Proof & benchmarks
Run on live capital. Measured. Reproducible.
These are real runs on live Binance Futures — not simulations. The headline: a 6D optimization that converged to the answer while remaining net-profitable for its entire run.
3-SAT
Valid assignment
29s · 10 fills
Optimization (Rosenbrock 6D)
graded PASS
5.6 h · ‖x−x*‖ 0.41
Linear system 8D
graded EXCELLENT
128s · err 0.004
Eigenvalue (Toeplitz 8×8)
4.8% error
68 min · 3.69 vs 3.88
E. coli metabolism
R² 0.81
69 min · graded PASS
Linear regression
graded EXCELLENT
5 min · 16 fills
Substrate live tests — all 8 solvers
Each solver validated with real capital.
| Solver | Result | Time | Fills |
|---|---|---|---|
| 3-SAT | Found valid assignment [F,T,T] | 29s | 10 |
| Linear regression | Converged | 288s | 16 |
| Optimization | x*=[2.92,4.00] vs [3,4], dist 0.077 | 458s | 14 |
| Eigenvalue | 4.617 vs 4.618 (err 0.0009) | 374s | 21 |
| Shortest path | Path [0,1,2] — correct | 369s | 31 |
| Polynomial root | Found root 2.0 — correct | 607s | 13 |
| Nonlinear system | [2.85,4.01] vs [3,4] — converging | 608s | 28 |
Ablation study
A controlled study across 8 solvers × up to 10 treatments isolates how each component (variable brackets, constraint spreads, contrastive closing, PnL-aware convergence) contributes to convergence.
Verified successes
Rosenbrock 6D, Toeplitz eigenvalue, and Euler ODE each have a full verified-success record with publication-ready data.
Applied domains
E. coli metabolism, Lennard-Jones clusters, and LLM steering demonstrate the substrate beyond finance.
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