Properties overview

Every property is one registry key per (gravity, redshift). Shapes below are for a single θ (leading axis 1); pass a stack of θ for batched output.

Key	Kind	Output (z = 0.25)	Coordinate
hmf	trained	(1, 23) cumulative n(>M), (Mpc/h)⁻³	log₁₀M left edges
b_cum	trained	(1, 30) b(>M) — ΛCDM; (1, 31) f(R)	log₁₀M thresholds
b_diff	derived	dict: x_grid, b_diff, b_err, cov, checks	log₁₀M
pk_mm	trained	(1, 147) P(k), (Mpc/h)³	k in h/Mpc
xi_mm	trained	(1, 113) ξ(r), signed	r in Mpc/h
xi_hh	derived	dict: xi_hh (Nbin, Nbin, Nr), b_bin, validity	r, log₁₀M bins
xi_hh_smallr	trained	small-r departure surface (used inside xi_hh)	r, threshold pairs
r_ab	trained	(1, 30, 30) cross-correlation coefficient matrix	threshold pairs
vel_m10 … vel_c22	trained	(1, 10, 60) mass-pair × r surface	pair_keys, r

Registered keys

• Both gravities (LCDM, fRn1) are registered for every property at z = 0.25.
• The matter sector (hmf, pk_mm, xi_mm) is additionally registered at z = 0.00.
• r_ab, xi_hh, bias, and velocity are not yet registered at z = 0.

The authoritative live list is haloemu list (or Reference → Registered artifacts).

Picking a property

• Number density vs mass → hmf.
• Linear bias of a mass-selected sample → b_cum (cumulative, >M) or b_diff (differential, at M).
• Matter power / correlation → pk_mm, xi_mm.
• Halo–halo correlation for a mass-bin pair → xi_hh (full scale) which internally uses xi_hh_smallr and r_ab.
• Pairwise velocity statistics → vel_*.