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Exotic States operators

11 operators in the exotic_states 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
ESO10Population growth operator: logistic growth with carrying capacity, spatial diffusion, immigration, and emigration.\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right) + \nabla \cdot (D\nabla N) + I - E
ESO11Cultural evolution operator: frequency-dependent cultural trait dynamics with migration, selection, drift, and spatial diffusion.\frac{df}{dt} = m(1-f) + f(1-f)[\beta_s - \beta_d - \alpha(2f-1)] + D\nabla^2 f
ESO12Game theory Nash equilibrium: best-response condition where no player improves by unilateral strategy deviation.u_i(s_i^, s_{-i}^) \geq u_i(s_i, s_{-i}^*) \quad \forall s_i \in S_i, \forall i
ESO13Behavioral economics (prospect theory): weighted utility with probability distortion and value function from Kahneman-Tversky framework.U(x) = \sum \pi(p_i) v(x_i), \quad \pi(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}}
ESO14Network formation operator: logistic link probability with dyadic covariates and node attribute interactions.P(A_{ij} = 1) = \frac{1}{1 + e^{-\theta_{ij}}}, \quad \theta_{ij} = \beta_0 + \beta_1 w_{ij} + \beta_2 z_i z_j
ESO15Economic inequality (Gini coefficient): mean absolute pairwise income difference normalized by population and mean income.G = \frac{1}{2n^2 \bar{y}} \sum_{i=1}^n \sum_{j=1}^n |y_i - y_j|, \quad 0 \leq G \leq 1
ESO16Financial market operator: geometric Brownian motion with drift, volatility, and Poisson jump process for asset prices.\frac{dS}{S} = \mu dt + \sigma dW + J dN(\lambda), \quad dW \sim \mathcal{N}(0, dt)
ESO17Innovation diffusion: knowledge production with scale effects, logistic saturation, and spillover externalities.\frac{dA}{dt} = \delta A^\phi L^\lambda + \gamma A \left(1 - \frac{A}{A_{max}}\right) + \eta_{spillover}
ESO18Urban economics operator: exponential rent gradient with distance decay and capitalized present-value land pricing.R(d) = R_0 e^{-\alpha d}, \quad P(d) = \int_0^\infty e^{-rt} R(d) dt = \frac{R(d)}{r}
ESO2Economic growth (Solow model): capital accumulation with savings, depreciation, and Cobb-Douglas production with technological progress.\frac{dK}{dt} = sY - \delta K, \quad Y = AK^\alpha L^{1-\alpha}, \quad \frac{dA}{dt} = gA
ESO6Phillips curve: inflation-unemployment tradeoff with adaptive expectations and supply shock term.\pi_t = \pi_t^e - \beta(u_t - u_n) + \epsilon_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":["ESO10"],"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​