Twisting the Rules: Mutation and the Structure of Theta Functions
![The scattering function [latex]\operatorname{Scat}(\mu\_{1}({\tilde{B}}))[/latex] is presented alongside its decomposition into contributions from the interval [latex]\eta\_{1}^{B}([-2,3])[/latex] and a function of query [latex]\eta\_{1}^{B}(Q)[/latex], demonstrating how the overall scattering is built from these constituent elements.](https://arxiv.org/html/2603.19391v1/x2.png)
A new study delves into how theta functions behave within cluster algebras during mutation, revealing surprising connections between mathematical structures and providing tools for computation.



![The concatenated repetition code, employing both RM(128,8) and RS( [latex]n_{RS}[/latex],16) constructions, defines the decoding frontier for HQC-128, demonstrating a pathway to robust information recovery despite potential data corruption.](https://arxiv.org/html/2603.20156v1/x1.png)
