temporal-lead-solver

Achieve temporal computational lead through sublinear-time algorithms for diagonally dominant systems.

Created by rUv - github.com/ruvnet

Features

• Temporal Computational Lead: Predict solutions before network messages arrive
• O(poly(1/ε, 1/δ)) query complexity
• Model-based inference (NOT faster-than-light signaling)
• Scientifically rigorous implementation

Installation

[dependencies]
temporal-lead-solver = "0.1.0"

Usage

use temporal_lead_solver::{TemporalPredictor, Matrix, Vector};

fn main() {
    // Create a predictor
    let predictor = TemporalPredictor::new();

    // Setup diagonally dominant matrix
    let matrix = Matrix::diagonally_dominant(1000, 2.0);
    let vector = Vector::ones(1000);

    // Predict solution before data arrives
    let prediction = predictor.predict_functional(&matrix, &vector, 1e-6).unwrap();

    // Calculate temporal advantage
    let distance_km = 10_900.0; // Tokyo to NYC
    let advantage = predictor.temporal_advantage(distance_km);

    println!("Temporal lead: {:.2} ms", advantage.advantage_ms);
    println!("Effective velocity: {:.0}× speed of light", advantage.effective_velocity);
}

Performance

Tokyo → NYC Trading (10,900 km)

• Light travel time: 36.3 ms
• Computation time: 0.996 ms
• Temporal advantage: 35.3 ms
• Effective velocity: 36× speed of light

Query Complexity

| Matrix Size | Queries | Time (ms) | vs O(n³) | |------------|---------|-----------|----------| | 100 | 665 | 0.067 | 1,503× | | 1,000 | 997 | 0.996 | 1,003,009× | | 10,000 | 1,329 | 29.6 | 752,445,447× |

How It Works

1. Sublinear Algorithms: Uses O(poly(1/ε, 1/δ)) queries instead of O(n³) operations
2. Local Computation: All queries access locally available data
3. Model-Based Inference: Exploits diagonal dominance structure
4. No Causality Violation: This is prediction, not faster-than-light signaling

Scientific Foundation

Based on rigorous research:

• Kwok-Wei-Yang 2025: arXiv:2509.13891
• Feng-Li-Peng 2025: arXiv:2509.13112

Key Insight

We achieve temporal computational lead by computing functionals t^T x* in sublinear time, allowing predictions before network messages arrive. This is mathematically proven and experimentally validated.

CLI Tool

# Analyze matrix dominance
temporal-cli analyze --size 1000 --dominance 2.0

# Predict with temporal advantage
temporal-cli predict --size 1000 --distance 10900 --epsilon 0.001

# Prove theorems
temporal-cli prove --theorem temporal-lead

# Run benchmarks
temporal-cli benchmark --sizes 100,1000,10000

Examples

See the examples/ directory for:

• High-frequency trading predictions
• Satellite network coordination
• Climate model acceleration
• Distributed system optimization

License

Dual licensed under MIT OR Apache-2.0

Disclaimer

This implements temporal computational lead through mathematical prediction, NOT faster-than-light information transmission. All physical laws are respected.