Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery

Alizer Wong; Heng Cui; Yi Tan; Xiongchao Zhan; Liang Lin; Yuxiang Guo; Zhaorong Dai; Zixin Zeng

cs.AIAug 19, 2026

Eureka: Task-Conditioned Meta-Agent Orchestration for Scientific Discovery

Authors: Alizer Wong, Heng Cui, Yi Tan, Xiongchao Zhan, Liang Lin, Yuxiang Guo, Zhaorong Dai, Zixin Zeng,

Organizations: ManXis · School of Information Engineering, Guangdong University of Technology · School of Automation, Guangdong University of Technology · School of Artificial Intelligence, South China Normal University ·

Abstract

We present Eureka, a task-conditioned Meta-Agent architecture that compiles long-horizon tasks into dynamic obligation graphs with explicit acceptance semantics. During execution, Eureka forms Macro-Agents with specialized state, memory, operators, tools, verifiers, and local topology via receding-horizon planning, architecture promotion, and minimal-sufficient compilation. When bottlenecks recur, cost-benefit-gated evolution updates the local architecture under constraints. Theoretically, we establish results on regret, planning invalidation, amortization, subtree interfaces, serializability, and verification. Experimentally, Eureka completes 170/170 recursive tasks and generates 3,948 certificates with no false acceptances. Active context compresses median input from 9,490 to 4,005 tokens; incremental processing avoids 65.38% recomputation across 12,000 tasks; 16,000 concurrent executions serialize consistently. The same Meta-Agent instantiates a Theory-Discovery Agent and a Math/Conjecture Agent. The former yields structural results in quantum-process and spacetime theory. The latter identifies bottlenecks in Riemann Hypothesis research and advances a positivity certificate for Suzuki's localized Weil quadratic form to 0 < a <= 69/200 = 0.345, reaching ~99.55% of (log 2)/2. These results suggest that scientific-agent capability depends not only on the base model but on whether an architecture can be formed to match the task's cognitive structure.

Figures & tables

Scientific track	Specialized agent formed by Eureka	Main advances	Current evidence status
Riemann Hypothesis	Math/Conjecture Agent	operator-access obstruction; finite/local Chebyshev cone separation; finite-cluster interpolation; localized Weil positivity certificate candidate $\lambda_{a}>0$ for $0<a\leq 69/200$	analytic derivation + 1,010-cell outward interval certificate candidate; not an RH proof
New Theoretical Structures	Theory-Discovery Agent	full-rank conjunction interiorization; algebraic null-sector decoupling; global acted-set normal form; behavioural-interface equivalence separation; operational intervention signature	exact/internal certificates and large-scale regression; some results still require external or formal review

Table 1

Figure 1: Overview of Eureka. The Meta-Agent compiles a task into a dynamic obligation graph, forms task-conditioned specialized agents when architecture hotspots emerge, governs local evolution, and coordinates recursive long-horizon execution under typed verification.

Symbol	Definition
$\Omega,\mathscr{F},\mathbb{P}$	underlying probability space for task stochasticity
$T$	a task instance; $\mu$ denotes the task distribution
$X_{t}$	latent task state at time $t$ , valued in a standard Borel space $\mathcal{X}$
$O_{t}$	observation available before action $A_{t}$ , valued in $\mathcal{O}_{\mathrm{obs}}$
$A_{t}$	orchestration/execution control action, valued in $\mathcal{A}_{\mathrm{ctrl}}$
$C_{0}$	initial Task Contract, Acceptance Contract, budget, permissions, and corpus cutoff

Table 3

Symbol	Definition
$S\subseteq V_{t}$	connected local subgraph of the current obligation graph, or a subgraph of its condensation DAG, under analysis
$\tau_{S}$	local stopping time at which subtree $S$ is completed or closed
$N_{S}$	number of future local service events generated by $S$ from the current time until $\tau_{S}$
$F_{S}$	one-time synthesis, state-migration, and interface-installation cost of promoting $S$ to a Macro-Agent
$G_{k},M_{k}$	incremental cost of the $k$ -th local service under generic execution and Macro-Agent execution, respectively
$\delta_{S},\bar{\delta}_{S}$	conservative lower and upper bounds on per-service cost savings

Table 4

Symbol	Definition
$\mathfrak{M}_{t}(S)$	finite set of admissible mutations that may be proposed for Macro-Agent subtree $S$ at time $t$
$m\in\mathfrak{M}_{t}(S)$	a specific architecture mutation
$\mathcal{A}_{S}^{(m)}$	candidate architecture obtained by applying mutation $m$ to current local architecture $\mathcal{A}_{S}$
$C_{m}^{\mathrm{evo}}$	fixed diagnosis, generation, evaluation, migration, and deployment cost of mutation $m$
$M_{k}^{(m)}$	incremental cost of the $k$ -th future local service under candidate architecture $\mathcal{A}_{S}^{(m)}$
$\gamma_{m},\bar{\gamma}_{m}$	conservative lower and upper bounds on per-service savings produced by mutation $m$

Table 5

Symbol	Definition
$\mathcal{J}_{\alpha}(\pi;T)$	expected total cost of fixed admissible policy $\pi$ at reliability threshold $1-\alpha$
$\pi^{[0]},\ldots,\pi^{[J]}$	hybrid policies obtained by successively replacing Eureka decision modules with an oracle under the same information constraint
$J$	number of independently replaceable decision modules; we use $J=6$
$\Delta_{j}^{\mathrm{H}}$	exact total-cost difference induced by the $j$ -th hybrid replacement
$d_{\mathrm{TV}}$	total variation distance between two probability measures
$\varepsilon_{j}$	cumulative total-variation discrepancy of decision module $j$ relative to its oracle kernel

Table 6

Task family	Eureka-generated agent	Core state	Main verification
Open Theory Discovery	Theory-Discovery Agent	hypotheses, assumptions, evidence, counterexamples, experiments	theory consistency, falsification, computational/experimental evidence
Open-Conjecture Mathematical Discovery	Math/Conjecture Agent	facts, claims, lemmas, proof obligations, exact receipts	exact computation, proof certificates, formal/programmatic verification

Table 7

Architecture dimension	Theory-Discovery Agent	Math/Conjecture Agent
Persistent state	Hypothesis-Evidence state	Fact-Claim-Proof state
Generative operators	hypothesis search, mechanism synthesis	lemma discovery, proof construction
Negative operators	falsification, alternative explanation	counterexample, proof obstruction
Verification	experiments, evidence, consistency	exact/formal proof verification
Parallel regions	independent falsification/retrieval/experiments	independent lemmas/retrieval/exact computation
Continuity requirement	persistent theory state	persistent proof state

Table 8

Metric	Result
Fixed recursive tasks completed	50 / 50
Random recursive tasks completed	120 / 120
Acceptance certificates	3,948
Uncertified accepts	0
False terminal states	0
Stagnation aborts	0

Table 9

Execution schedule	Median completion time	Relative speed
Round-based	0.5058 s	1.0000 $\times$
Eureka streaming	0.2724 s	1.8569 $\times$

Table 10

Evolution policy	Median total cost	Success rate
No Evolution	2686.8	58.09%
Always Evolve	3637.7	58.83%
Evolve on Stall	2860.1	58.00%
Eureka Governed Evolution	2525.4	60.55%

Table 11

Runtime mechanism	Main result
Compiled active context	57.8% median context reduction
Incremental dependency rebuild	65.38% recomputation avoided
Dependency slicing	56.69% recomputation-ratio reduction
Delta deterministic closure	60.58% rule-work reduction
Closed common-subderivation reuse	81.82% duplicate evaluations avoided
Certified-equivalence representation	70.97% representation reduction

Table 12

Ablation	Result
Independent repeated open search	58.488% success
Memoized first open-search result	24.492% success
Approximate semantic merge	100% false merge on adversarial set
Exact/certified merge	0% false merge
Combined runtime open-action changes	0 / 12,000

Table 13

Concurrency metric	Result
Concurrent executions	16,000
Serial-equivalent final states	16,000 / 16,000
Unsafe commits	0
Unnecessary rebase reduction	75.0%
Fanout reusable prefill	64.24%

Table 14

Task family	Eureka-generated architecture	Core persistent state	Main discovery outputs	Discovery result
Open Theory Discovery	Theory-Discovery Agent	hypotheses, assumptions, evidence, counterexamples, experiments	conjunction interiorization; assumption elimination; global acted-set normal form; behavioural/interface separation; operational signature	5 / 5
Open-Conjecture Mathematical Discovery	Math/Conjecture Agent	facts, claims, lemmas, proof obligations, exact receipts	mixed-branch second-order projection; two-axis increment/orbit law; extent-inverse-map correspondence	3 / 3

Table 15

End-to-end evidence dimension	Result
Recursive long-horizon tasks completed	170 / 170
Acceptance certificates generated	3,948
Theory-discovery structures accepted	5 / 5
Mathematical discovery structures accepted	3 / 3
Mathematical deterministic composite checks	2,200 / 2,200
Mathematical additional stochastic checks	960 / 960

Table 16

Robustness dimension	Evaluation scale	Result
Architecture invariance under entity renaming	5,000	5,000 / 5,000
Theory transfer task families	8	8 / 8
Theory capability coverage	11 dimensions	11 / 11
Math primitive generality categories	10	10 / 10
Math deterministic composite checks	2,200	2,200 / 2,200
Math stochastic checks	960	960 / 960

Table 17

Planning strategy	Median total orchestration cost	Median planning cost	Median outer round trips
Full Upfront Planning	11,573.5	5,820	44
Recursive Polling	8,039.0	3,636	13
Streaming without Backpressure	5,756.5	2,704	6
Eureka Receding-Horizon + Backpressure	4,506.0	2,084	9

Table 18

Promotion policy	Promotion rate	False-promotion rate	Missed-beneficial rate	Median execution cost
Complexity-Only Promotion	53.90%	14.90%	–	–
Structural Promotion Gate	32.92%	7.46%	–	–
Eureka Cost-Aware Lazy Promotion	39.19%	0.04%	8.71%	2,277.13
Cost-optimal reference	–	–	0%	2,262.65

Table 19

Meta-control configuration	Median total cost	Median planning cost	Median execution-context cost	Median outer round trips	P90 total cost
Receding-horizon controller	5,231.5	2,386.0	2,808.0	10	10,478
Full Eureka Meta-Control	4,272.0	1,823.5	2,388.0	8	8,565

Table 20

Theoretical result	Experimental intervention	Observed result
Receding-Horizon Planning	Upfront / polling / streaming / backpressure	Planning cost 2,084 , lowest among four strategies
Promotion Amortization	Complexity / structural / cost-aware gate	False promotion 0.04% ; cost within 0.64% of reference
Information-Sufficient Context	Full history vs. compiled context	9,490 → 4,005 , success unchanged
Incremental Reconstruction	Full vs. dependency-local rebuild	65.38% recomputation avoided; final state 100% identical
Safe Parallel Merge	Concurrent vs. serial reference	16,000/16,000 serial-equivalent; unsafe commits = 0
Governed Evolution	No / always / stall / governed	Cost 2,525.4 , success 60.55%

Table 21

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LLM-based agents have shown increasing potential in automating scientific discovery. Given an optimizable metric and an execution environment, they can propose, validate, and iterate scientific solutions, and have produced results that outperform human-designed approaches. As model capabilities continue to improve, we argue that the bottleneck for autonomous scientific discovery is shifting from prescribing agent workflows to designing agent environments: the resources, constraints, and interfaces that shape agent behavior. We frame this as environment engineering: building environments that amplify productive behaviors, such as open-ended exploration, systematic artifact management, and inter-agent collaboration, while suppressing harmful behaviors, such as reward hacking and high-friction human oversight. We present EurekAgent, an environment-engineered agent system for metric-driven autonomous scientific discovery. EurekAgent engineers the environment along four dimensions: permissions engineering for bounded agent execution and isolated evaluation; artifact engineering for filesystem and Git-based collaboration; budget engineering for budget-aware exploration; and human-in-the-loop engineering for easy human supervision and intervention. EurekAgent sets new state-of-the-art results on multiple mathematics, kernel engineering, and machine learning tasks, including new state-of-the-art 26-circle packing results discovered with less than $11 in total API cost. We open-source our code and results, and call for environment engineering as a core research direction for developing reliable autonomous research agents.

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