Axiom 🛠️

A Rust library implementing the framework from "Resolving CAP Through Automata-Theoretic Economic Design" by Dr. Craig S. Wright. Axiom provides a partition-tolerant distributed system with iterative state updates, economic incentives, and provable convergence, designed for real-time applications.

Features 🚀

• Partition-Aware State Machines: Nodes adapt states based on network conditions, using iterative updates instead of supermajority thresholds.
• Economic Incentives: Rewards align nodes with local consensus, stabilizing the system.
• Iterative Consensus: Converges when states are within a small range (ε), ensuring robustness.
• Async Networking: Built with Tokio for high-performance simulations.

Usage 💻

use axiom::{AxiomConsensus, AxiomIncentive, AxiomStateMachine, Network};

#[tokio::main]
async fn main() -> Result<(), Box<dyn std::error::Error>> {
    let state_machine = AxiomStateMachine::new(0.1);
    let incentive = AxiomIncentive::new(1.0, 0.1);
    let consensus = AxiomConsensus::new(0.01);
    let mut network = Network::new(5, state_machine, incentive, consensus, 0.9, 20);
    network.simulate().await?;
    Ok(())
}

Mathematical Basis 📐

• State Update: ( s_i^{(t)} = s_i^{(t-1)} \cdot (1 - w) + s_{\text{target}}^{(i)} \cdot w ), where ( w ) is ( \alpha ) (normal) or ( p ) (partitioned).
• Incentive: ( u_i^{(t)} = r - c \cdot |s_i^{(t)} - \bar{s}_{G_t^{(i)}}^{(t)}| ).
• Convergence: Achieved when ( \max(s_i^{(t)}) - \min(s_i^{(t)}) < \epsilon ).

License 📜

MIT