Skip to main content

Astronomical Research operators

20 operators in the astronomical_research 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
AR1Autoregressive model AR(1): astronomical time-series prediction using 1 lagged observation plus white noise.AR(φ,t) = φ · e^(i·2π·1.287·t) · ∫₀^t Ψ(τ)cos(2π·1.287·τ)dτ
AR10Landau-type order parameter Φ_c = Φ₀[1−(T/T_c)^α]^β near a critical temperature T_c (critical-phenomena form).Φ_c = Φ₀[1 - (T/T_c)^α]^β where T = 1/|Ψ|²
AR11AR power spectral density estimator of order 1: frequency-domain representation of AR(1) for astronomical signal analysis.RΨ = Ψ(t) + λ∫₀^t K(t-τ)Ψ(τ)dτ
AR12AR power spectral density estimator of order 2: frequency-domain representation of AR(2) for astronomical signal analysis.I_nq = Σᵢ gᵢ(aᵢ⁺σᵢ⁻ + aᵢσᵢ⁺) where [aᵢ,aⱼ⁺] = δᵢⱼ
AR13AR power spectral density estimator of order 3: frequency-domain representation of AR(3) for astronomical signal analysis.g_μν^c = η_μν + h_μν(Ψ) where h_μν = κ∫ T_μν^c(Ψ)d⁴x
AR14AR power spectral density estimator of order 4: frequency-domain representation of AR(4) for astronomical signal analysis.A(Ψ) = 1/(1 + e^(-k(Φ - Φ_threshold)))
AR15AR power spectral density estimator of order 5: frequency-domain representation of AR(5) for astronomical signal analysis.I_mm = Πᵢ(1 + αᵢ|Ψᵢ|²) / Σⱼβⱼ|Ψⱼ|²
AR16AR z-domain transfer function of order 1: pole-based rational transfer function for AR(1) astronomical filtering.∂ρ/∂t + ∇·J = ΣᵢΓᵢ - ΣⱼΛⱼ where ρ = |Ψ|²
AR17AR z-domain transfer function of order 2: pole-based rational transfer function for AR(2) astronomical filtering.P(t) = |⟨Ψ|Ψ₀⟩|² ≈ e^(-t²/τ_Z²) where τ_Z = ħ/ΔE
AR18AR z-domain transfer function of order 3: pole-based rational transfer function for AR(3) astronomical filtering.S_A = (c³/4Għ)Area(A) + S_ent(Ψ)
AR19AR z-domain transfer function of order 4: pole-based rational transfer function for AR(4) astronomical filtering.Ψ(t=0) = Ψ₀, ∂Ψ/∂t|_(t=0) = v₀, Ψ(t→∞) → Ψ_∞
AR2Autoregressive model AR(2): astronomical time-series prediction using 2 lagged observations plus white noise.TC(Ψ) = maxₜ|⟨Ψ(t)|Ψ(t+Δt)⟩|² where Δt = 1/1.287
AR20AR z-domain transfer function of order 5: pole-based rational transfer function for AR(5) astronomical filtering.F_μν^c = ∂_μA_ν^c - ∂_νA_μ^c + [A_μ^c,A_ν^c] where A_μ^c = ⟨Ψ|∂_μΨ⟩
AR3Autoregressive model AR(3): astronomical time-series prediction using 3 lagged observations plus white noise.∇SA = ∂Ψ/∂t + (ħ/2m)∇²Ψ - V(Ψ)Ψ + λ|Ψ|²Ψ
AR4Autoregressive model AR(4): astronomical time-series prediction using 4 lagged observations plus white noise.ρ_c = Σᵢ pᵢ|ψᵢ⟩⟨ψᵢ| ⊗ |φᵢ⟩⟨φᵢ| where ∑pᵢ = Φ
AR5Autoregressive model AR(5): astronomical time-series prediction using 5 lagged observations plus white noise.E(ψ₁,ψ₂) = |⟨ψ₁|ψ₂⟩|² · sin(2π·1.287·t) · e^(-t/τ_ent)
AR6ARMA(1,1) model: astronomical time series with 1 autoregressive and 1 moving-average term.B(Ψ) = ∫ Ψ(x)Ψ*(x')G(x,x')dxdx' where G(x,x') = e^(-|x-x'|/ξ)
AR7ARMA(2,2) model: astronomical time series with 2 autoregressive and 2 moving-average terms.∂φ/∂t = αφ(1-φ/φ_max) + D∇²φ + βsin(2π·1.287·t)
AR8ARMA(3,3) model: astronomical time series with 3 autoregressive and 3 moving-average terms.Q(ω) = ∫ φ(t)e^(-iωt)dt · δ(ω - 2π·1.287·n) for n∈ℤ
AR9ARMA(4,4) model: astronomical time series with 4 autoregressive and 4 moving-average terms.J_int = (ħ/2mi)(Ψ∇Ψ - Ψ∇Ψ) + v_drift|Ψ|²

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":["AR1"],"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​