νGundam: A unified framework for point-redshift and probability-density-function-aware spatial correlation functions

Photometric-redshift uncertainties redistribute galaxy pairs along the line of sight (LOS) and across projected-separation bins, which dilutes spatial clustering measurements. Modern photo-z methods provide full per-object redshift probability density functions (PDFs), but propagating them directly through standard pair-count estimators remains computationally demanding. We present 1.2 ν Gundam a unified framework for point-redshift and PDF-aware spatial correlation functions. Our aim is to propagate radial PDFs at the pair-count level while retaining a common interface for exact, compressed, and stochastic projected-clustering calculations. The code implements four PDF-aware modes: exact empirical-PDF integration on a shared radial grid, Gaussian-mixture (GMM) compression, Monte Carlo (MC) sampling, and a quantile-compression method, 16quant. All modes accumulate pair counts on a resolved $(r_ ,π)$ grid, from which ξ(r_ ,π) and cumulative w_ (r_ ;Π) are reconstructed. We validated these methods with DESI galaxies and CosmoDC2 mocks using pair-level diagnostics, controlled degradation, convergence tests, and an exact-grid benchmark. p p p p The PDF-aware modes produce nearly indistinguishable LOS redistribution kernels, while point-photo-z estimates discard probabilistic pair information. Controlled Gaussian and empirical-PDF experiments show that radial uncertainty mainly redistributes the existing clustering signal to larger π, and that the LOS depth required to recover the truth-redshift projection scales approximately with the effective pairwise radial dispersion. For practical settings, MC, 16quant, and GMM reproduce the exact-grid result with fractional root-mean-square (RMS) residuals below 5%. Applied to DESI red and blue Bright Galaxy Survey samples, MC sampling recovers their spectroscopic clustering shapes and relative amplitudes for r_ p -1 Mpc -1 Mpc , respectively. Projected clustering with redshift PDFs is best understood as a pair-redistribution problem. When propagated consistently, the projected signal can be recovered accurately and efficiently. The LOS integration depth is nevertheless sample-dependent and should be treated as part of the measurement definition rather than as a fixed technical choice.