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Condensed Matter operators

5 operators in the condensed_matter category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
CDO1NFW dark matter halo density profile and enclosed mass for galaxy rotation curves.\rho(r) = \frac{\rho_0}{\frac{r}{r_s}\left(1 + \frac{r}{r_s}\right)^2}, \quad M(<r) = 4\pi \int_0^r \rho(r') r'^2 dr'
CDO3CMB temperature anisotropy expanded in spherical harmonics with angular power spectrum.\frac{\Delta T}{T}(\theta,\phi) = \sum_{l=2}^\infty \sum_{m=-l}^l a_{lm} Y_{lm}(\theta,\phi), \quad C_l = \langle |a_{lm}|^2 \rangle
CDO5Inflationary cosmology: Friedmann equation with scalar field driving exponential expansion.H^2 = \frac{8\pi G}{3} \left[\frac{1}{2} \dot{\phi}^2 + V(\phi)\right], \quad \ddot{\phi} + 3H\dot{\phi} + V'(\phi) = 0
CDO7Cosmological distance operators: luminosity distance and angular diameter distance as integrals over redshift.d_L(z) = (1+z) \int_0^z \frac{c dz'}{H(z')}, \quad d_A(z) = \frac{d_L(z)}{(1+z)^2}
CDO8Linear structure formation equation: growth of density perturbations in an expanding universe.\frac{d^2\delta}{dt^2} + 2H\frac{d\delta}{dt} = 4\pi G \bar{\rho} \delta, \quad \delta(\vec{x},t) = \frac{\rho(\vec{x},t) - \bar{\rho}(t)}{\bar{\rho}(t)}

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["CDO1"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​