RS-Foldφ-lattice
Glass-box protein folding. Every distance derived from the golden ratio. No training data. No free parameters. Watch the physics work.
pip install rsfold
rsfold fold --sequence NLYIQWLKDGGPSSGRPPPS --output result.pdb
rsfold benchmark --output results.jsonSource on GitHub · MIT License · Benchmarks →
Energy Trace
Contact Map
What Is This?
RS-Fold is a protein structure prediction engine built entirely from first principles. Unlike statistical methods that learn patterns from known structures, RS-Fold derives every geometric constraint from a single mathematical object: the golden ratio φ = (1+√5)/2.
The protein you see above was folded in your browser, right now, using only the amino acid sequence as input. No neural network. No database lookup. No server. Pure physics running in JavaScript.
The result is a “glass-box” model: every force, every distance, and every contact decision can be traced back to a specific theorem proved in Lean 4.
The φ-Lattice
Every distance in the model is a power or root of φ applied to measured bond lengths. Nothing is fitted.
How It Works
Encode
Each amino acid is represented as an 8-channel chemistry vector (volume, charge, polarity, H-bond donors/acceptors, aromaticity, flexibility, sulfur content). These are physical observables, not learned embeddings.
DFT-8 Spectral Analysis
A sliding 8-point Discrete Fourier Transform extracts frequency content from each chemistry channel. The dominant DFT mode, amplitude, and phase at each residue become a WToken — the “recognition fingerprint” of that position.
Predict Contacts
Residue pairs are scored by phase coherence, amplitude resonance, mode compatibility, and chemistry gating (charge attraction, H-bonds, aromatic stacking). The top N/φ² contacts are kept — a budget derived from the contact theorem, not tuned.
Minimize J-Cost
The energy function is the Recognition Science cost J(r) = ½(r + 1/r) − 1 applied to distance ratios. Backbone bonds, helix contacts, tertiary contacts, sterics, and compactness all use J-cost. Gradient descent with momentum drives the structure to the φ-lattice minimum.
RS-Fold vs AlphaFold
| RS-Fold | AlphaFold | |
|---|---|---|
| Approach | First-principles physics | Deep learning on MSA + templates |
| Parameters | Zero (all derived from φ) | ~93 million trained weights |
| Training data | None | ~170,000 PDB structures |
| Typical RMSD | 8–16 Å | ~1 Å |
| Explainability | Every force has a Lean proof | Attention weights (opaque) |
| Novel folds | Can design folds not in PDB | Limited to evolutionary space |
| Speed | ~30 ms in browser | Minutes on GPU |
| Runs offline | Yes (browser or CLI) | Requires server + GPU |
RS-Fold does not compete with AlphaFold on accuracy. It answers a different question: why does a protein fold the way it does, not just what shape does it take? The glass-box mechanism enables protein design from first principles — including folds that evolution never explored.
Machine-Verified Derivation Chain
Every geometric constant traces back to a Lean 4 theorem with zero sorry.
Empirical Validation
10/10 Helix Design
10 helical sequences designed from φ-geometry alone. All formed helices when cross-validated with ESMFold and AlphaFold. 10/10 negative controls (Pro insertions) disrupted the helix as predicted.
PDB Geometry <2% Error
Derived bond lengths (Cα–Cα = 3.85Å, H-bond = 2.85Å) match the Protein Data Bank to within 2%.
Contact Quantization
PDB contact-distance histograms show peaks at φ0, φ1, φ2, φ2.5Å — exactly the φ-ladder rungs the theory predicts.
Static W-Token Contacts
W-token-based contact prediction was not better than random in ablation studies. The theory now rests on the 8-tick dynamic clock, not static sequence encoding. This is disclosed as a falsified claim.
Install the CLI
For longer sequences or batch processing, use the Python package.
pip install rsfold
rsfold fold --sequence NLYIQWLKDGGPSSGRPPPS --output result.pdb
rsfold benchmark --output results.jsonSource: github.com/jonwashburn/recognition-science · License: MIT · Benchmark results →