Matter clustering — pk_mm, xi_mm

The matter power spectrum and correlation function.

pk = reg.predict("pk_mm", "LCDM", 0.25, [0.31, 0.677, 0.967, 0.83])   # (1, 147)
xi = reg.predict("xi_mm", "LCDM", 0.25, [0.31, 0.677, 0.967, 0.83])   # (1, 113) SIGNED

Key	Output	Coordinate	Units
pk_mm	(1, 147)	k in h/Mpc	(Mpc/h)³
xi_mm	(1, 113)	r in Mpc/h	dimensionless, signed

The xi_mm support is r ∈ [2.04, 124.8] Mpc/h; this also bounds the radii that xi_hh can request.

Representation

• pk_mm = emulated boost over EH98 linear theory, with the low-k limb anchored to P_lin below k = 0.03 h/Mpc (blended to fully-emulated by 0.1). The anchor closes the frozen-seed large-scale offset.
• xi_mm = EH98 ξ_lin + emulated Δξ (signed; crosses zero near the BAO).

See Representations.

Accuracy (z = 0.25)

• ΛCDM clustering 0.3–0.8 % in the validated windows; xi_mm masked RMS ≈ 0.49 %, BAO band χ_rms ≈ 0.46.
• f(R) composed boosts 0.5–0.9 % LOO.

ξ near the BAO zero crossing

Fractional errors are meaningless where |ξ| < 0.01. The suite masks that region and reports χ vs the across-box SEM instead. Don't divide by ξ there.

Redshift

Registered at z = 0.25 and z = 0.00 for both gravities.

f(R)

Both are MGBoostEmulator artifacts composed with the pinned ΛCDM base — multiplicative ratio for pk_mm, additive Δξ for xi_mm.

Frozen-seed offset

All 64 design models share five IC seeds, so ensemble-mean ξ amplitudes at r ≳ 30 Mpc/h carry a frozen ~+2–3 % offset vs truth (confirmed at both independent-seed fiducials). pk_mm is closed by the low-k anchor; xi_mm remains open (r-space and Hankel-hybrid anchors were tested and rejected). Design-internal comparisons are unaffected. See Caveats.

Evidence harnesses

pk_xi_validation.py (the Phase-2 [pk-gate]/[xi-gate]), fRn1_fiducial_oos.py, k_sweep.py, ablation_sweep.py.