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Many Body operators

10 operators in the many_body 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
MBO1Species-area relationship for coral reef biodiversity with power-law scaling.S = cA^z, \quad z = 0.20-0.35 \text{ for coral reefs}, \quad A = \text{reef area}
MBO10Marine genetic diversity: expected heterozygosity and nucleotide diversity metrics.H_e = 1 - \sum_{i=1}^n p_i^2, \quad \pi = \sum_{i\neq j} p_i p_j \pi_{ij}
MBO11Seagrass blue carbon sequestration rate from net primary production and burial fraction.C_{sequestered} = \int_0^T NPP \cdot (1 - R) \cdot f_{burial} dt
MBO12Marine invasive species spread: logistic growth with competitive displacement and density effects.\frac{dI}{dt} = rI\left(1 - \frac{I}{K}\right) + \alpha I(N - I) - \beta I^2
MBO13Ocean acidification chemistry: carbonate ion evolution from CO2 absorption and alkalinity changes.\frac{d[CO_3^{2-}]}{dt} = -k[CO_2] + \beta \frac{dTA}{dt} - \gamma \frac{dDIC}{dt}
MBO14Marine microbiome dynamics: microbial growth with mutualistic/competitive interactions and diffusion.\frac{dM_i}{dt} = \mu_i M_i + \sum_j \epsilon_{ij} M_i M_j - \delta_i M_i + \nabla \cdot (D_i \nabla M_i)
MBO2Marine food web dynamics: predator-prey interactions with logistic growth and trophic efficiency.\frac{dB_i}{dt} = r_i B_i \left(1 - \frac{B_i}{K_i}\right) + \sum_j e_{ij} a_{ij} B_i B_j - \sum_k a_{ki} B_i B_k
MBO3Ocean current larval dispersal: connectivity probability via advection-diffusion kernel.P_{connectivity} = \int_0^\infty \phi(t) \cdot \exp\left[-\frac{(x - ut)^2}{4Dt}\right] dt
MBO5Maximum sustainable yield for fisheries: optimal harvest rate from logistic growth model.Y = \frac{rB}{2} \left(1 - \frac{B}{K}\right), \quad MSY = \frac{rK}{4}, \quad B_{MSY} = \frac{K}{2}
MBO6Marine biological carbon pump: net carbon flux from photosynthesis, respiration, and sinking.F_{carbon} = \int_0^{200m} (P - R - E) dz + F_{sinking} - F_{respiration}

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":["MBO1"],"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​