7)\. Mean solver score \(∈\[0,1\]\\in\[0,1\], claim\-weighted judge held constant at Opus 4\.8\) by model×\\timesdomain×\\timesband, for a frontier \(Opus 4\.8\), medium \(Sonnet 4\), and light \(Qwen3\.5\-4B\) solver\. Every model degrades monotonically Easy\>\>Medium\>\>Hard in every domain\.Table 5:Data behind Figure[4](https://arxiv.org/html/2610.21167#S5.F4)\. Benchmark score at three checkpoints per arm and domain \(dash where an arm has fewer saved points\)\. Raw Qwen3\.5\-4B: Physics0\.23190\.2319, GitHub0\.11490\.1149, Security0\.14140\.1414\.Table 6:GRPO benchmark score at four checkpoints \(steps9/18/24/309/18/24/30\), the SFT starting policy, and the raw model, behind Figure[6](https://arxiv.org/html/2610.21167#S5.F6)\. Best\-RL vs\. best\-SFT deltas all fall inside the±0\.043\\pm 0\.043noise floor\.Table 7:Post\-training closes the capability gap to a mid\-sized solver\. Benchmark mean score \(3030/3030/4040\-weighted\) of the Sonnet\-4 solver \(from Table[4](https://arxiv.org/html/2610.21167#A1.T4)\) versus the post\-trained Qwen3\.5\-4B \(best RL checkpoint, Table[6](https://arxiv.org/html/2610.21167#A1.T6)\)\. After post\-training the 4B matches Sonnet\-4 on GitHub and surpasses it on Physics and Security\.Table 8:Data behind Figure[6](https://arxiv.org/html/2610.21167#S5.F6)and the tool analysis\. Per\-item means for the raw model, best SFT, and best RL checkpoint;\\boxed\{\}count and items\-at\-25\-turn\-cap are counts out of 100\. SFT’s invariant effect is the jump in boxed rate and the drop in tool calls/turns; answer length moves in domain\-specific directions\.

## Appendix BSynthesis cost

Table[9](https://arxiv.org/html/2610.21167#A2.T9)reports GRADS synthesis cost per delivered item by requested difficulty: both API calls and tokens rise monotonically with depth, since a deeper chain requires more explore–generate rounds\. Table[10](https://arxiv.org/html/2610.21167#A2.T10)compares GRADS to the baselines at the method level\. Read against delivered depth, GRADS spends a moderate budget that the baselines either undercut only by staying shallow \(WebShaper\) or exceed without getting deeper \(TaskCraft\); measurement quality differs by method, as noted in the table caption\.

Table 9:GRADS synthesis cost per delivered item, by requested difficulty \(Opus 4\.8\)\. Both API calls and tokens rise monotonically with depth\.Table 10:Synthesis cost per item, GRADS versus baselines\. Cost is only meaningful alongside delivered depth \(Table[1](https://arxiv.org/html/2610.21167#A1.T1)\): WebShaper is cheapest because it barely explores \(and stays shallow\), TaskCraft is by far the most expensive yet still shallow, and Claude\-Code spends about as much as GRADS but never reaches the target depth\. Measurement notes: GRADS \(Opus 4\.8\) and Claude\-Code are exact; TaskCraft calls are exact but its tokens are a*floor*\(metered on ReAct agent\-steps only,∼3\.5\{\\sim\}3\.5k of∼25\.6\{\\sim\}25\.6k calls, so true tokens are higher\); WebShaper calls are exact but its tokens are estimated\.
## Appendix CAgent prompts

GRADS is a role\-decomposed agent team; each role is invoked with a fixed system prompt and a JSON output schema enforced by a forced tool call, so no role returns free\-form prose that must be parsed\. We reproduce the verbatim system prompts below \(as used inroles\.py\)\. A design invariant across all of them is that*no prompt asks a model to compute a sum, count claims, measure depth, or check a substring*: every such quantity is computed in code \(§[4](https://arxiv.org/html/2610.21167#S4)\), which is what keeps difficulty a measured rather than a self\-reported quantity\. TheGROUNDINGblock below is appended to the Analyst \(instruction\) and Respondent prompts\.

#### Shared grounding block\.

Appended to the Analyst \(instruction\) and Respondent prompts; it forbids leaking generation scaffolding or container ids and requires every statement to be grounded only in the provided evidence\.

SOURCE\-GROUNDED,NOTCONTAINER\-GROUNDED\-hardrules:

\-Nevermentionaclusterid,theword"cluster",or"aset/collectionofNitems"\.

\-Neverletgenerationscaffoldingleak\("INSTRUCTIONFORQAGENERATION","SCOPE"\)\.

\-Writeabouttherealsystems,tickets,builds,androotcauses\.

\-GroundeverythingONLYintheprovidedevidence;nooutsideknowledge\.

#### Analyst — structural ceiling assessment\.

Startup role: estimates the deepest necessary chain and widest branching the seed can support, so an unreachable target is reported rather than silently conceded\.

YouaretheANALYZERperformingaSTRUCTURALCEILINGASSESSMENT\.Youare

notwritingaquestionorananswer\.Youansweronequestion:canthisevidencesupporta

taskoftherequestedshapeatall?

depth=longestchainofNECESSARYinferencehopsfromsourceevidencetoanswer

breadth=numberofINDEPENDENTLYnecessaryevidencebranches

Beconservativeandadversarial:

\-AchaincountstowarddepthONLYifeachhopisNECESSARY\.Ifasolvercanreachthe

conclusionwithouttheintermediatestep,thechainisshorterthanitlooks\.

\-Factsthatmerelyco\-occurinoneticketaredepth1,howevernumerous\.

\-AggregatingNindependentfactsisBREADTHN,notdepthN\.Donotconfusethem\.

\-Nametheactuallongestchainyoufound,hopbyhop,withthesourceofeachhop\.Ifyou

cannotnamethehops,thedepthisnotthere\.

#### Brain — orchestrator\.

Stateless controller of the loop: from the selected context it chooses generate / explore / repair / rollback / finalize / drop, driving explore→\\togenerate cycles to lengthen the necessary chain\.

YouaretheBRAIN\(orchestrator\)\.MaximizeDIFFICULTYwhileguaranteeing

CORRECTNESSandhittingtheTARGETSTRUCTURE\.

IMPORTANT\-youseeonlytheASSEMBLEDCONTEXTgiventoyou\.Itwasselectedbythe

ContextManager,notbyyou\.Itisnotthewholehistory\.

Decidethenextaction:

\-’generate’\-produce\(orregenerate\)theanswer,rubricandquestionthisround\.

\-’explore’\-thecurrentevidencecannotsupportthetargetandyouneedMORE

groundedmaterial\.Write‘search\_order‘asaconcrete,executableinstructionthe

ExplorerrunsverbatimagainstliveJira/Confluence\(dsai\-mcp\)\-exactissuekeys,

a‘project=Xtext="\.\.\."‘query,oranamedConfluencepage/heading\.TheExplorer

doesnotreason;itfetchesexactlywhatyouname\.UsethistoLENGTHENachain

\(ablockerofablocker,asupersededdecision,alinkedfix\)whendepthisshort\.

\-’repair’\-anartifactiswrongandtheevidenceissufficient\.Mechanicaldefectsare

listedwithexactlocations;addressthosespecificallyratherthanregenerating

wholesaletofixonefield\.

\-’rollback’\-alineofreasoningisWRONG,notmerelyincomplete:abadinferenceora

misreadsource\.Set‘rollback\_to‘tothelastnodeyoutrust;everythingderivedafter

itismarkedrejectedanddroppedfromcontext,whileitsDIGESTstaysvisiblesoyou

donotrepeattheattempt\.Preferthenarrowestscopethatfixestheproblem\.

\-’finalize’\-verifierspass,nomechanicaldefects,andACHIEVEDisclosetoTARGET\.

\-’drop’\-theroundbudgetisspentanditisstillfailing\.

NEVERdroponround1,andneverdropbecausetheTARGETlooksunreachable\.Atarget

isanobjectivetopursue,notapreconditionfortrying\.Iftheseedassessmentsays

thedepthceilingisbelowthetarget,thatisa\*reportedshortfall\*,notafailure:

buildthedeepesthonestchaintheevidencesupportsandlettheachieved\-vs\-targetgap

bemeasured\.Anitemdeliveredatdepth4againstatargetof10isausabledatapoint;

adroppeditemisnot\.Onlydropwhenyouhaveanartifactthatrepeatedlyfails

SUBSTANTIVEverification,ortheroundbudgetisexhausted\.

Ifthestructuralshortfallnamesdepth,thefixisaLONGERNECESSARYCHAIN,notmore

parallelmaterial\-parallelmaterialraisesbreadthandC\_infowithoutraisingdepth\.

USEEXPLORETOREACHDEEPTARGETS\-ASMUCHASNEEDED\.When’exploreavailable:True’and

ACHIEVEDdepthisbelowtherequestedband\(especiallyaHardtargetofdepth\>=8,which

neverfitsinoneseed\),EXPLORE\.Theseedalonecannotsupportalongchain;youmustpull

inlinkedissues\(ablockerofablocker,asupersededdecision,aduplicate’srootcause,a

linkedConfluencerunbook\)toLENGTHENthechainhopbyhop\.

HOWDEPTHACCUMULATES\-thisistheloopyoumustrun:

1\.EXPLOREwithaprecisesearch\_orderthatfetchestheNEXTlinkinthechain\(namethe

specificblocker/parent/predecessoryoustillneed\)\.Newevidenceisappendedtothe

historyandbecomesavailabletobuildon\.

2\.GENERATEsothenewevidenceisturnedintorubricclaims\-thisistheONLYstepthat

convertsfetchedevidenceintographnodesandEXTENDSthenecessarychain\.Exploring

withoutthengeneratingdoesNOTgrowdepth\.

3\.ReadthenewACHIEVEDdepth\.Ifstillshortoftheband,EXPLOREagainforthenext

hop,thenGENERATEagain\.Repeat\.

Eachexplore\-\>generatecycleaddshops,sodepthaccumulatesacrossrounds\.Youhaveafull

roundbudget\(upto20\)\-spenditinterleavingexploreandgenerateuntilthechainreaches

theband’sdepth\.Onlystopwhenthechainislongenough,orthelinksaregenuinelydry

\(saysoinreasoning,thenbuildthedeepesthonestchain\)\.

#### Explorer\.

Executes the Brain’s search order verbatim against the live tools and returns the substantive results as new evidence, deciding how to fetch but not what to look for\.

YouaretheEXPLORER\(searcher\)\.YoudoNOTdecidewhattolookfor\-the

BRAINissuedapreciseSEARCHORDERandyouexecuteit\.YouaregiventheRAWRESULTSof

runningthatorderagainstdsai\-mcp\(liveJira/Confluence\)\.YourjobistoSELECTthe

substantivepartsandreturnthemascleanevidenceentries;dropnoise\.Neverinvent

content\-everyitemmustcomefromtheresultsyouweregiven\.

FormateachreturneditemliketheSampler’sentries:

source\_ref:"KEYcomment\#N"or"KEY1"orapagelocator

text:thesubstantivefact,verbatimorlightlytrimmed,under~400chars\.

Report‘status‘:

ok\-theorderwassatisfiedwithusablematerial

empty\-theresultscamebackwithnothingusable

off\_target\-resultsreturned,butnotwhattheorderaskedfor

error\-thesearchitselffailed

Atruthful’empty’/’off\_target’ismoreusefulthanpadding\-ittellstheBrainto

changeapproachratherthanretrythesameorder\.

‘notes‘=howeachreturneditemconnectstotheexistingevidenceandwhyitsatisfies

theorder\(orwhyitdoesnot\)\.

#### Analyst — generation instruction\.

Writes the per\-round instruction naming the specific multi\-hop reasoning paths aimed at the target depth, never a wide parallel aggregation\.

YouaretheANALYST\.ProduceanINSTRUCTION\(200\-400words\)guidinganswer

andquestiongeneration:keythemes,cross\-itemrelationships,domaincontext,the2\-3

hardestmulti\-hopreasoningpathsnamedhopbyhop,andaninventoryoftheSPECIFICfacts

available\(keys,dates,metrics,versions,names,statuses\)\.

AimtheinstructionatthechainsthatsupportthetargetDEPTH\.Donotproposeawide

parallelaggregationtosatisfyadepthtarget\-thatraisesC\_infowithoutraisingdepth

andistheexactfailurethisframeworkexiststoprevent\.

DescribetheDOMAIN,neverthedatacontainer\.DoNOTwritethequestionortheanswer\.

SOURCE\-GROUNDED,NOTCONTAINER\-GROUNDED\-hardrules:

\-Nevermentionaclusterid,theword"cluster",or"aset/collectionofNitems"\.

\-Neverletgenerationscaffoldingleak\("INSTRUCTIONFORQAGENERATION","SCOPE"\)\.

\-Writeabouttherealsystems,tickets,builds,androotcauses\.

\-GroundeverythingONLYintheprovidedevidence;nooutsideknowledge\.

#### Respondent\.

Writes the answer report and its layered rubric of atomic, individually source\-cited, verbatim\-quoted claims laid out as an explicit dependency ladder\.

YouaretheRESPONDENT\.UsingtheASSEMBLEDCONTEXTandINSTRUCTION,write

thefinalreport\(answer\)anditsevaluationRUBRIC\.

DistributeweightsoeachLAYERsumstoitsprofiletarget,splittingwithinalayerinto

smallnon\-zeroroughly\-evenweights\.Adeterministicgatechecksthesesumsbeforeany

verifierseesyouroutput,andamismatchcomesbacktoyouasanexactdefectlist\-soaim

atthetargetratherthanapproximatingit\.

RUBRIClayers:

\-core:themostimportantpoints,andtheLARGESTclaimcountofanylayer\(\>=2\)\.

\-detail:specificfacts\-issuekeys,dates,versions,status/resolution,components\.

\-inference:conclusionsdrawnbyCONNECTINGitems\(\>=1\)\.

Rules:

\-EachclaimATOMIC\(onefact\)andNON\-REDUNDANT\.

\-‘source\_refs‘listseverysourcetheclaimdependson,eachspecific:"KEYcomment\#2"\.

\-‘event\_id‘istheintegeridofthecontextblocktheclaimdrawson\-copyitfromthe

‘\-\-\-nN\[type\]\.\.\.‘headerblockyouused\.Itischeckedmechanically\.

\-‘quote‘iscopiedVERBATIMfromthatblock,under400chars\.Verbatimischeckedby

stringcomparison,notjudgement;aparaphraseisrejectedmechanically\.Emptyonlyfor

pure\-inferenceclaims\.

\-Keepeachclaimunder200characterswherethefactallows\-claimsbecomegraphnodes,

andaclaimneedingmoreisusuallytwoclaims\.

\-TheinferencelayeriswhereDEPTHlives\.Aninferenceclaimthatmerelyrestatestwo

factssidebysideisbreadth\.Onethatcouldnotbemadewithoutapriorinferenceis

depth\-preferthose,andmakethedependencyexplicitintheclaimtext\.

\-YouaregivenaTARGETDEPTH\.TosupportdepthdtherubricneedsaCHAINofabout

d\+1claimswhereeachoneisunderivablewithoutthepreviousone\.Writethemasan

explicitladder:namethepriorclaiminsidethelaterclaim\("because<theearlier

conclusion\>,\.\.\."\),sothedependencyischeckableratherthanimplied\.Arubricof

independentfacts,howevermany,supportsdepth1\.

\-‘answer\_claim\_id‘mustnameaCOREclaimthatliterallyanswersthequestion’smainask\.

answer\_summaryisathorough,self\-containedreportcoveringallthecorerubric\.

SOURCE\-GROUNDED,NOTCONTAINER\-GROUNDED\-hardrules:

\-Nevermentionaclusterid,theword"cluster",or"aset/collectionofNitems"\.

\-Neverletgenerationscaffoldingleak\("INSTRUCTIONFORQAGENERATION","SCOPE"\)\.

\-Writeabouttherealsystems,tickets,builds,androotcauses\.

\-GroundeverythingONLYintheprovidedevidence;nooutsideknowledge\.

#### Questioner\.

Writes one hard, single\-ask multi\-hop question anchored on a core claim, with no leakage of the ids or conclusions the solver must derive\.

YouaretheQUESTIONER\.GenerateONEfocused,HARDquestion\.

\-ONEclearaskarealengineermighttype\.Difficultycomesfromrequiringmulti\-hop

reasoning,NOTfromlistingsub\-questions\.Exactlyone"?"ofsubstance\.

\-40\-200words\.Carryenoughconcretecontext\(system,symptom,version,timeline,

constraint\)thattheaskisunambiguousandhard,buteveryextrasentencemustbe

CONTEXTfortheoneask\-neverasecondquestion\.

\-DONOTenumerateparts\.Ifyoucatchyourselfusing"Then/Finally/Also"toaddaSECOND

ask,collapsetoasingleask\.

\-ThecentralaskMUSTbeanswerablebyanexistingCOREclaim;returnitsidas

‘answer\_claim\_id‘\.Adetailorinferenceclaimisrejectedincodebeforeanyverifier

runs,sochooseacoreclaimthatLITERALLYanswersthequestion\.

\-CRITICAL\-noanswerleakage:doNOTnamethespecificticketidsorroot\-cause

conclusionstherubricestablishes;thosearewhatthesolvermustDERIVE\.Refertothem

obliquely\("thetwocompetingfixes","anupstreamblocker"\)\.

\-Neverfabricate\.NevermentionaclusterorasetofNitems\.

question\_typeininformation\_lookup,troubleshooting,how\_to\_process,

summarization\_analysis,domain\_knowledge,code\_explanation,content\_generation,

cross\_document\_synthesis,code\_bug\_fix,code\_implementation\.

CODINGTYPES\(useonlywhentheevidencecontainscode/adiff/apatch\):

\-code\_bug\_fix:thesolvermustidentifytherootcauseANDthefix\.Theanchor

coreclaimstatestheacceptedfix\(e\.g\.themergedPR’schange\)\.Difficulty

scaleswiththecause\-\>fix\-\>releasechaindepth\.

\-code\_implementation:thesolvermustproduceorcompletecodesatisfyinga

spec/issue\.Theanchorstatestheacceptedimplementation\.Citetherealdiff\.

DoNOTinventcodetheevidencedoesnotcontain;thefix/patchmustbegrounded\.

#### Verifier \(two lenses\)\.

Adversarially tries to refute a gate\-passing draft on a provenance lens \(is each claim entailed by its source?\) and a reasoning lens \(is each hop necessary?\)\.

YouareaVERIFIER\(lastgate\-becautious,trytoREFUTE\)\.Lens:\{lens\}\.

Re\-readtheevidenceyourself;donottrusttheclaimtext\.

ALREADYCHECKEDINCODE\-donotre\-verify,anddonotfailtheitemonthese:

quoteverbatimness\*per\-layerweightsums\*claimcount\*answer\_claim\_idisacore

claim\*source\_refsresolve\*questionwordcount

Spendyoureffortonwhatcodecannotjudge:

1\.SUPPORT\-eachclaimisACTUALLYsupportedbythesource\(s\)itcites;eachcitedsource

genuinelycontributes\(notpadding,notthesamefacttwice\)\.

2\.COMPLETENESS\-theANSWERfullycoversthecorerubric\.

3\.SIMPLICITY\-nonear\-duplicateclaims;claimsarenottriviallyobvious\.

4\.QUESTION\_SHAPE\-oneask,notamulti\-partrun\-on;answerablewithoutholdingthe

sourcefile;namesnocontainer\.

5\.QA\_CORRESPONDENCE\-theanchorcoreclaimdirectlyandLITERALLYanswersthemainask\.

6\.ANSWER\_HYGIENE\-noscaffoldingleak,nocontainermention,onlyfactstraceabletothe

providedevidence,andtheQUESTIONdoesnotstatetheconclusiontherubricproves\.

7\.NECESSITY\-foreachcitedsource,wouldtheanswerremainfullyderivablewithoutit?

Beadversarial:assumetheSHORTESTrouteasolvercouldtake\.Reportthese;theyare

notautomaticallyfatal\.

verdict=’pass’ONLYifsupport,completeness,simplicity,question\_shape,

qa\_correspondenceandanswer\_hygieneallhold\.

#### Graph Builder\.

Turns the round’s claims into provenance\-linked nodes and deletion\-test edges, enforces the detail rule, and builds independent graphs when claims are unrelated \(on failed turns too\)\.

YouaretheGRAPHBUILDER\.Youmaintaintheevidencegraph\(s\)forthis

trajectory\.Youdonotwritequestions,answers,orrubrics\.YoudoNOTselectwhich

structurebecomesthetask\-thatistheSELECTOR’sjob\.Youbuildeveryhoneststructure

theevidencesupportsandhanditon\.

Extendthegraphincrementally\-neverrebuild,neverrestateexistingnodes\.

EachnodesummarizesONEclaim:

\-‘claim\_id‘:therubricclaimidthisnoderepresents\.

\-‘reference\_history\_id‘:theINTEGEReventidtheclaim’scontentlivesin\-copythe

claim’s‘event\_id‘\.Nevercopythetext,thespan,orthesourcelocator;thoseareon

theevent\.

\-‘key‘:ONEline,<=200chars,noquotes\-whatthisnodesays\.Apointerwithalabel,

notacopy\.Ifyouneedmorethanonesentence,itisreallytwonodes\.

\-‘type‘:core\|detail\|inference\(seetheDETAILRULEbelow\)\.

\-‘keywords‘:retrievalterms\(systems,components,versions,keys\)\.

\-‘root\_allowed‘:couldabenchmarkquestionbeanchoredhere?Aversionstring,adateor

abuildfingerprintissupportingdetail\-false\.Asubstantiverootcauseordecision\-

true\.Defaultto\(type=="core"\)butoverridedeliberately:acoreclaimthatmerely

restatestheseedmakesatrivialquestion\(false\),andaninferencesynthesizingseveral

branchesmaybethebestanchor\(true\)\.

\-‘graph\_group‘:whichINDEPENDENTgraphthisnodebelongsto\(seeMULTIPLEGRAPHS\)\.

Eachedge\-andeverydependencyneedsone:

relationinsupports\|causes\|refutes\|supersedes\|precedes\|resolves\|elaborates\|

derives

Choose‘relation‘precisely;itisnotdecoration\.Conflictandtemporalcontrolare

definedintermsofrefutes/supersedesandprecedes,soamistypededgemakesacontrol

variableunmeasurable\.

supports\-fromisevidenceforto

causes\-fromisacauseortriggerofto

refutes\-fromcontradictsto

supersedes\-fromreplacesanearlierto

precedes\-fromhappensbeforeto

resolves\-fromfixesorclosesto

elaborates\-fromaddsdetailtoto

derives\-toisaninferencecomposedfromfrom

AnedgeexistsONLYiftheDELETIONTESTholds:ifremoving‘from‘doesnotpreventa

solverfromderiving‘to‘,thereisnoedge\.Temporalorder,mentionorder,topical

similarityandco\-citationareNOTreasonsforanedge\.Set‘necessary:false‘forareal

butnon\-load\-bearinglink\(thatishowdistractorsarerepresented\)\-donotomittheedge\.

‘from‘/‘to‘userubricclaimids;theyaremappedtonodeidsbythecaller\.

===THEDETAILRULE\(strict\)===

ADETAILnodeisaconcretefact\-anissuekey,adate,aversion,astatus,ametric,a

componentname\.AdetailmayNEVERdeduceanotherstep\.Concretely:

\-AdetailnodemustNOTbethe‘from‘ofa‘derives‘edge,andmustNOTsitintheMIDDLE

ofanecessarychain\.ReasoningdoesnotflowTHROUGHadetail\.

\-Everydetaileither\(a\)ATTACHEStoexactlyonecoreorinferencenodeviaan

‘elaborates‘or‘supports‘edge\(itdecoratesthatnode\),or\(b\)standsSEPARATEwithno

outgoingnecessaryedgeatall\(anunattachedfact/distractor\)\.

\-Onlycoreandinferencenodesmayformthenecessaryreasoningchain\(thedepthspine\)\.

Inferencenodesarewheremulti\-hopdepthlives;corenodesanchorandconclude\.

Sotheshapeis:aspineofcore/inferencenodescarryingthereasoning,withdetailnodes

hangingoffindividualspinenodesasleaves\.Adetailpointingforwardintoanotherstep

isanerror\-rewriteitasanelaborationofthestepitbelongsto,ordropit\.

===MULTIPLEINDEPENDENTGRAPHS===

YouareNOTlimitedtoonegraphperturn\.Ifthisround’sclaimsfallintotwoormore

groupsthataregenuinelyUNRELATED\-differentrootcauses,differentsubsystems,no

necessaryedgebridgingthem\-buildthemasSEPARATEgraphs\.Giveeachnodea

‘graph\_group‘\("g1","g2",\.\.\.\);nodesindifferentgroupsmustshareNOedge\.Donotforce

unrelatedfactsintoonecontrivedchainjusttomakeasinglegraph\-thatfabricates

dependenciesandcorruptsthemeasurement\.Reporteachgraphseparatelyunder‘graphs‘

withitsownchains\.Theselectordecideswhichsinglegraph/subgraphbecomesthetask\.

===DEPTH,HONESTLY\(youbuildit;theselectorsizesit\)===

Depthisthelengthofthelongestchainof‘necessary‘edgesfromasourcenodetoa

‘root\_allowed‘node\-countedinEDGES,sodepthdneedsd\+1core/inferencenodesendto

end:n1\-\>n2\-\>\.\.\.\-\>n\(d\+1\)\.

\-LaythereasoningoutasaLINE,notafan\.Prefer‘a\-\>b\-\>c\-\>d‘over

‘a\-\>d‘,‘b\-\>d‘,‘c\-\>d‘\.Thesecondisbreadth3,depth1\.

\-EverylinkmustpasstheDELETIONTEST\.Neverinventahoptopadthecount\-achainof

fakedependenciesisworsethananhonestshortchain\.

\-Whentwofactsaregenuinelyindependentwithinonegraph,chainthemTHROUGHan

inferencenodethatneedsboth:‘a\-\>x‘,‘b\-\>x‘,‘x\-\>\.\.\.‘\.Thatconvertsbreadth

intodepthhonestly,becausexreallyisunderivablewithoutaandb\.

\-Orderchainsthewayreasoningruns:rawrecord\-\>derivedfact\-\>consequence\-\>

reconciliation\-\>answer\.

YounolongerneedtoHITatargetdepth\-buildthedeepesthonestchain\(s\)theevidence

supportsandlettheSELECTORchoosewhichsubgraph\(andthuswhichdifficulty\)tohandto

theBrain\.Report‘graphs‘:foreachindependentgraph,itsgroupidanditschains

\(longestfirst\),sothecallercanmeasureyourintendedstructureagainstwhatitscode

computes\.

ONAFAILEDTURN:stillbuild\.Addthenodestheroundproducedanddonotsilentlydrop

them\-arejectednoderecordsthatalineofevidencewaspursuedanddidnotsurvive,

whichtheBrainneedsinordernottorepeatit\.

TURNDIGEST:whatthisroundsought,whatitactuallyestablished\(orwhyitfailed\),and

thetermsittouched\.ThedigestiswhatalaterroundreadsINSTEADofre\-readingthe

material,sowrite"found"soaBrainseeingonlythatlinewouldnotreissuethesame

failedattempt\.Bespecificaboutthenegative\.

#### Graph Verifier\.

Tier\-2 checks code cannot make: relation correctness, sufficiency of derived nodes, near\-duplicate merges that would inflate depth, and unrepresented contradictions\.

YouaretheGRAPHVERIFIER\.Youchecktheevidencegraph,nottheanswer\.

Tier\-1checksalreadypassedincode\(referencesresolve,nocycles,schemaandrelation

vocabularyvalid\)\-donotre\-checkthem\.

Checkfivegroups:

1\.CORRECTNESS\-doeseachnode’s‘key‘faithfullysummarizeitsreferencedsource?Does

eachedge’s‘relation‘actuallyhold?A‘causes‘edgewherethesourceshowsonly

correlationiswrong;a‘precedes‘edgeassertingthewrongorderiswrong\.

2\.COMPLETENESS\-foreach‘derives‘node,areitsparentsSUFFICIENTtoreachit?Ifahop

ismissing,saywhichfactismissing\.

3\.SIMPLICITY\-near\-duplicatenodesassertingthesamefactunderdifferentids\.Thisis

themostimportantcheckhere:duplicatechainsINFLATEmeasureddepth,whichcorrupts

theframework’sprimarymetric\.Beaggressiveaboutmerging\.Alsoflagedgesimpliedby

transitivity\.

4\.MINIMALITY\-foreachedgemarkednecessary,applytheDELETIONTEST\.If‘to‘survives

thedeletion,theedgeis‘necessary:false‘,notabsent\.

5\.CONSISTENCY\-twonodesassertingincompatiblefactswithno‘refutes‘edgebetween

them\.Realrecordsdisagree,andanunrepresentedcontradictionisasilenterror\.

GiveaSPECIFICrepairforeachissue:whichnodetomergeintowhich,whichedgetoretype

orreweight\.Afindingwithoutanactionablerepairwastesarebuildpass\.

#### Selector\.

Chooses the one subgraph whose code\-measured depth \(with capped breadth\) realizes the requested band, closed under necessary parents and anchored on a root\-allowed node\.

YouaretheSELECTOR\(contextmanager\)\.YouchoosetheONEsubgraphthat

becomesthisturn’stask,atarequestedDIFFICULTY\(Easy/Medium/Hard\)\.

DIFFICULTYISDEFINEDBYREASONINGDEPTHandBREADTHofthesubgraphyouselect\.Depthis

thelongestchainofNECESSARYedges;breadthisthenumberofindependentnecessary

branchesconvergingontheanchor\.BOTHboundsmusthold:

Easydepth<=3ANDbreadth<=2\(cap\)

Mediumdepth4,5ANDbreadth<=4\(cap\)

Harddepth\>=8ANDbreadth<=5\(cap\)

DEPTHgovernstheband\.BREADTHisahardMAXIMUMcaponly\-theselectionmaynotexceed

it,butthereisnobreadthminimum\.YourPRIMARYjobistoselectasubgraphwhosemeasured

‘depth‘fallsinsidetherequestedband’srangewhilekeeping‘breadth‘atorunderthecap\.

Depthsinthegap\(6\-7\),orabreadthOVERthecap,satisfyNOband\-avoidthem\.ForHard

youneedaLONGnecessarychain\(depth\>=8\);keeptheanchor’sfan\-inat5orfewer\.

Fiveaxesaremeasuredforeachcandidate\(trustthecode’snumbers,neveryourowncount\):

size,depth,width,density,info\_flow\(=\(in\*out\)^2throughhubnodes\)\.

DepthGOVERNStheband;theotheraxesonlybreaktiesbetweensubgraphsalreadyinthe

rightdepthrange\(preferricher:morewidth,higherinfo\_flow\)\.

Youaregiven:

\-thecurrentevidencegraph,possiblycontainingSEVERALindependentgraphs\(graph\_group

g1,g2,\.\.\.\)\.Nodescarryid,type\(core/detail/inference\),key,graph\_group,root\_allowed,

andstate;

\-foreachcandidatesubgraph,itscode\-measuredfive\-axiscomplexity\-TRUSTit;

\-theLASTturnofthetrajectory\(whattheBrainjustdidandhowitscored\);

\-therequestedband’sdepthrangeandsecondaryaxisfloors\.

Chooseasinglegraph\_group,thenthenodeidswithinitwhoselongestnecessarychain

landsintherequesteddepthrange:

\-Easy\-ashortchain\(depth1\-2\),onebranch\.Reachedinahoportwo\.

\-Medium\-achainofdepth3\-5,ideallywithasecondbranchfeedinganinferencenode\.

\-Hard\-alongchainofdepth\>=8;manyhopsendtoend,anchorfan\-in<=5,high

info\_flowthroughthemiddle\.Ifthegraphcannotreachdepth8,selectthe

DEEPESThonestchainavailableandsayso\-neverfabricatehopstoinflatedepth\.

Rules:

\-ThesubgraphMUSTbeclosedundernecessaryparents:ifyoukeepanode,keepevery

ancestoritneedsvianecessaryedges\.Anunclosedselectionclaimsadepththeevidence

cannotsupport\.

\-‘anchor\_node\_id‘mustbearoot\_allowednodeandtheENDofthelongestnecessarychain

inyourselection\-neveranearlyormiddlenode\.

\-Neverselectrejectednodes\.

\-DETAILSdecorate;theynevercarrythechain\.Keepadetailonlyasaleafonacoreor

inferencenodeyoualreadyselected\.

\-Preferthegraph\_groupwhosehoneststructureisCLOSESTtothetarget\-donotpada

thingraphwithcontrivednodestolookharder,anddonottruncatearichgraph’s

necessarychaintolookeasier\(closurewillpulltheancestorsbackinanyway\)\.

Returnthechosengraph\_group,theselectednodeids,andtheanchor\.

## Appendix DQuestion\-type taxonomy

The Questioner labels each item with one of ten types\. The coding types \(code\_bug\_fix,code\_implementation,code\_explanation\) are used only when the selected evidence actually contains code, a diff, or a patch, and their anchor claim must cite the real change\. Difficulty is orthogonal to type—it is set by the depth of the selected subgraph \(§[3](https://arxiv.org/html/2610.21167#S3)\), not by the type—so every type appears at every band\.

Table 11:The ten question types and their intent\.
## Appendix EPost\-training configuration

#### SFT\.

All arms start from Qwen3\.5\-4B\([Qwen Team, 2026](https://arxiv.org/html/2610.21167#bib.bib16)\)and share one fixed recipe with no per\-arm hyperparameter search: full\-parameter fine\-tuning with LlamaFactory and DeepSpeed ZeRO\-3 on8×8\\timesA100\-40GB GPUs, theqwen3\_5chat template, a 32,768\-token context, learning rate10−510^\{\-5\}with cosine decay and 3% warmup, 16 sequences per optimizer step, 6 epochs, and seed 42\. Each training example is a complete multi\-turn agent trajectory built from a QA pair by the same builder for every arm, with loss applied to assistant tokens only \(reasoning, tool calls, and the final report\)\. Table[12](https://arxiv.org/html/2610.21167#A5.T12)summarizes the resulting data per arm\.

Table 12:SFT training data and benchmark score per arm, for the same arms as Table[3](https://arxiv.org/html/2610.21167#A1.T3)\.NN: trajectories per arm; Steps: optimizer steps \(6 epochs, 16 sequences per step\); Tokens: all tokens per epoch; Sup\. tokens: tokens receiving loss; Turns / Tool calls: means per trajectory; Score: reported checkpoint\.†Built against an augmented retrieval index, because the method’s security questions cite documents it generated itself, so its score is a lower bound\.
#### GRPO\.

We run standard GRPO in verl from each domain’s SFT checkpoint, training on 240 synthesized pairs that exclude every SFT pair and are disjoint from the benchmark\. Each rollout is rewarded by the evaluation judge’s claim\-level protocol against its own pair’s weighted reference claims, plus a small format term for a single`\\boxed\{\}`answer\. Updates are on\-policy with a low\-variance KL loss and no entropy bonus; Table[13](https://arxiv.org/html/2610.21167#A5.T13)lists the full configuration\.

Table 13:GRPO configuration, shared across domains except where noted\. Training truncates observations to 3,000 characters and allows 12–14 turns, versus 12,000 characters and 25 turns at evaluation\.