Eight ways to put a problem into the market.
Each solver encodes a class of problems as orders and reads the answer from fills. All eight have been validated with real capital on live Binance Futures.
Continuous optimization
liveFind the minimum of any objective.
Minimize a smooth multi-dimensional function. The market relaxes downhill along the negative gradient encoded as constraint forces.
Boolean satisfiability (SAT)
liveSatisfy every clause at once.
3-SAT and k-SAT. Each violated clause becomes a penalty force; equilibrium is a satisfying assignment.
Linear systems & regression
liveSolve Ax = b, fit y = mx + c.
Residual r = Ax − b becomes a restoring force F = −Aᵀr that vanishes exactly at the solution.
Eigenvalue problems
liveRecover spectra from the market.
Dominant and interior eigenvalues of structured matrices via substrate relaxation.
Shortest path
liveOptimal routes through a graph.
Path-cost constraints push flow onto the minimum-cost route; fills read out the path.
ODE initial-value problems
betaIntegrate dynamics forward.
Euler residual of the discretized ODE is driven to zero step by step.
Polynomial roots
betaFind where it vanishes.
Root residual p(x) becomes the force; equilibrium sits on a root.
Nonlinear systems
betaSolve F(x) = 0.
General nonlinear root-finding via Jacobian-scaled constraint forces.
The same engine solves science, biology, and ML problems.
Find the minimum-energy configuration of an atomic cluster — a hard global-optimization problem in chemistry and materials.
Optimize glycolysis pathway fluxes in central metabolism — constrained optimization on a real biological network.
Steer a language model's activations toward a target behaviour using the MCM gas engine as the optimizer.
Mean-variance allocation, calibration, and cointegration are optimization problems — solved as computations, with the path itself the return.
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