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

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

Usage

`rust
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

$3

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

$3

| 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

$3

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

`bash


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.