Entity Catalog — WEYL Cosmology

Entities are the real-world quantities that become channels in the trace vector. Each maps to [0,1]ⁿ through the embedding.

14 observable channels across 8 modules

Observable Channels

Channel	Description	Source Module
`hJ`	Lensing amplitude per bin	`limber_integral`
`hb`	Boost-corrected lensing	`boost_factor`
`z_eff`	Effective redshift per bin	`cosmology_background`
`Sigma`	Modified-gravity lensing potential	`sigma_evolution`
`Sigma_0`	Present-day Σ value	`sigma_evolution`
`sigma8`	RMS matter fluctuation amplitude	`sigma_evolution`
`D1`	Linear growth factor D₁(z)	`cosmology_background`
`H_z`	Hubble parameter H(z) [km/s/Mpc]	`cosmology_background`
`chi`	Comoving distance χ(z)	`cosmology_background`
`Omega_m`	Matter density fraction Ω_m(z)	`cosmology_background`
`C_ell`	Angular power spectrum C(ℓ)	`limber_integral`
`T_Weyl`	Weyl transfer function	`weyl_transfer`
`J`	Source-lens-observer geometry	`limber_integral`
`chi2_red`	Reduced chi-squared fit	`weyl_theorems`

Cosmology Background

Source: closures/weyl/cosmology_background.py

4 entities: D₁(z) growth factor, H(z) Hubble expansion, χ(z) comoving distance, Ω_m(z) matter fraction. Computed from Friedmann equations with Planck 2018 parameters (Ω_m,0 = 0.315, h₀ = 0.674).

Sigma Evolution

Source: closures/weyl/sigma_evolution.py

3 entities: Σ modified-gravity lensing potential, Σ₀ present-day value, σ₈(z) fluctuation amplitude. Σ₀ ≠ 1 maps to Collapse regime (T-WL-7).

Limber Integral

Source: closures/weyl/limber_integral.py

3 entities: hJ lensing amplitude, C(ℓ) angular power spectrum, J source-lens geometry. Computed via Limber approximation for DES Y3 tomographic bins (z = [0.295, 0.467, 0.626, 0.771]).

Boost Factor

Source: closures/weyl/boost_factor.py

1 entity: hb boost-corrected lensing amplitude. Nonlinear boost grows with multipole ℓ (T-WL-10).

Beyond Limber

Source: closures/weyl/beyond_limber.py

Corrections beyond the Limber approximation for low-ℓ modes.

Weyl Transfer

Source: closures/weyl/weyl_transfer.py

1 entity: T_Weyl transfer function connecting matter perturbations to lensing observables.

Frozen Cosmological Parameters

Parameter	Value	Source
`z_star`	1100.0	CMB last scattering
`sigma8_planck`	0.811	Planck 2018
`Omega_m_0`	0.315	Present-day matter density
`h_0`	0.674	Hubble constant

DES Y3 Tomographic Bins: z = [0.295, 0.467, 0.626, 0.771]

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