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We present a statistical analysis of large-scale filamentary structure using Sloan Digital Sky Survey (SDSS) data and synthetic cosmological simulations. A 112 630-galaxy catalog within the redshift range 0.06 < z < 0.09 is used to construct a two-dimensional density field via angular binning and Gaussian smoothing, after which a morphology-based filament detection algorithm is applied.
To quantify filament strength, we define a percentile-based observable given by the 98th percentile of the filament intensity field. This procedure is applied consistently to both observational data and an ensemble of 10 000 simulated realizations, yielding a statistical distribution of threshold values. The observed threshold is compared to the simulation distribution using cumulative distribution functions and dispersion measures. We find that the SDSS value lies within the expected range, indicating statistical consistency with ?CDM (Lambda Cold Dark Matter) cosmological models.
As a complementary analysis, we fix the filament intensity threshold to the observed value and measure the fraction of the field exceeding this threshold. The observed fraction lies toward the lower tail of the simulated distribution, suggesting a mild tendency toward less spatially extended high-intensity filamentary structures.
Finally, we discuss limitations related to survey geometry and the projection of the three-dimensional galaxy distribution onto a two-dimensional field, which can reduce the apparent contrast and spatial coherence of filamentary structures.