Sealed solvers

32 sealed solvers. Each one is a real endpoint that runs a named numerical method over a fixed operator chain and seals the result in a signed receipt. The table is generated from the x-solver metadata the machine publishes for each route.

Solver	Domain	Numerical method	Operator chain	Unit
`/api/zeq/acoustic`	Acoustics	FV Helmholtz eigensolver	KO42, WM1	Hz
`/api/zeq/action`	Symplectic Mechanics	Leapfrog symplectic map	KO42-tensioned	E
`/api/zeq/auto`	Solver dispatch	NL classifier then dispatch	inherits target solver	varies
`/api/zeq/buckling`	Structural Stability	Generalized eigenvalue FEM	KO42, BEAM_DEFLECTION	N
`/api/zeq/climate`	Geophysical Fluid Dynamics	Finite-volume Lax-Friedrichs	KO42, OC1	h
`/api/zeq/closedform`	Closed-Form Master Field	Analytic branch (compile + cn via AGM) + KO42 perturbation	KO42-tensioned	phi
`/api/zeq/compute`	wizard-selected	7-step wizard protocol	KO42 + up to 3 operators	per-operator
`/api/zeq/device`	Semiconductor Devices	Poisson/Laplace solver (PCG)	KO42, CMP11	V
`/api/zeq/dock`	Molecular Docking	Global optimization (6 DOF)	KO42, BINDING_AFFINITY	epsilon
`/api/zeq/epi`	Epidemiology	Compartmental ODE	KO42, CELL_GROWTH	R0
`/api/zeq/evolve`	Molecular Dynamics	Velocity-Verlet (symplectic)	KO42-tensioned	epsilon
`/api/zeq/fea`	Structural FEA	Q4 FEM, matrix-free PCG	KO42, FEA_DISPLACEMENT, BEAM_DEFLECTION	m
`/api/zeq/flow`	Fluid Dynamics	Semi-Lagrangian projection (Stam)	KO42, FL3	m/s
`/api/zeq/fracture`	Fracture Mechanics	Bond-based peridynamics	KO42, STRESS_ANALYSIS	sigma
`/api/zeq/gauge`	Lattice Gauge Theory	Monte Carlo lattice	KO42, HEP4	plaq
`/api/zeq/grid`	Power Systems	Linear DC power-flow solve	KO42, POWER_ELECTRICAL	pu
`/api/zeq/heat`	Thermal Diffusion	Crank-Nicolson / FTCS / ADI	KO42, CHE17	T
`/api/zeq/kalman`	State Estimation	Recursive Bayes / Riccati (Joseph)	KO42, CS47	err
`/api/zeq/lorenz`	Chaotic Dynamics	RK4	KO42, NL10	1/t
`/api/zeq/lotka`	Population Ecology	ODE integrator (conserved H)	KO42, CELL_GROWTH	T
`/api/zeq/multibody`	HULYAS Master Field (N-body)	RK4 (N-body)	KO42-tensioned	J
`/api/zeq/opt`	Optimization	Numerical optimization (descent)	KO42, CS75	f
`/api/zeq/protect`	PulseGuard Protection	ZEQ-PROTECT operators + Zeq proper-time modulation	KO42 + ZEQ-PROTECT-001/002	P
`/api/zeq/quant`	Quantitative Finance	Monte Carlo (vs Black-Scholes)	KO42, BLACK_SCHOLES	$
`/api/zeq/react`	Reaction-Diffusion	Reaction-diffusion integrator	KO42, ICO9	c
`/api/zeq/sat`	Computational Complexity	DPLL + unit propagation	KO42, CS81	decisions
`/api/zeq/schrodinger`	Quantum Mechanics	FD eigensolver (Sturm bisection)	KO42, QM5	E
`/api/zeq/solve`	HULYAS Master Field	RK4	KO42-tensioned	J
`/api/zeq/tumor`	Growth-Front Dynamics	Reaction-diffusion PDE	KO42, CELL_GROWTH	c
`/api/zeq/unified`	Multi-Domain Composition	Safe evaluator — algebraic / sequential-RK4 / fallback	dynamic (from the operators you pass)	dynamic
`/api/zeq/wave`	Wave Mechanics	Leapfrog (energy-conserving)	KO42, WM1	E
`/api/zeq/zeta`	Analytic Number Theory	Riemann-Siegel root count	KO42	zeros

`/api/zeq/acoustic`

Helmholtz acoustics — -p'' = k^2 p, open/closed ends (finite-volume + half-cell mass, Sturm bisection).


Domain	Acoustics
Numerical method	FV Helmholtz eigensolver
Operator chain	KO42, WM1
Unit	Hz
Endpoint	POST /api/zeq/acoustic

curl -sS -X POST https://zeq.me/api/zeq/acoustic \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/action`

Least-action symplectic mechanics — leapfrog Hamiltonian flow q<-q+(h/2)p; p<-p-h*gradV; q<-q+(h/2)p.


Domain	Symplectic Mechanics
Numerical method	Leapfrog symplectic map
Operator chain	KO42-tensioned
Unit	E
Endpoint	POST /api/zeq/action

curl -sS -X POST https://zeq.me/api/zeq/action \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/auto`

Auto-router — classifies a natural-language query and dispatches to the best-fit solver, which seals under its own source.


Domain	Solver dispatch
Numerical method	NL classifier then dispatch
Operator chain	inherits target solver
Unit	varies
Endpoint	POST /api/zeq/auto

curl -sS -X POST https://zeq.me/api/zeq/auto \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/buckling`

Beam-column buckling — Kphi = P * Kgphi (Hermitian beam FEM); smallest eigenvalue vs the Euler critical load.


Domain	Structural Stability
Numerical method	Generalized eigenvalue FEM
Operator chain	KO42, BEAM_DEFLECTION
Unit	N
Endpoint	POST /api/zeq/buckling

curl -sS -X POST https://zeq.me/api/zeq/buckling \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/climate`

Geophysical fluid dynamics — the shallow-water equations solved with a Lax-Friedrichs finite volume scheme.


Domain	Geophysical Fluid Dynamics
Numerical method	Finite-volume Lax-Friedrichs
Operator chain	KO42, OC1
Unit	h
Endpoint	POST /api/zeq/climate

curl -sS -X POST https://zeq.me/api/zeq/climate \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/closedform`

Closed-form master-equation solve — the analytic counterpart to /api/zeq/solve. Compiles polynomial couplings into effective (mu2_eff, lambda_eff, F_eff) and evaluates the EXACT branch of d2phi/dt2 = mu2_effphi + lambda_effphi^3 + F_eff (all / KO42 tensioner): free, uniform-accel, harmonic, hyperbolic, driven, and Duffing phi0cn(Omegat,k) via AGM. KO42 first-order on the linear branches; phi^2 / sqrt / exp shapes refused by name. Ships an independent RK4 closed-vs-open cross-check.


Domain	Closed-Form Master Field
Numerical method	Analytic branch (compile + cn via AGM) + KO42 perturbation
Operator chain	KO42-tensioned
Unit	phi
Endpoint	POST /api/zeq/closedform

curl -sS -X POST https://zeq.me/api/zeq/closedform \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "mu2_eff": 1,
         "lambda_eff": 1,
         "F_eff": 1,
         "couplings": [
           {}
         ],
         "operators": [
           {}
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "compile": {
           "scale": 1
         },
         "phi0": 1
       }'

`/api/zeq/compute`

Operator compute — the billing spine. Runs the 7-step Zeqond protocol (SELECT · BIND · VALIDATE · COMPUTE · VERIFY · PULSE · RETURN) over KO42 + up to 3 operators and seals a signed receipt.


Domain	wizard-selected
Numerical method	7-step wizard protocol
Operator chain	KO42 + up to 3 operators
Unit	per-operator
Endpoint	POST /api/zeq/compute

curl -sS -X POST https://zeq.me/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/device`

Semiconductor devices — PN-junction built-in voltage and Poisson/Laplace electrostatics (matrix-free Jacobi-PCG).


Domain	Semiconductor Devices
Numerical method	Poisson/Laplace solver (PCG)
Operator chain	KO42, CMP11
Unit	V
Endpoint	POST /api/zeq/device

curl -sS -X POST https://zeq.me/api/zeq/device \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/dock`

Molecular docking — rigid-body 6-DOF minimisation of the Lennard-Jones + Coulomb interaction energy.


Domain	Molecular Docking
Numerical method	Global optimization (6 DOF)
Operator chain	KO42, BINDING_AFFINITY
Unit	epsilon
Endpoint	POST /api/zeq/dock

curl -sS -X POST https://zeq.me/api/zeq/dock \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/epi`

Compartmental epidemiology — SIR/SEIR ODEs; basic reproduction number R0 and epidemic peak.


Domain	Epidemiology
Numerical method	Compartmental ODE
Operator chain	KO42, CELL_GROWTH
Unit	R0
Endpoint	POST /api/zeq/epi

curl -sS -X POST https://zeq.me/api/zeq/epi \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/evolve`

Molecular dynamics — velocity-Verlet NVE over a Lennard-Jones + harmonic potential, energy-conserving.


Domain	Molecular Dynamics
Numerical method	Velocity-Verlet (symplectic)
Operator chain	KO42-tensioned
Unit	epsilon
Endpoint	POST /api/zeq/evolve

curl -sS -X POST https://zeq.me/api/zeq/evolve \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/fea`

Structural FEA — plane-stress K*u=f (Q4 elements, matrix-free Jacobi-PCG); tip deflection vs Euler-Bernoulli.


Domain	Structural FEA
Numerical method	Q4 FEM, matrix-free PCG
Operator chain	KO42, FEA_DISPLACEMENT, BEAM_DEFLECTION
Unit	m
Endpoint	POST /api/zeq/fea

curl -sS -X POST https://zeq.me/api/zeq/fea \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/flow`

Incompressible Navier-Stokes — du/dt+(u.grad)u = -grad p + nu*laplacian(u), div u = 0 (Stam stable fluids).


Domain	Fluid Dynamics
Numerical method	Semi-Lagrangian projection (Stam)
Operator chain	KO42, FL3
Unit	m/s
Endpoint	POST /api/zeq/flow

curl -sS -X POST https://zeq.me/api/zeq/flow \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/fracture`

Bond-based peridynamics — mode-I crack; bonds break on irreversible stretch, cascaded quasi-static equilibrium.


Domain	Fracture Mechanics
Numerical method	Bond-based peridynamics
Operator chain	KO42, STRESS_ANALYSIS
Unit	sigma
Endpoint	POST /api/zeq/fracture

curl -sS -X POST https://zeq.me/api/zeq/fracture \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/gauge`

Lattice gauge theory — compact U(1), Wilson action; mean plaquette vs the exact I1(beta)/I0(beta).


Domain	Lattice Gauge Theory
Numerical method	Monte Carlo lattice
Operator chain	KO42, HEP4
Unit	plaq
Endpoint	POST /api/zeq/gauge

curl -sS -X POST https://zeq.me/api/zeq/gauge \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/grid`

Power systems — DC power flow B*theta=P; line flows and Kirchhoff current law checked.


Domain	Power Systems
Numerical method	Linear DC power-flow solve
Operator chain	KO42, POWER_ELECTRICAL
Unit	pu
Endpoint	POST /api/zeq/grid

curl -sS -X POST https://zeq.me/api/zeq/grid \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/heat`

Heat / thermal diffusion — dT/dt = alpha * laplacian(T) in 1-D and 2-D, Crank-Nicolson / FTCS / ADI, checked vs the exact Fourier decay.


Domain	Thermal Diffusion
Numerical method	Crank-Nicolson / FTCS / ADI
Operator chain	KO42, CHE17
Unit	T
Endpoint	POST /api/zeq/heat

curl -sS -X POST https://zeq.me/api/zeq/heat \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/kalman`

Kalman filter — predict/update with Joseph-form covariance; converges to the discrete-algebraic-Riccati fixed point.


Domain	State Estimation
Numerical method	Recursive Bayes / Riccati (Joseph)
Operator chain	KO42, CS47
Unit	err
Endpoint	POST /api/zeq/kalman

curl -sS -X POST https://zeq.me/api/zeq/kalman \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/lorenz`

Lorenz system — x'=sigma(y-x), y'=x(rho-z)-y, z'=xy-beta*z, RK4; phase-volume contraction invariant.


Domain	Chaotic Dynamics
Numerical method	RK4
Operator chain	KO42, NL10
Unit	1/t
Endpoint	POST /api/zeq/lorenz

curl -sS -X POST https://zeq.me/api/zeq/lorenz \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/lotka`

Lotka-Volterra predator-prey — dx/dt=ax-bxy, dy/dt=dxy-gy; conserved first integral.


Domain	Population Ecology
Numerical method	ODE integrator (conserved H)
Operator chain	KO42, CELL_GROWTH
Unit	T
Endpoint	POST /api/zeq/lotka

curl -sS -X POST https://zeq.me/api/zeq/lotka \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/multibody`

N-body master-equation engine — pairwise Newtonian gravity when positions are supplied, RK4 time-stepping.


Domain	HULYAS Master Field (N-body)
Numerical method	RK4 (N-body)
Operator chain	KO42-tensioned
Unit	J
Endpoint	POST /api/zeq/multibody

curl -sS -X POST https://zeq.me/api/zeq/multibody \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/opt`

Numerical optimization — min f(x) by descent; convergence checked against the known optimum.


Domain	Optimization
Numerical method	Numerical optimization (descent)
Operator chain	KO42, CS75
Unit	f
Endpoint	POST /api/zeq/opt

curl -sS -X POST https://zeq.me/api/zeq/opt \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/protect`

PulseGuard protection heartbeat — computes ZEQ-PROTECT-001 |sin(5phi)|/f_pulse and ZEQ-PROTECT-002 0.5+0.3sin(t/30) from the Zeqond phase, maps a liveness signal (health up/slow/down, or liveness 0..1, or an HTTP status) to a branch (harmonic guard / hyperbolic alarm), and seals the attestation with R(t)=S(t)[1+alphasin(2pi1.287*t)]. guardState OK/DEGRADED/BREACH.


Domain	PulseGuard Protection
Numerical method	ZEQ-PROTECT operators + Zeq proper-time modulation
Operator chain	KO42 + ZEQ-PROTECT-001/002
Unit	P
Endpoint	POST /api/zeq/protect

curl -sS -X POST https://zeq.me/api/zeq/protect \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "t": 1,
         "phase": 1,
         "health": "up",
         "liveness": 1,
         "status": 1
       }'

`/api/zeq/quant`

Quantitative finance — geometric-Brownian-motion Monte-Carlo option pricing, verified vs the Black-Scholes closed form.


Domain	Quantitative Finance
Numerical method	Monte Carlo (vs Black-Scholes)
Operator chain	KO42, BLACK_SCHOLES
Unit	$
Endpoint	POST /api/zeq/quant

curl -sS -X POST https://zeq.me/api/zeq/quant \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/react`

Reaction-diffusion chemical kinetics — coupled species diffuse and react on a grid; steady state / pattern checked.


Domain	Reaction-Diffusion
Numerical method	Reaction-diffusion integrator
Operator chain	KO42, ICO9
Unit	c
Endpoint	POST /api/zeq/react

curl -sS -X POST https://zeq.me/api/zeq/react \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/sat`

Boolean satisfiability — random 3-SAT (hardness peak alpha~4.26), DPLL + unit propagation; assignment certified.


Domain	Computational Complexity
Numerical method	DPLL + unit propagation
Operator chain	KO42, CS81
Unit	decisions
Endpoint	POST /api/zeq/sat

curl -sS -X POST https://zeq.me/api/zeq/sat \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/schrodinger`

Time-independent Schrodinger — Hpsi = Epsi, tridiagonal finite-difference spectrum (Sturm bisection) vs the exact analytic levels.


Domain	Quantum Mechanics
Numerical method	FD eigensolver (Sturm bisection)
Operator chain	KO42, QM5
Unit	E
Endpoint	POST /api/zeq/schrodinger

curl -sS -X POST https://zeq.me/api/zeq/schrodinger \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/solve`

HULYAS master-field solver — integrates the master equation Box-phi - mu^2(r)phi - lambda*phi^3 - e^(-phi/phi_c) + phi_42 * Sum C_k(phi) by RK4.


Domain	HULYAS Master Field
Numerical method	RK4
Operator chain	KO42-tensioned
Unit	J
Endpoint	POST /api/zeq/solve

curl -sS -X POST https://zeq.me/api/zeq/solve \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/tumor`

Fisher-KPP tumor growth-front — du/dt = D u_xx + r u(1-u); front speed vs the Ablowitz-Zeppetella exact wave.


Domain	Growth-Front Dynamics
Numerical method	Reaction-diffusion PDE
Operator chain	KO42, CELL_GROWTH
Unit	c
Endpoint	POST /api/zeq/tumor

curl -sS -X POST https://zeq.me/api/zeq/tumor \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/unified`

Unified multi-domain composer — evaluates a supplied operator list into ONE sealed value with a safe evaluator (no eval/Function): algebraic product, sequential/RK4, or fallback, under the KO42 frame. Operator chain, unit and master equation are derived at runtime.


Domain	Multi-Domain Composition
Numerical method	Safe evaluator — algebraic / sequential-RK4 / fallback
Operator chain	dynamic (from the operators you pass)
Unit	dynamic
Endpoint	POST /api/zeq/unified

curl -sS -X POST https://zeq.me/api/zeq/unified \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/wave`

Wave equation — 2-D membrane d2u/dt2 = c^2 * laplacian(u), energy-conserving leapfrog; exact standing-mode check.


Domain	Wave Mechanics
Numerical method	Leapfrog (energy-conserving)
Operator chain	KO42, WM1
Unit	E
Endpoint	POST /api/zeq/wave

curl -sS -X POST https://zeq.me/api/zeq/wave \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

`/api/zeq/zeta`

Riemann zeta — Riemann-Siegel Z(t); nontrivial zeros of zeta(1/2+it) counted vs N(T).


Domain	Analytic Number Theory
Numerical method	Riemann-Siegel root count
Operator chain	KO42
Unit	zeros
Endpoint	POST /api/zeq/zeta

curl -sS -X POST https://zeq.me/api/zeq/zeta \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{
         "operators": [
           "KO42"
         ],
         "inputs": {
           "mass": 70,
           "r": 1
         },
         "consts": {
           "t": 1
         },
         "domain": "Acoustics",
         "query": "speed of sound in air at 20 C"
       }'

Generated from x-solver in https://zeq.me/openapi.json by scripts/generate-reference.mjs.

/api/zeq/acoustic​

/api/zeq/action​

/api/zeq/auto​

/api/zeq/buckling​

/api/zeq/climate​

/api/zeq/closedform​

/api/zeq/compute​

/api/zeq/device​

/api/zeq/dock​

/api/zeq/epi​

/api/zeq/evolve​

/api/zeq/fea​

/api/zeq/flow​

/api/zeq/fracture​

/api/zeq/gauge​

/api/zeq/grid​

/api/zeq/heat​

/api/zeq/kalman​

/api/zeq/lorenz​

/api/zeq/lotka​

/api/zeq/multibody​

/api/zeq/opt​

/api/zeq/protect​

/api/zeq/quant​

/api/zeq/react​

/api/zeq/sat​

/api/zeq/schrodinger​

/api/zeq/solve​

/api/zeq/tumor​

/api/zeq/unified​

/api/zeq/wave​

/api/zeq/zeta​