Quantum Finance.
Proven Mathematics.
QuanticFork fuses quantum computing with rigorous mathematical proof to generate trading strategies, convergence guarantees, and fractal market models that classical systems cannot reach.
Interactive Proof Explorer
Visualize mathematical structures in real time. Adjust parameters to explore fractal dimensions, Mandelbrot convergence, and Mobley function stability.
Theorem Engine
Active mathematical proofs, conjectures, and convergence results generated by QuanticFork's automath core.
Mobley Fixed-Point Theorem
∀ c ∈ D(0, 1/φ), M has exactly two fixed points in ℂ
The Mobley function's fixed-point structure has been formally verified. For all parameters within the golden-ratio disk, the iteration converges to one of exactly two attractors.
Quantum Portfolio Convergence
Convergence rate: O(1/√T) with quantum advantage η = 2.718
Portfolio density matrices converge to the optimal allocation under Grover-accelerated search. Quadratic speedup over classical mean-variance optimization.
Fractal Market Dimension Stability
Hurst exponent H = 0.63 ± 0.04 (persistent trend)
Market microstructure exhibits stable fractal dimension within the Hausdorff range. The Hurst exponent confirms long-memory persistence suitable for quantum arbitrage.
Topological Hedging Completeness
over the quantum state space ℋ = L²(Ω, ℱ, 𝒫)
If the fundamental group of the hedging manifold has the predicted structure, then market completeness follows from algebraic topology. Active verification via quantum homology computation.
Recursive Intelligence Stability
||R(n) − R*|| ≤ C·λ⊃n;, λ = 0.847
Self-improving systems converge to a stable intelligence level R* with geometric convergence rate λ < 1. The noise term ε ensures exploration of the proof landscape without divergence.
Quantum Entanglement Arbitrage Bound
Bell inequality violation: S = 2.73 > 2 (quantum advantage confirmed)
Entangled portfolio states can detect arbitrage opportunities exponentially faster than separable (classical) strategies. The Bell inequality violation proves genuine quantum advantage.
Fractal Dimension Gallery
Live-computed fractal structures revealing hidden market topology. Each fractal is generated in-browser using QuanticFork's rendering engine.
Mandelbrot Set
The canonical fractal. Its boundary has Hausdorff dimension 2, encoding infinite complexity at every scale.
Julia Set (c = -0.7 + 0.27i)
A connected Julia set revealing the attractor basins used in portfolio convergence proofs.
Mobley Function Basin
The Mobley function M(z) = z² + φz + c with golden-ratio coupling. Fixed-point basins colored by convergence speed.
Burning Ship Fractal
Absolute-value iteration models asymmetric market crashes. Used in tail-risk quantification.
Convergence Dashboard
Real-time proof status across all active mathematical investigations.
| Proof ID | Domain | Status | Convergence | Iterations | Confidence | Tier |
|---|---|---|---|---|---|---|
| QF-001 | Fixed-Point Theory | PROVED | 1.0000 | 2,847 | 99.97% | S |
| QF-002 | Portfolio Convergence | PROVED | 1.0000 | 14,203 | 99.94% | S |
| QF-003 | Entanglement Arbitrage | PROVED | 1.0000 | 8,741 | 99.99% | S |
| QF-004 | Fractal Dimension | CONVERGING | 0.8714 | 31,506 | 87.14% | A |
| QF-005 | Recursive Intelligence | EXPLORING | 0.4523 | 127,304 | 45.23% | B |
| QF-006 | Topological Hedging | CONJECTURE | 0.6218 | 52,891 | 62.18% | B |
| QF-007 | Quantum Decoherence | CONVERGING | 0.7892 | 19,432 | 78.92% | A |
| QF-008 | Grover Speedup Bound | PROVED | 1.0000 | 4,102 | 99.91% | S |
| QF-009 | Shor Factor Hedge | CONVERGING | 0.8341 | 67,288 | 83.41% | A |
| QF-010 | Black-Scholes Extension | PROVED | 1.0000 | 1,293 | 99.98% | S |
Architecture
Four-layer quantum-mathematical pipeline from raw qubits to proven strategies.
Proof Engine
Automated theorem proving, conjecture generation, convergence analysis
Quantum Finance
Portfolio optimization, arbitrage detection, risk quantification
Quantum Runtime
Qubit allocation, gate compilation, error correction, decoherence management
QPU Interface
Superconducting, trapped-ion, photonic backend abstraction layer
QuanticFork CLI
Interact with the proof engine directly. Submit theorems, run convergence tests, explore fractal dimensions.
vs. The Competition
QuanticFork vs. classical and quantum competitors.
| Capability | QuanticFork | D-Wave | IonQ | Rigetti | Classical |
|---|---|---|---|---|---|
| Automated Theorem Proving | ✓ | ✗ | ✗ | ✗ | ✗ |
| Fractal Market Modeling | ✓ | ✗ | ✗ | ✗ | partial |
| Quantum Portfolio Optimization | ✓ | ✓ | ✓ | ✓ | ✗ |
| Convergence Guarantees | ✓ | ✗ | ✗ | ✗ | limited |
| Entanglement Arbitrage | ✓ | ✗ | ✗ | ✗ | ✗ |
| Interactive Proof Explorer | ✓ | ✗ | ✗ | ✗ | ✗ |
| Financial Strategy Generation | ✓ | ✗ | ✗ | ✗ | manual |
Pricing
From proof exploration to institutional quantum trading.
Explorer
- Interactive proof explorer
- Fractal dimension gallery
- 10 proof queries/day
- Community theorem library
- Public convergence dashboard
Quant
- Unlimited proof engine access
- Quantum portfolio optimization
- Real-time fractal analytics
- Convergence guarantees
- API access + CLI tools
- Priority quantum compute
Sovereign
- Private QPU allocation
- Custom theorem development
- Proprietary strategy generation
- On-premise deployment
- Dedicated mathematician team
- SLA with convergence guarantees
Join the Quantum Frontier
Early access to the proof engine, quantum strategies, and fractal analytics. Limited to 200 seats.