Mathematical Intelligence Online

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.

Fractal Dimension: D = 1.5849 | Hausdorff measure converges | Basin area: 1.5065 | Status: PROVED

Theorem Engine

Active mathematical proofs, conjectures, and convergence results generated by QuanticFork's automath core.

Proved

Mobley Fixed-Point Theorem

M(z) = z² + φz + c, where φ = (1+√5)/2
∀ 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.

Proved

Quantum Portfolio Convergence

Σ(t) = argmin ||ρ(t) - ρ*||&sub2; s.t. Tr(ρ) = 1
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.

Converging

Fractal Market Dimension Stability

D⊂H;(S⊂t;) ∈ [1.42, 1.67] for t ∈ [T−252, T]
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.

Conjecture

Topological Hedging Completeness

π⊂1;(H) ≅ ℤ⊂2; ⊕ ℤ⊂3; implies every contingent claim is replicable
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.

Exploring

Recursive Intelligence Stability

R(n+1) = R(n) + α·∇L(R(n)) + β·ε⊂n;
||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.

Proved

Quantum Entanglement Arbitrage Bound

P(arbitrage) ≤ exp(−Ω(n)) for n-qubit portfolio encoding
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

D = 2.0000 (boundary) | Hausdorff

The canonical fractal. Its boundary has Hausdorff dimension 2, encoding infinite complexity at every scale.

Julia Set (c = -0.7 + 0.27i)

D = 1.3934 | Connected

A connected Julia set revealing the attractor basins used in portfolio convergence proofs.

Mobley Function Basin

D = 1.5849 | Two Attractors

The Mobley function M(z) = z² + φz + c with golden-ratio coupling. Fixed-point basins colored by convergence speed.

Burning Ship Fractal

D = 1.782 | Market Volatility Model

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-001Fixed-Point TheoryPROVED1.00002,84799.97%S
QF-002Portfolio ConvergencePROVED1.000014,20399.94%S
QF-003Entanglement ArbitragePROVED1.00008,74199.99%S
QF-004Fractal DimensionCONVERGING0.871431,50687.14%A
QF-005Recursive IntelligenceEXPLORING0.4523127,30445.23%B
QF-006Topological HedgingCONJECTURE0.621852,89162.18%B
QF-007Quantum DecoherenceCONVERGING0.789219,43278.92%A
QF-008Grover Speedup BoundPROVED1.00004,10299.91%S
QF-009Shor Factor HedgeCONVERGING0.834167,28883.41%A
QF-010Black-Scholes ExtensionPROVED1.00001,29399.98%S

Architecture

Four-layer quantum-mathematical pipeline from raw qubits to proven strategies.

Layer 4 — Intelligence

Proof Engine

Automated theorem proving, conjecture generation, convergence analysis

Layer 3 — Strategy

Quantum Finance

Portfolio optimization, arbitrage detection, risk quantification

Layer 2 — Compute

Quantum Runtime

Qubit allocation, gate compilation, error correction, decoherence management

Layer 1 — Hardware

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.

quanticfork v0.9.1

vs. The Competition

QuanticFork vs. classical and quantum competitors.

CapabilityQuanticForkD-WaveIonQRigettiClassical
Automated Theorem Proving
Fractal Market Modelingpartial
Quantum Portfolio Optimization
Convergence Guaranteeslimited
Entanglement Arbitrage
Interactive Proof Explorer
Financial Strategy Generationmanual

Pricing

From proof exploration to institutional quantum trading.

Explorer

$0/forever
Explore mathematical structures
  • Interactive proof explorer
  • Fractal dimension gallery
  • 10 proof queries/day
  • Community theorem library
  • Public convergence dashboard
Start Exploring

Sovereign

Custom
Dedicated quantum infrastructure
  • Private QPU allocation
  • Custom theorem development
  • Proprietary strategy generation
  • On-premise deployment
  • Dedicated mathematician team
  • SLA with convergence guarantees
Contact Sales

Join the Quantum Frontier

Early access to the proof engine, quantum strategies, and fractal analytics. Limited to 200 seats.