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Differential operators

27 operators in the differential 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
BM86Magnetic constitutive relation: magnetization proportional to applied magnetic field intensity.B_m^{(86)} = \mu H
CDO2Second-order ordinary differential equation: standard form for linear oscillator problems.w(a) = w_0 + w_a(1 - a), \quad \rho_{DE}(a) = \rho_{DE,0} \exp\left[3\int_a^1 \frac{1 + w(a')}{a'} da'\right]
CDO4Fourth-order differential equation for beam bending and elastic stability problems.P(k) = \frac{2\pi^2}{k^3} \Delta^2(k), \quad \xi(r) = \frac{1}{2\pi^2} \int_0^\infty P(k) \frac{\sin kr}{kr} k^2 dk
CDO6Sixth-order differential equation for advanced structural and continuum mechanics.H(z) = H_0 \sqrt{\Omega_r(1+z)^4 + \Omega_m(1+z)^3 + \Omega_k(1+z)^2 + \Omega_\Lambda}
CF6Skin friction coefficient: wall shear stress normalized by dynamic pressure for boundary layers.C_f^{(6)} = \frac{\tau_w}{\frac{1}{2}\rho v^2}
CNT190Binomial coefficient C(n,190) for combinatorial counting.φ · sin(2π·(1.287/0.618)·t) = φ · sin(2π·2.082·t)
CNT191Generalized binomial coefficient formula for 191 selections from n objects.√(L·R) · 0.95 where L = logical processing, R = intuitive processing
CNT192Sum of binomial coefficients for 192 positions, related to the binomial theorem.sin(2π·1.287·t) + cos(2π·0.618·t) + sin(2π·2.082·t)·cos(2π·0.618·t)
CNT193Multinomial coefficient for distributing 193 objects into groups of specified sizes.Intent · HolographicEncode · Consciousness
ESO1First-order temporal wave equation for exotic state evolution.D(p) = a - bp, \quad S(p) = c + dp, \quad D(p^) = S(p^)
ESO3Third exotic state temporal evolution operator.E_d = \frac{% \Delta Q}{% \Delta P} = \frac{dQ}{dP} \cdot \frac{P}{Q}, \quad E_s = \frac{% \Delta Q_s}{% \Delta P}
ESO4Fourth exotic state temporal evolution operator.\max U(x_1, x_2) \quad \text{subject to} \quad p_1 x_1 + p_2 x_2 = I
ESO5Fifth exotic state temporal evolution operator.Q = f(K, L, T) = A K^\alpha L^\beta T^\gamma, \quad \alpha + \beta + \gamma = 1
ESO7Seventh exotic state temporal evolution operator.\frac{M}{P} = L(Y, i) = kY - hi, \quad i = r + \pi^e
ESO8Eighth exotic state temporal evolution operator.Y = C(Y - T) + I(r) + G + NX, \quad \frac{M}{P} = L(Y, r)
ESO9Ninth exotic state temporal evolution operator.\frac{dx_i}{dt} = \sum_j A_{ij}(x_j - x_i) + \alpha x_i(1 - x_i) + \eta_i(t)
MBO4Laplace equation with Dirichlet boundary conditions for potential theory.E_{MPA} = \frac{S_{inside}}{S_{total}} \cdot \frac{B_{inside}}{B_{outside}} \cdot e^{-\beta D} \cdot (1 + \gamma C)
MBO61Neumann boundary condition: specifying the normal derivative of the solution on the boundary.\frac{\partial u}{\partial n}\bigg|_{\partial\Omega} = h(x)
MBO7Robin (mixed) boundary condition: linear combination of function value and normal derivative.E_{whale} = M_{carcass} \cdot \sum_{t=0}^{T} \eta_t \cdot e^{-\lambda t} \cdot S_{species}(t)
MBO8Interface jump conditions: discontinuities in function value and normal derivative across a boundary.P_{storm} = 1 - \exp\left[-\alpha W \cdot \left(\frac{A_{mangrove}}{A_{coastline}}\right)^\beta\right]
MBO9Green's identity: reciprocity relation for harmonic functions on a boundary.P_{bleach} = \frac{1}{1 + \exp[-\beta(\Delta T \cdot t_{exposure} - \theta)]}
MIO24Double integral over a planar region for area, mass, and moment computation.v_{max} = k \cdot L^{0.5} \cdot M^{0.17} \cdot \eta_{propulsion} \cdot \left(1 - \frac{T}{T_{opt}}\right)^2
MIO3Simpson's rule: numerical integration using parabolic approximation over subintervals.\frac{dS_{arm}}{dt} = \alpha(I_{local} - S_{arm}) + \beta \sum_{j \in \mathcal{N}(i)} (S_j - S_{arm}) + \gamma I_{central}
MIO5Composite Simpson's rule: extended numerical integration for higher accuracy.E_{school} = E_{solitary} \cdot \left[1 - \eta \cdot e^{-d/L} \cdot \cos\left(\frac{2\pi x}{\lambda_{vortex}}\right)\right]
MIO6Gaussian quadrature: numerical integration using optimal abscissas and weights.\frac{d\vec{x}}{dt} = v \cdot \hat{n} + \beta \cdot \nabla B + \gamma \cdot \nabla T + \delta \cdot \nabla S + \vec{\eta}(t)
MIO8Volume integral of density for total mass computation.I_{song} = \sum_{i=1}^{N} \left[ \log_2 \left(\frac{1}{P(phrase_i)}\right) + \alpha \cdot H(phrase_{i+1}|phrase_i) \right]
MIO9Volume integral variant for mass computation with different density profiles.\frac{dA_{ij}}{dt} = \gamma(1 - A_{ij})I_{interaction} - \delta A_{ij}

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":["BM86"],"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​