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![The study demonstrates that the position expectation values of electrons and positrons within PsCl exhibit a phase relationship with an applied laser pulse, varying predictably with pulse frequency; specifically, frequencies corresponding to transparent regions, the first positron resonance, and the first electronic resonance ([latex]\mathcal{E}\_{0}=0.0001\,\mathrm{a.u.}[/latex]) induce distinct responses within a computational grid defined by [latex]r\_{\text{max}}=100[/latex] and [latex]l\_{\text{max}}=9[/latex].](https://arxiv.org/html/2603.17203v1/x2.png)

![The study investigates the expected finite-volume energy levels within the [latex] K\pi K\bar{K} [/latex] channel, focusing on the region surrounding the [latex] K^* [/latex] resonance, where the resonance mass is approximately 960 MeV, significantly above the [latex] K\pi [/latex] threshold of 742 MeV, thereby establishing a clear separation between resonance features and background contributions.](https://arxiv.org/html/2603.17900v1/x1.png)