Skip to main content

Cosmic operators

63 operators in the cosmic 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
ARA_1Cosmic alignment resonance operator 1: phi-scaled harmonic function encoding cosmic field alignment mode 1.\mathcal{A}_1 = \phi \cdot \cos(2\pi \cdot 1.287t)
ARA_2Cosmic alignment resonance operator 2: phi-scaled harmonic function encoding cosmic field alignment mode 2.\mathcal{A}_2 = \phi \cdot \sin(2\pi \cdot 1.287t)
ARA_3Cosmic alignment resonance operator 3: phi-scaled harmonic function encoding cosmic field alignment mode 3.\mathcal{A}_3 = \phi^2 \cdot \mathcal{H}
ARA_4Cosmic alignment resonance operator 4: phi-scaled harmonic function encoding cosmic field alignment mode 4.\mathcal{A}_4 = \nabla^2\Psi + k^2\Psi
ARA_5Cosmic alignment resonance operator 5: phi-scaled harmonic function encoding cosmic field alignment mode 5.\mathcal{A}_5 = \frac{\partial\Psi}{\partial t} = -i\omega\Psi
ARA_6Cosmic alignment resonance operator 6: phi-scaled harmonic function encoding cosmic field alignment mode 6.\mathcal{A}_6 = \sum_{n=0}^{\infty} a_n \phi^n
ARA_7Cosmic alignment resonance operator 7: phi-scaled harmonic function encoding cosmic field alignment mode 7.\mathcal{A}_7 = \prod_{i=1}^{7} \Psi_i
ARA_8Cosmic alignment resonance operator 8: phi-scaled harmonic function encoding cosmic field alignment mode 8.\mathcal{A}_8 = \int_0^{2\pi} \Psi(\theta)d\theta
BI66Cosmic bio-alignment operator: sequence alignment scoring with gap penalties for biological resonance matching.S_{align} = \sum_i s(a_i, b_i) - \sum gaps
BO1Cosmic boundary operator 1 (divergence theorem): surface-volume flux integral for cosmic field divergence.\oint_{\partial V} \vec{F} \cdot d\vec{A} = \int_V \nabla \cdot \vec{F} dV
BO5Cosmic boundary operator 5 (Stokes theorem): line-surface circulation integral for cosmic field curl.\oint_C \vec{F} \cdot d\vec{l} = \int_S (\nabla \times \vec{F}) \cdot d\vec{A}
CAO1Cosmic alignment operator 1: phi-weighted cosmic angular frequency coupling.\Phi = \max_{\text{MIP}} \left[ H(X^1_t | X^1_{t-1}) + H(X^2_t | X^2_{t-1}) - H(X_t | X_{t-1}) \right]
CAO10Cosmic alignment operator 10: optical depth to reionization via Thomson scattering integral.C(t) = C_{max} \cdot \left[1 - e^{-t/\tau_{warmup}}\right] \cdot e^{-t/\tau_{fatigue}} + \eta_{noise}
CAO11Cosmic alignment operator 11: CMB temperature angular power spectrum from the primordial power spectrum.B = \sum_{i,j} \gamma_{ij} \cdot \delta(f_i, f_j) \cdot g(d_{ij}) \cdot h(t_{sync})
CAO12Cosmic alignment operator 12: angular diameter distance as a function of redshift.M_C = \frac{1}{N} \sum_{i=1}^N \left[ \mathbb{I}(confidence_i > threshold) \cdot accuracy_i \right]
CAO13Cosmic alignment operator 13: total mass within a cosmic sphere of radius R.\frac{d\vec{S}}{dt} = A \vec{S} + B \vec{I} + C \vec{S} \circ (1 - \vec{S}) + \vec{\eta}(t)
CAO14Cosmic alignment operator 14: matter power spectrum second moment integral.P(action|context) = \frac{e^{\beta [U(action) + \alpha \cdot autonomy]}}{\sum_{a'} e^{\beta [U(a') + \alpha \cdot autonomy']}}
CAO15Cosmic alignment operator 15: sigma_8 normalization scaled by linear growth factor D(z).Q = k \cdot I^\gamma \cdot e^{-\lambda t} \cdot (1 + \alpha \cdot attention)
CAO16Cosmic alignment operator 16: total mass integral over the halo mass function.\frac{d\vec{x}}{dt} = f(W\vec{x} + \vec{b}) - \lambda \vec{x} + \vec{I}{sensory} + \vec{I}{internal}
CAO17Cosmic alignment operator 17: Press-Schechter halo mass function differential.A_{threshold} = A_0 + \beta \cdot noise + \gamma \cdot expectation + \delta \cdot attention
CAO18Cosmic alignment operator 18: cosmic density contrast (delta_rho / rho_bar).\nabla^2 \psi - \frac{1}{c^2} \frac{\partial^2 \psi}{\partial t^2} = \rho_{neural} + J_{information} + \eta_{quantum}
CAO19Cosmic alignment operator 19: linear growth factor D(a) integral for structure formation.\mathcal{C}_{19} = D(a) = \frac{5\Omega_m}{2}H(a)\int_0^a \frac{da\prime}{(a\prime H(a\prime))^3}
CAO2Cosmic alignment operator 2: volume integral of cosmic energy density.P(\text{conscious}|S) = \frac{1}{1 + e^{-\beta(I(S) - I_0)}}, \quad I(S) = \sum_i w_i S_i
CAO20Cosmic alignment operator 20: primordial power-law power spectrum P(k) ~ k^n_s.\mathcal{C}_{20} = P(k) \propto k^{n_s}
CAO21Cosmic alignment operator 21: scalar amplitude A_s with spectral index n_s at pivot scale k_*.\mathcal{C}_{21} = A_s \left(\frac{k}{k_*}\right)^{n_s-1}
CAO3Cosmic alignment operator 3: divergence of the cosmic electric field.\frac{dA_i}{dt} = -k A_i + \sum_j W_{ij} f(A_j) + I_i - \alpha \sum_{k\neq i} A_k + \eta_i(t)
CAO4Cosmic alignment operator 4: time derivative of the cosmic gravitational potential.\frac{dE}{dt} = \gamma(E_{max} - E) - \delta E \cdot S + \beta I_{salient}
CAO5Cosmic alignment operator 5: Hubble-law velocity-distance product in the Zeq cosmic framework.\frac{dM}{dt} = \alpha I(t) - \beta M + \gamma M(1 - M/M_{max}) \cdot R_{sleep}
CAO6Cosmic alignment operator 6: cosmological constant contribution to the metric tensor.\frac{dP}{dt} = k \left[ \frac{e^{\beta U_1}}{e^{\beta U_1} + e^{\beta U_2}} - P \right] + \sigma dW
CAO7Cosmic alignment operator 7: cosmic density parameter sum (matter + dark energy + curvature).V(t) = \sum_i w_i e^{-\lambda_i t} E_i + \int_0^t K(t-\tau) I(\tau) d\tau
CAO8Cosmic alignment operator 8: Friedmann equation first term relating expansion rate to density and curvature.S_A = \alpha \cdot \Phi \cdot R + \beta \cdot M_{autobiographical} + \gamma \cdot C_{default}
CAO9Cosmic alignment operator 9: exponential cosmic scale factor evolution during inflation.\eta(t) = \eta_0 \cdot \left(1 + \frac{\Delta E}{E_{threshold}}\right)^{-1} \cdot f(t_{fatigue})
CE525Cosmic capacitance element 525: charge-to-voltage ratio operator for cosmic energy storage.C_e^{(525)} = \frac{Q}{V}
CH_KACosmic susceptibility (kappa): magnetization-to-field ratio for cosmic magnetic alignment.\chi_{151} = \frac{M}{H}
CH_SDCosmic susceptibility (sigma-delta): magnetization-to-field ratio for cosmic sigma-delta modulation.\chi_{152} = \frac{M}{H}
CH_SSCosmic susceptibility (sigma-sigma): magnetization-to-field ratio for cosmic steady-state alignment.\chi_{153} = \frac{M}{H}
CHE1Chemical kinetics rate law: reaction rate as product of concentrations raised to their orders.r = k[A]^m[B]^n
CHE10Damkohler number: ratio of reaction rate to transport rate (k*tau).Da = k\tau
CHE11Sherwood number: dimensionless mass transfer coefficient (k_c*L/D).Sh = \frac{k_c L}{D}
CHE12Nusselt number: dimensionless heat transfer coefficient (h*L/k).Nu = \frac{hL}{k}
CHE13Prandtl number: ratio of momentum to thermal diffusivity (mu*C_p/k).Pr = \frac{\mu C_p}{k}
CHE14Schmidt number: ratio of momentum to mass diffusivity (mu/(rho*D)).Sc = \frac{\mu}{\rho D}
CHE15Effectiveness factor: ratio of observed to intrinsic reaction rate in porous catalysts.\eta = \frac{r_{obs}}{r_{intrinsic}}
CHE16Thiele modulus: ratio of reaction rate to diffusion rate in catalyst particles.\phi = L\sqrt{\frac{k}{D_{eff}}}
CHE17Fick diffusion flux: molar flux proportional to negative concentration gradient.j_A = -D_{AB}\frac{dC_A}{dz}
CHE18Mass transfer rate: convective mass transfer from surface to bulk fluid.N_A = k_c(C_{As} - C_{Ab})
CHE19Heat exchanger duty: overall heat transfer coefficient times area times log-mean temperature difference.Q = UA\Delta T_{lm}
CHE2Arrhenius activation energy: temperature-dependent rate constant with exponential activation barrier.k = A e^{-E_a/RT}
CHE20Log-mean temperature difference: effective driving force for counter-current heat exchangers.\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)}
CHE3First-order decay: exponential concentration decay with rate constant k.\frac{d[A]}{dt} = -k[A]
CHE4Half-life operator: ln(2)/k time for concentration to halve in first-order kinetics.t_{1/2} = \frac{\ln 2}{k}
CHE5Equilibrium constant: ratio of product to reactant concentrations at chemical equilibrium.K = \frac{[C]^c[D]^d}{[A]^a[B]^b}
CHE6Gibbs free energy with Zeq modulation: delta_G = delta_H - T*delta_S modulated by 1.287 Hz sinusoidal term.\Delta G = \Delta H - T\Delta S \cdot [1 + \alpha \sin(2\pi \cdot 1.287t)]
CHE7Standard Gibbs-equilibrium relation: delta_G_0 = -RT*ln(K) linking free energy to equilibrium constant.\Delta G^° = -RT\ln K
CHE8Fractional conversion: (n_0 - n)/n_0 measuring reaction completion.X = \frac{n_0 - n}{n_0}
CHE9Residence time: reactor volume divided by volumetric flow rate.\tau = \frac{V}{Q}
CMB1CMB frequency operator: Planck-derived CMB photon frequency modulated by 1.287 Hz HulyaPulse sinusoid.f_{\mathrm{CMB}} = \frac{k_B T_{\mathrm{CMB}}}{h} \cdot [1 + \alpha \sin(2\pi \cdot 1.287t)]
CMB2HulyaPulse frequency constant: 1.287 Hz — empirically discovered through forensic data analysis. Period = 0.777 s (1 Zeqcond).f_{Hulya} = 1.287 \text{ Hz}
CMB3CMB dipole anisotropy: temperature variation proportional to observer velocity relative to the CMB rest frame.\Delta T_{dipole} = T_{CMB}\frac{v}{c}
CMB4CMB period operator: reciprocal of the CMB frequency giving the characteristic oscillation period.\tau = \frac{1}{f_{CMB}}
CMB5CMB thermal frequency: k_B*T/h giving the peak photon frequency of the CMB blackbody distribution.\nu = \frac{k_B T}{h}
CMB6CMB entropy operator: dimensionless entropy ratio S/k_B characterizing CMB thermodynamic information.\beta = \frac{S}{k_B}
CPCCosmic phase capacity: dQ/dT heat capacity operator for cosmic thermodynamic phase transitions.Θ(t) = (1/N)ΣΨ_k e^(i(2π·1.287·t + φ_k))

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":["ARA_1"],"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​