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Universal Operators operators

12 operators in the universal_operators 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
UNO1Planetary boundary operator: normalized ratio of current to pre-industrial concentration against threshold, measuring safe operating space.B_i = \frac{C_{current} - C_{pre-industrial}}{C_{threshold} - C_{pre-industrial}}, \quad 0 \leq B_i \leq 1 \text{ safe}
UNO10Ecological footprint operator: sum of land-use demands with equivalence and yield factors, compared to biocapacity.EF = \sum_i \frac{C_i}{Y_i} \cdot EQF_i \cdot YF_i, \quad BA = \frac{EF}{BC}
UNO11Natural capital operator: initial stock plus cumulative investment minus depletion minus depreciation over time.K_{natural}(t) = K_0 + \int_0^t [I(\tau) - D(\tau)] d\tau - \delta K(\tau)
UNO12Tipping cascade operator: probability of cascading tipping events through networked Earth system elements with neighbor amplification.P_{cascade} = 1 - \prod_{i=1}^n \left[1 - p_i \cdot (1 + \alpha \sum_{j\in\mathcal{N}(i)} p_j)\right]
UNO13Restoration trajectory operator: logistic recovery toward maximum with disturbance decay and facilitation-driven acceleration.\frac{dR}{dt} = \alpha (R_{max} - R) - \beta R \cdot D + \gamma R(1 - R) \cdot C_{facilitation}
UNO14Universal nature operator: matrix-driven ecosystem state evolution with logistic saturation, spatial diffusion, human forcing, and stochastic noise.\frac{d\vec{N}}{dt} = A\vec{N} + B\vec{N} \circ (1 - \vec{N}) + C\nabla^2 \vec{N} + \vec{F}{human} + \vec{\eta}{stochastic}
UNO2Biosphere integrity operator: weighted sum of genetic diversity, functional diversity, and ecosystem resilience metrics.I = \alpha \cdot H_{genetic} + \beta \cdot F_{functional} + \gamma \cdot R_{resilience}
UNO3Nature contribution operator: weighted biodiversity change rates scaled by area, value, and degradation resistance.NCP = \sum_i w_i \cdot \frac{dB_i}{dt} \cdot A_i \cdot V_i \cdot (1 - R_{degradation})
UNO6Ecological memory operator: exponentially-weighted historical integral of ecosystem disturbance events with baseline memory.M(t) = \int_0^t E(\tau) \cdot \exp\left[-\frac{t-\tau}{\lambda}\right] d\tau + M_0 e^{-t/\lambda}
UNO7Regime shift operator: bistable logistic dynamics with Hill-function harvesting and stochastic perturbation for tipping-point detection.\frac{dx}{dt} = rx\left(1 - \frac{x}{K}\right) - \frac{cx^2}{x^2 + h^2} + \eta(t)
UNO8Nature-based solutions operator: benefit-cost ratio of avoided emissions, carbon removal, and co-benefits versus implementation costs.E_{NBS} = \frac{C_{avoided} + C_{removed} + B_{co-benefits}}{C_{implementation} + C_{maintenance}}
UNO9Biocultural diversity operator: geometric mean of biological and cultural Shannon entropies scaled by linkage strength.D_{biocultural} = \sqrt{H_{biological} \cdot H_{cultural}} \cdot C_{linkage}

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":["UNO1"],"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​