Andy: A Mathematical Agent for Rigorous Proof and Autonomous Research

Abstract:Andy is an autonomous mathematical research agent that solves and verifies submitted problems, formulates new research problems, and constructs rigorous proofs. It separates proof generation from correctness evaluation and supports knowledge acquisition, targeted revision, and multistage verification. This paper illustrates the workflow using a published result on self-triggered impulsive consensus as a starting point. Andy formulates a global exponential leader-follower synchronization problem for delayed heterogeneous networks with switching communication topologies. The proposed hybrid control combines self-triggered impulses with execution delay and recovery-phase continuous feedback. After each delayed impulse, this feedback cancels the delayed error channel during a recovery window. Sufficient conditions for global exponential synchronization are established, and Zeno behavior is excluded for both the sampling and impulse sequences. A numerical example confirms the result. This case demonstrates Andy's ability to learn from existing results, formulate meaningful research problems, and develop and verify rigorous proofs.

14 pages, 3 figures. Research logs, reports, and simulation code are available at this https URL

Artificial Intelligence (cs.AI); Optimization and Control (math.OC)

arXiv:2608.15052 [cs.AI]

(or arXiv:2608.15052v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.15052 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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