$ν$Gundam: a unified framework for point-redshift and PDF-aware spatial correlation functions
Context. Photometric-redshift uncertainties redistribute galaxy pairs along the line of sight (LOS), diluting spatial clustering measurements. Propagating full redshift probability density functions (PDFs) through standard pair-count estimators remains computationally demanding. Aims. We present $ν$Gundam, a unified framework to propagate radial PDFs at the pair-count level while retaining a common interface for exact, compressed, and stochastic projected-clustering calculations. Methods. The code implements four modes: exact empirical-PDF integration, Gaussian-mixture compression, Monte Carlo (MC) sampling, and a quantile-compression method. All modes accumulate pair counts on a resolved ($r_\mathrm{p},π$) grid, from which $ξ(r_\mathrm{p},π)$ and $w_\mathrm{p}(r_\mathrm{p};Π)$ are reconstructed. We validate these with DESI galaxies and CosmoDC2 mocks. Results. The PDF-aware modes produce nearly indistinguishable LOS redistribution kernels, while point-photo-$z$ estimates discard probabilistic pair information. Radial uncertainty mainly redistributes the clustering signal to larger $π$; the depth required to recover the truth projection scales with the pairwise radial dispersion. For practical settings, MC, quantile, and Gaussian-mixture compression reproduce the exact result with fractional RMS residuals below 5%. Applied to DESI Bright Galaxy Survey samples, MC sampling recovers spectroscopic clustering shapes and relative amplitudes for $r_\mathrm{p}\gtrsim0.8\,h^{-1}\mathrm{Mpc}$ using sample-dependent recovery depths of ~400 and ~$180\,h^{-1}\mathrm{Mpc}$ for red and blue galaxies. Conclusions. Projected clustering with redshift PDFs is a pair-redistribution problem. When propagated consistently, the signal is recovered accurately and efficiently. The integration depth is sample dependent and should be part of the measurement definition rather than a fixed choice.