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Tensor operators

11 operators in the tensor 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
TNO10Genetic rescue operator: heterozygosity increase from introducing new genetic diversity to a small population.\Delta H = \frac{2N_m H_{source}}{N_{total}} \cdot \left(1 - \frac{F}{2}\right) \cdot e^{-t/\tau}
TNO11Fire ecology probability model: fire occurrence from fuel, weather, ignition, and suppression factors.P_{fire} = f(Fuel) \cdot g(Weather) \cdot h(Ignition) \cdot (1 - p_{suppression})
TNO12Watershed hydrological function: runoff from precipitation with storage, evapotranspiration, and infiltration.Q_{out} = \int_0^t P(t) \cdot \left[1 - \exp\left(-\frac{t}{\tau}\right)\right] dt - ET - I
TNO13Species distribution model: logistic regression of occurrence probability from environmental predictors.P(occurrence) = \frac{1}{1 + \exp[-\beta_0 - \sum \beta_i X_i - \sum \gamma_{ij} X_i X_j]}
TNO14Ecological network dynamics: growth, inter-patch dispersal, and disturbance coupling across landscapes.\frac{dE}{dt} = \alpha E(1 - E/K) + \beta \sum_{j\in\mathcal{N}(i)} (E_j - E_i) - \gamma E \cdot D
TNO2Animal migration operator: movement driven by memory, resources, social cues, and genetic programming.\frac{d\vec{x}}{dt} = v\left[\hat{n}{memory} + \alpha \hat{n}{resource} + \beta \hat{n}{social} + \gamma \hat{n}{genetic}\right]
TNO3Pollinator network specialization index: Shannon diversity of plant-pollinator interactions.H_2' = -\sum_{i=1}^S \sum_{j=1}^S p_{ij} \ln p_{ij}, \quad p_{ij} = \frac{n_{ij}}{N}
TNO4Soil carbon turnover model: input, decomposition, and temperature-dependent losses.\frac{dC}{dt} = I - kC + \alpha \frac{dP}{dt} - \beta \frac{dT}{dt}
TNO5Forest growth operator: biomass accumulation from photosynthetically active radiation and environmental factors.\frac{dB}{dt} = \alpha PAR \cdot f(T) \cdot g(W) \cdot h(N) - \beta B^\gamma
TNO7Conservation prioritization: multi-criteria scoring combining species value, connectivity, threats, and costs.P = \sum_i w_i S_i + \alpha \sum_{i\neq j} C_{ij} + \beta \sum_k T_k - \gamma \sum_l C_l
TNO9Climate refuge identification: gradient-based assessment of temperature, precipitation, and habitat connectivity.R = \nabla T \cdot \vec{v}{species} + \alpha \nabla P + \beta \nabla H + \gamma C{connectivity}

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":["TNO10"],"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​