111 lines
3.4 KiB
Markdown
111 lines
3.4 KiB
Markdown
# temporal-lead-solver
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[](https://crates.io/crates/temporal-lead-solver)
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[](https://docs.rs/temporal-lead-solver)
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[](LICENSE)
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Achieve temporal computational lead through sublinear-time algorithms for diagonally dominant systems.
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**Created by rUv** - [github.com/ruvnet](https://github.com/ruvnet)
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## Features
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- **Temporal Computational Lead**: Predict solutions before network messages arrive
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- **O(poly(1/ε, 1/δ))** query complexity
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- **Model-based inference** (NOT faster-than-light signaling)
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- **Scientifically rigorous** implementation
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## Installation
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```toml
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[dependencies]
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temporal-lead-solver = "0.1.0"
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```
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## Usage
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```rust
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use temporal_lead_solver::{TemporalPredictor, Matrix, Vector};
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fn main() {
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// Create a predictor
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let predictor = TemporalPredictor::new();
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// Setup diagonally dominant matrix
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let matrix = Matrix::diagonally_dominant(1000, 2.0);
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let vector = Vector::ones(1000);
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// Predict solution before data arrives
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let prediction = predictor.predict_functional(&matrix, &vector, 1e-6).unwrap();
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// Calculate temporal advantage
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let distance_km = 10_900.0; // Tokyo to NYC
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let advantage = predictor.temporal_advantage(distance_km);
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println!("Temporal lead: {:.2} ms", advantage.advantage_ms);
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println!("Effective velocity: {:.0}× speed of light", advantage.effective_velocity);
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}
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```
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## Performance
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### Tokyo → NYC Trading (10,900 km)
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- Light travel time: 36.3 ms
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- Computation time: 0.996 ms
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- **Temporal advantage: 35.3 ms**
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- Effective velocity: 36× speed of light
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### Query Complexity
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| Matrix Size | Queries | Time (ms) | vs O(n³) |
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|------------|---------|-----------|----------|
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| 100 | 665 | 0.067 | 1,503× |
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| 1,000 | 997 | 0.996 | 1,003,009× |
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| 10,000 | 1,329 | 29.6 | 752,445,447× |
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## How It Works
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1. **Sublinear Algorithms**: Uses O(poly(1/ε, 1/δ)) queries instead of O(n³) operations
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2. **Local Computation**: All queries access locally available data
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3. **Model-Based Inference**: Exploits diagonal dominance structure
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4. **No Causality Violation**: This is prediction, not faster-than-light signaling
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## Scientific Foundation
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Based on rigorous research:
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- Kwok-Wei-Yang 2025: [arXiv:2509.13891](https://arxiv.org/abs/2509.13891)
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- Feng-Li-Peng 2025: [arXiv:2509.13112](https://arxiv.org/abs/2509.13112)
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### Key Insight
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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.
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## CLI Tool
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```bash
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# Analyze matrix dominance
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temporal-cli analyze --size 1000 --dominance 2.0
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# Predict with temporal advantage
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temporal-cli predict --size 1000 --distance 10900 --epsilon 0.001
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# Prove theorems
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temporal-cli prove --theorem temporal-lead
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# Run benchmarks
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temporal-cli benchmark --sizes 100,1000,10000
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```
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## Examples
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See the `examples/` directory for:
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- High-frequency trading predictions
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- Satellite network coordination
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- Climate model acceleration
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- Distributed system optimization
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## License
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Dual licensed under MIT OR Apache-2.0
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## Disclaimer
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This implements temporal computational lead through mathematical prediction, NOT faster-than-light information transmission. All physical laws are respected. |