Solver suite

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

live

Find the minimum of any objective.

Minimize a smooth multi-dimensional function. The market relaxes downhill along the negative gradient encoded as constraint forces.

Typical
8 min–6 h
Size
up to 8D
Status
live
VerifiedRosenbrock 6D → x*≈[1,1,1,1,0.96,0.70], graded PASS in passive mode

Boolean satisfiability (SAT)

live

Satisfy every clause at once.

3-SAT and k-SAT. Each violated clause becomes a penalty force; equilibrium is a satisfying assignment.

Typical
30s–5 min
Size
up to 8 vars
Status
live
Verified3-SAT → valid assignment in 29s, 10 fills

Linear systems & regression

live

Solve Ax = b, fit y = mx + c.

Residual r = Ax − b becomes a restoring force F = −Aᵀr that vanishes exactly at the solution.

Typical
2–8 min
Size
up to 8D
Status
live
VerifiedLinear 8D → error 0.004, graded EXCELLENT in 128s

Eigenvalue problems

live

Recover spectra from the market.

Dominant and interior eigenvalues of structured matrices via substrate relaxation.

Typical
5–70 min
Size
up to 8×8
Status
live
VerifiedToeplitz 8×8 interior → 3.69 vs 3.88 (4.8% error)

Shortest path

live

Optimal routes through a graph.

Path-cost constraints push flow onto the minimum-cost route; fills read out the path.

Typical
5–10 min
Size
small graphs
Status
live
VerifiedGraph → path [0,1,2] correct, 31 fills

ODE initial-value problems

beta

Integrate dynamics forward.

Euler residual of the discretized ODE is driven to zero step by step.

Typical
5–12 min
Size
low order
Status
beta
VerifiedVan der Pol / dy/dt=−y → converged

Polynomial roots

beta

Find where it vanishes.

Root residual p(x) becomes the force; equilibrium sits on a root.

Typical
8–12 min
Size
single / systems
Status
beta
VerifiedFound root 2.0 (correct)

Nonlinear systems

beta

Solve F(x) = 0.

General nonlinear root-finding via Jacobian-scaled constraint forces.

Typical
8 min–1 h
Size
up to 8D
Status
beta
VerifiedE. coli flux balance → R²=0.81, graded PASS
Applied — beyond finance

The same engine solves science, biology, and ML problems.

Scientific computing
Lennard-Jones cluster energy

Find the minimum-energy configuration of an atomic cluster — a hard global-optimization problem in chemistry and materials.

Computational biology
E. coli metabolism

Optimize glycolysis pathway fluxes in central metabolism — constrained optimization on a real biological network.

Machine learning
LLM steering

Steer a language model's activations toward a target behaviour using the MCM gas engine as the optimizer.

Quant finance
Portfolio & risk as optimization

Mean-variance allocation, calibration, and cointegration are optimization problems — solved as computations, with the path itself the return.

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