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Morphic Info operators

18 operators in the morphic_info 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
MIO1Whale echolocation beamforming: pressure field with exponential attenuation and Bessel-function angular directivity for cetacean sonar.P(\theta, f) = P_0 \cdot e^{-\alpha(f) r} \cdot \left[\frac{J_1(k a \sin\theta)}{k a \sin\theta}\right]^2 \cdot \Gamma_{target}(f)
MIO10Marine ecosystem energy flow: trophic energy transfer with efficiency coefficients, metabolic losses, and input/output fluxes.\frac{dE_i}{dt} = \sum_j \epsilon_{ij} E_j - \mu_i E_i + I_i - O_i
MIO11Shark electrosensing: bioelectric field detection via ampullae of Lorenzini with inverse-square distance and angular sensitivity.E_{detect} = \frac{I}{4\pi\sigma r^2} \cdot \cos\theta \cdot \eta_{ampullae}
MIO12Sea turtle magnetoreception: Landau-Lifshitz-Gilbert equation for biological magnetite nanoparticle alignment in Earth's field.\frac{d\vec{n}}{dt} = \gamma \cdot \vec{n} \times \vec{B}_{earth} + \alpha \cdot \vec{n} \times \frac{d\vec{n}}{dt}
MIO13Coral spawning synchronization: phase-coupled lunar-tidal oscillation with thermal noise triggering mass reproductive events.\phi_{spawn} = \phi_0 + A \cdot \sin(\omega t + \theta_{moon} + \theta_{tide}) + \eta_{thermal} \cdot \Delta T
MIO14Marine animal communication range: maximum detection range from source level, noise level, and frequency-dependent absorption.R_{max} = \frac{1}{\alpha(f)} \ln\left(\frac{SL - NL}{DT}\right), \quad \alpha(f) = 0.036 f^{1.5} \text{ dB/km}
MIO15Plankton population dynamics: logistic growth with grazing pressure, diffusion-advection transport, and nutrient input.\frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right) - \alpha P Z + \nabla \cdot (D\nabla P - \vec{v} P) + I_{nutrient}
MIO16Deep sea pressure adaptation: Gibbs energy pressure dependence with volume change, compressibility, and equilibrium shift terms.\Delta G(P) = \Delta G(0) + \Delta V \cdot P - \frac{1}{2}\beta \cdot P^2 + k_B T \ln\left(\frac{K(P)}{K(0)}\right)
MIO17Bioluminescent communication: received intensity with exponential attenuation, geometric spreading, spectral filtering, and quantum efficiency.I_{received} = I_0 \cdot e^{-c(\lambda) R} \cdot \frac{A_{eye}}{R^2} \cdot T_{filter}(\lambda) \cdot \eta_{quantum}
MIO18Whale lung collapse physics: Laplace pressure plus elastic shell stress plus tissue pressure governing alveolar collapse at depth.P_{collapse} = \frac{2\gamma}{r} + \frac{E t}{r(1-\nu^2)} + P_{tissue}
MIO19Marine animal buoyancy control: net buoyancy force from displaced water, body mass, hydrodynamic lift, and drag.F_b = g \cdot (\rho_{water} V_{displaced} - m_{body}) + F_{lift} - F_{drag}
MIO2Dolphin click signal processing: temporal resolution and range resolution from maximum click frequency for echolocation.\tau_{resolution} = \frac{1}{2f_{max}}, \quad \Delta R = \frac{c \tau_{resolution}}{2}
MIO20Cetacean deep diving physiology: oxygen depletion rate from allometric metabolism, pressure-dependent lung gas exchange, and nonlinear consumption.\frac{dO_2}{dt} = -k_{metabolic} M^{0.75} + \alpha \frac{dP}{dt} V_{lung} \eta_{collaps} - \beta O_2^{1.5}
MIO21Fish hearing enhancement: incident pressure amplification via impedance matching, otolith gain, and lateral-line coupling.P_{ear} = P_{incident} \cdot \left(1 + \frac{\rho_{fish} c_{fish}}{\rho_{water} c_{water}}\right) \cdot G_{otolith} \cdot \eta_{neural}
MIO22Marine animal thermal regulation: Newton cooling, metabolic heat generation, swimming friction heating, and core-shell temperature gradient.\frac{dT}{dt} = \alpha(T_{water} - T) + \beta P_{metabolic} + \gamma v_{swim}^2 - \delta(T - T_{core})
MIO23Coral calcification rate: light-driven deposition offset by acid dissolution and temperature-dependent bleaching inhibition.\frac{dCaCO_3}{dt} = \alpha \cdot I_{light} \cdot e^{-kz} \cdot \eta_{zoox} - \beta \cdot [H^+] \cdot A_{surface} - \gamma \cdot T_{stress}
MIO4Coral-zooxanthellae symbiosis: light-dependent symbiont growth with thermal stress bleaching and quadratic self-limitation.\frac{dC}{dt} = \alpha \cdot I \cdot e^{-kz} \cdot Z - \beta \cdot C \cdot T_{stress} - \gamma C^2
MIO7Cephalopod dynamic camouflage: chromatophore superposition with Gaussian spatial kernels and phase-modulated color adaptation.I_{skin}(x,y,t) = \sum_{chromatophores} A_i(t) \cdot G\left(\frac{|\vec{r}-\vec{r}_i|}{\sigma_i(t)}\right) \cdot e^{j\phi_i(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":["MIO1"],"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​