Relativity operators

24 operators in the relativity 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.

Operator	Description	Equation
`ECHO2`	Geometric intuition amplifier integrating the golden ratio over a manifold boundary for Zeq resonance.	`G_int = ∮_∂M φ · dS · ℜ(e^(iλ(M)V))`
`GMC0`	Christoffel connection coefficients computed from the metric tensor derivatives.	`dω + ½[ω, ω] = 0`
`GR31`	Equivalence principle: gravitational and inertial acceleration are locally indistinguishable.	`a_g = a_i`
`GR32`	Einstein tensor built from the Ricci tensor and the scalar curvature.	`G_μν = R_μν - ½Rg_μν`
`GR33`	Einstein field equations relating spacetime curvature to the stress-energy tensor.	`G_μν + Λg_μν = 8πG/c⁴ T_μν`
`GR34`	Geodesic equation of motion for free-fall in curved spacetime.	`d²x^μ/dτ² + Γ^μ_αβ dx^α/dτ dx^β/dτ = 0`
`GR35`	Combined gravitational and velocity time dilation near a mass.	`Δt' = Δt/√(1-v²/c²)`
`GR36`	Radial length contraction in a gravitational field.	`L = L₀√(1-v²/c²)`
`GR37`	Schwarzschild radius — the event-horizon radius of a non-rotating mass.	`r_s = 2GM/c²`
`GR38`	Linearised wave equation for gravitational radiation.	`□h_μν = -16πG/c⁴ T_μν`
`GR39`	Cosmological constant expressed via the dark-energy density parameter.	`Λ = 3H₀² Ω_Λ/c²`
`GR40`	Friedmann equation governing the expansion of a homogeneous, isotropic universe.	`(ȧ/a)² = 8πG/3ρ - kc²/a² + Λc²/3`
`GR41`	Cosmological redshift relating observed and emitted wavelengths.	`z = (λ_obs - λ_emit)/λ_emit`
`GR42`	Relativistic energy: total energy of a particle including rest mass energy with Lorentz factor.	`E = \gamma m c^2`
`GR43`	Relativistic momentum: momentum of a particle with Lorentz factor correction at high velocities.	`p = \gamma m v`
`GR44`	Energy-momentum relation connecting total energy, momentum, and rest mass of a relativistic particle.	`E^2 = (pc)^2 + (mc^2)^2`
`GR45`	Mercury perihelion precession predicted by general relativity, a key test of the theory.	`\Delta\phi = \frac{6\pi GM}{c^2 a(1-e^2)}`
`GR46`	Gravitational light deflection angle for a photon passing near a massive body.	`\delta = \frac{4GM}{c^2 b}`
`GR47`	Gravitational redshift relating the wavelength shift of light escaping a gravitational well.	`z = \sqrt{\frac{1-r_S/r_e}{1-r_S/r_o}} - 1`
`GR48`	Shapiro time delay: extra travel time of light passing near a massive object.	`t_{Shapiro} = \frac{2GM}{c^3}\ln\frac{4r_1 r_2}{b^2}`
`GR49`	Einstein ring radius for gravitational lensing of light by a massive object.	`\theta_E = \sqrt{\frac{4GM}{c^2}\frac{D_{LS}}{D_L D_S}}`
`GR50`	Lense-Thirring frame-dragging precession rate caused by a rotating massive body.	`\Omega_{LT} = \frac{2GJ}{c^2 r^3}`
`LYRA2`	Lyra metric tuner modulating the spacetime metric with HulyaPulse 1.287 Hz oscillation.	`LYRA02 = g_{μν}^{(L)} = g_{μν} · (1 + ε_L · sin(2π·1.287·t) · ⟨T⟩)`
`LYRA5`	Lyra metric oscillator: a driven wave equation coupling curvature to the HulyaPulse frequency.	`LYRA05: ∂²χ/∂t² + (2π·1.287)² χ + ζ(φ)∂_t χ = β_L (R - 8πT)·sin(2π·1.287·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":["ECHO2"],"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.

Compute with one of these​

See also​

Compute with one of these

See also