Evidence for Log-Periodic Modulation in the Redshift Distribution of High-Redshift Compact Sources

We investigate whether the redshift distribution of high-redshift compact sources identified in early James Webb Space Telescope (JWST) observations contains a statistically coherent periodic component in the logarithmic redshift variable $x=\ln(1+z)$. Using a publicly available catalog of 341 sources, we perform an unbinned frequency analysis in which the smooth redshift dependence is removed using a baseline probability distribution. The resulting baseline-corrected power spectrum exhibits a prominent feature at $ω_{\rm peak}=18.33$, corresponding to a logarithmic spacing $Δx\simeq0.34$, or a multiplicative spacing of approximately 1.41 in $1+z$. Monte Carlo realizations of the smooth null model give a local tail probability $p_{\rm local}\simeq2.8\times10^{-3}$. Accounting for the frequency scan over the theoretically motivated interval $16\leqω\leq21$ gives a global false-alarm probability $p_{\rm global}\simeq7.6\times10^{-3}$. Cross-validation, repeated train/test holdout analyses, and field-dependent tests are used to examine the robustness of the feature against statistical fluctuations and sample heterogeneity. The statistical analysis is independent of the physical nature of the individual compact sources. If confirmed with larger and more homogeneous samples, an approximately constant spacing in $\ln(1+z)$ would indicate a preferred multiplicative scale in the high-redshift source distribution. Recurrent cosmological condensate dynamics provide one possible physical interpretation, but the statistical result itself does not depend on this mechanism.