1：Experimental Design and Method Selection:

The study involved developing a direct coordinate-based Triple-Correlation algorithm (dTC) to analyze multiplexed super-resolution images. The algorithm was designed to compute the probability density of geometric configurations from single-molecule localizations in three channels, avoiding the computational cost of 4D Fourier Transforms.

2：Sample Selection and Data Sources:

Simulations were performed with designed triangular configurations on a canvas, and experimental data were obtained from U2OS cells labeled with specific proteins (e.g., EdU, PCNA, MCM, RPA) using immunofluorescence and SMLM techniques.

3：List of Experimental Equipment and Materials:

Equipment included a customized Leica DMI 300 inverse microscope, various lasers (e.g., 750 nm, 639 nm, 561 nm, 488 nm), a Zeiss HCX PL APO 63X NA = 1.47 OIL CORR TIRF Objective, a Photometrics Prime95B sCMOS camera, and antibodies (e.g., Alexa Fluor conjugates). Materials included U2OS cells, DMEM, FBS, Penicillin-Streptomycin, Hydroxyurea, EdU, Aphidicolin, Triton, paraformaldehyde, and imaging buffer components.

4：47 OIL CORR TIRF Objective, a Photometrics Prime95B sCMOS camera, and antibodies (e.g., Alexa Fluor conjugates). Materials included U2OS cells, DMEM, FBS, Penicillin-Streptomycin, Hydroxyurea, EdU, Aphidicolin, Triton, paraformaldehyde, and imaging buffer components. Experimental Procedures and Operational Workflow:

4. Experimental Procedures and Operational Workflow: Cells were prepared, labeled, and imaged using SMLM. Images were aligned using a polynomial mapping algorithm. Single-molecule localization was performed using Maximum Likelihood Estimation (MLE) on GPU. The dTC algorithm was applied to compute Triple-Correlation profiles and identify significant geometric configurations.

5：Data Analysis Methods:

Data were analyzed using the dTC algorithm to compute Triple-Correlation functions, identify local maxima, and quantify molecular densities. Statistical analyses included unpaired t-tests for comparisons.