Prime factorization algebra instead of black-box embeddings. 28× faster than cosine similarity. Deterministic, auditable, and LangChain-ready.
The core idea
Instead of "King ≈ Queen (cosine 0.87)", we give you: "King = 2×3×5, Queen = 2×5×7. They share {2,5}."
Performance
Verified across 50,000 pairwise operations. No approximations.
| Feature | Triadic Engine | Cosine similarity | BM25 |
|---|---|---|---|
| Deterministic results | ✓ | ✗ (seed-dependent) | ✓ |
| Explainable output | ✓ (shared primes) | ✗ (black box) | ✗ |
| Composition algebra | ✓ (LCM) | ✗ | ✗ |
| Subsumption check | ✓ (GCD mod) | ✗ | ✗ |
| Model auditing | ✓ (108K discrepancies/2M) | ✗ | ✗ |
| Speed (50K ops) | ✓ 28× faster | baseline | ~3× faster |
API Reference
Convert concepts → prime integers. 4 projection modes: random, PCA, consensus, contrastive.
GCD similarity search. O(F×B) instead of O(N²). Returns top-k similar concepts with shared factors.
Compare two embedding models structurally. Found 108K discrepancies across 2M semantic chains.
Detect multiplicative rule violations in your data. Severity: CLEAN, INFO, WARNING, CRITICAL.
Persistent indices per user/project. Encode once, search forever. Up to 10 namespaces on Pro.
Async CSV processing for millions of concepts. Poll status with /batch/{job_id}.
Pricing
Perfect for exploring
$249/year (save 28%)
Annual contracts available
Integrations
Drop-in replacement for VectorStoreRetriever. Use Triadic as your RAG retrieval backend in any LangChain chain.
Use Triadic as a custom retriever in LlamaIndex query engines. Compatible with the standard retriever interface.