How a market solves your problem.
Samādhān rests on one observation: liquid markets already perform a physical computation — they relax toward equilibrium. If you can shape that equilibrium to encode your problem, the market solves it for you.
Prices follow an Ornstein–Uhlenbeck process
On liquid venues, the mid-price mean-reverts:dp = −θ(p−μ)dt + σ·dW. Prices want to return to μ (pull θ) while wiggling with volatility σ. Samādhān calibrates θ, σ, μ from 500 recent candles and the volume point-of-control before any compute.
Constraints become forces
A mathematical constraint creates a force on the variables, just like a physical one. For a linear system, the residual r = Ax − b yields a restoring force F = −Aᵀr that is large when x is wrong and exactly zero at the solution. For optimization, the force is the negative gradient. For SAT, each violated clause adds a penalty force. The OU dynamics plus these forces give a solver: a directional pull toward the answer, plus noise that explores the space.
An affine bridge between math and price
Market parameters live in price-space ($95,000); your variables live in number-space (~1–10). A normalization preserving the market's pull-to-noise ratio maps one to the other, so a strongly mean-reverting market becomes a strong, low-noise solver and a volatile market becomes a more exploratory one.
From zero-risk simulation to live substrate.
Passive WebSocket simulation. Read the market's dynamics; no orders, no risk. Free.
Genuinely market-driven (z-score), still no capital deployed.
Real orders on a live exchange. The market does ~95% of the compute — and pays you to do it. Pro.
Multi-pair substrate for larger / coupled problems. Pro.
Guardrails are part of the solver.
Adaptive loss thresholds close runaway positions before they hurt — convergence and capital safety in one loop.
Stop-market brackets cap downside on each encoded variable.
Per-pair caps, search-range limits, and a global kill-switch. Substrate runs on your own non-custodial exchange keys.
Read the full encoding–decoding theory.
The complete pipeline, with worked numeric examples, lives in the Market Computation Model research.