Study of the Connected Four-Point Correlation Function of Galaxies from DESI Data Release 1 Luminous Red Galaxy Sample

We present a measurement of the non-Gaussian four-point correlation function (4PCF) from the DESI DR1 Luminous Red Galaxy (LRG) sample. For the gravitationally induced parity-even 4PCF, we detect a signal with a significance of 14.7$\sigma$ using our fiducial setup. We assess the robustness of this detection through a series of validation tests, including auto- and cross-correlation analyses, sky partitioning across multiple patch combinations, and variations in radial scale cuts. Due to the low completeness of the sample, we find that differences in fiber assignment implementation schemes can significantly impact estimation of the covariance and introduce biases in the data vector. After correcting for these effects, all tests yield consistent results. This is one of the first measurements of the connected 4PCF on the DESI LRG sample: the good agreement between the simulation and the data implies that the amplitude of the density fluctuation inferred from the connected 4PCF is consistent with the Planck $\Lambda$CDM cosmology. The methodology and diagnostic framework established in this work provide a foundation for interpreting parity-odd 4PCF.