Danus uses a main planner, parallel workers, and a shared verified fact graph to construct long research-level mathematical proofs across six case studies.
On Injectivity of Phase Retrieval
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
In this short note, we prove that if $A \in \mathbb C^{N \times M}$ with $N=4M-5$ has i.i.d.\ standard complex Gaussian entries, then the probability that the phase retrieval map generated by $A$ is not injective is positive. This proves Part (1) of a conjecture of Cynthia Vinzant, which was later restated by Afonso S. Bandeira in \cite{BDL+26}. The main result of this paper was obtained using generative AI, in particular the Rethlas system.
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Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Danus uses a main planner, parallel workers, and a shared verified fact graph to construct long research-level mathematical proofs across six case studies.