Technology
Our innovations span two research axes that reinforce each other:
- Augmented artificial intelligence
- Mathematics in very high-dimensional spaces
Since for us information is the invariant, our approach is to change the paradigm, to think differently. To explore new avenues of research in mathematics, notably what we call spectral mathematics. This allows us to formulate new hypotheses that we verify every day: information does not travel through silicon but flows through a broader mathematical space, freed from certain constraints that the laws of physics impose on all transformation.
Augmented artificial intelligence
Density
The cognitive engine builds an optimal semantic trajectory before each generation, then validates the response on output. Between each turn, the system recalibrates its constraints based on the conversation — it learns and refines itself as it accompanies you.
Observable result: given the same question, on the same model, the engine produces shorter responses containing more useful information. More propositions per paragraph, near-zero reformulation.
| Metric | Bare LLM | With engine | Gain |
|---|---|---|---|
| Tokens per response (complex question) | ~800 | ~350 | -56% |
| Useful propositions per paragraph | 2-3 | 5-7 | ×2.5 |
| Reformulations / fillers | 30-40% | <5% | -90% |
Memory
Exchanged information persists between sessions. Indexed by semantic relevance — by meaning, cognitive salience, intellectual interest.
Recall is automatic: before each response, the system injects relevant context. Continuous pre-retrieval, model-independent.
Classical RAG vs Native semantic retrieval
Classical RAG (Retrieval-Augmented Generation) splits documents into chunks, transforms them into vectors via an external embedding model (OpenAI, Cohere...), stores them in a vector database (Pinecone, Weaviate...) and searches by cosine similarity. Indexing is fragmented, search is approximate, and switching models loses all context.
Our approach is structurally different. HoloRAG indexes by cognitive salience, not by chunks. VDID assigns a unique vector identity to every piece of information. Pre-retrieval injects relevant context before generation, in a single pass. All of this runs in under 5 ms, regardless of the model used.
| Metric | Standard RAG | Our system |
|---|---|---|
| Recall latency | 200-800ms | <5ms |
| Indexing | Chunks + embeddings | Native continuous semantic |
| Loss on model switch | Total | Zero |
| Data exploited | Raw history | Cognitive salience |
Portability
Switch models mid-conversation. Claude to GPT. GPT to Gemini. One click.
The conversation continues. The new model has full context. Memory follows. Tone may vary — each model has its personality — but substance, context and history remain intact.
Migration cost between providers: zero.
Frugality
The system operates in a single pass. One request, one response, one API call.
The architecture inverts the curve: the more the system is used, the less it consumes per request. Persistent memory avoids recomputing what has already been established. Pre-retrieval replaces multiple queries with a single injection.
| Metric | Multi-agent architecture | Our system |
|---|---|---|
| Passes per request | 3-8 | 1 |
| Typical latency | 15-90s | 2-5s |
| Marginal cost (with history) | Constant or increasing | Decreasing |
| API calls per response | 3-12 | 1 |
Encryption
Every archived memory block is encrypted client-side before storage. Post-quantum cryptography by mathematical construction — resistance depends on the structure of the space, independent of parameters.
Security rests on a mathematical proof, not on the assumed difficulty of a computation. Intercepting an encrypted message compromises neither past nor future messages.
The key is the movement. The object does not exist.
| Property | Classical encryption (AES/RSA) | Our system |
|---|---|---|
| Quantum resistance | Partial (AES-256) | By construction |
| Key | Static, stored | Alive, relational |
| Failure mode | Key theft | No single point |
| Evolution over time | None | Continuous reinforcement |
Mathematics
Solving
Vktor Spectral® is our high-performance solver. It encodes complex structures — graphs, biological sequences, chemical spectra — into a proprietary high-dimensional mathematical space. Runs without training or GPU, and without specialised infrastructure. A laptop is enough.
The result is deterministic: the same input always produces the same vector. The search is exact, reproducible, and executes in milliseconds where standard methods take seconds or minutes.
| Domain | Result | Speed |
|---|---|---|
| MaxCut — Combinatorial optimisation | 71 Gset instances, 0.990 ratio | 7 to 39× vs BLS |
| Genomics — DNA similarity search | 100% human chromosome 1 | ×13,915 vs BLAST |
| Mass Spectrometry — Chemical compound identification | 94% top-1 on 102,578 spectra | ×9,700 vs MatchMS |
| Proteomics — Protein identification | 87% top-1 on 574,627 proteins | ×2,229 vs NCBI blastp |
Six families of industrial problems
MaxCut resolution alone opens six families of industrial problems. Three reduce to it with no algorithmic modification — exact polynomial reductions. The remaining three adapt only the final rounding phase.
No competitor covers all six verticals from a single engine.
| Family | Problem | Domain |
|---|---|---|
| .Ising | Ising ground state | Quantum Computing |
| .QUBO | QUBO | Optimization solvers |
| .Partition | Graph bisection | EDA / VLSI |
| .kCut | Max-k-Cut | Telecom / Scheduling |
| .MaxCut | Maximum Cut | Research / Benchmarks |
| .Cluster | Spectral clustering | Data / ML |
The ground state of an Ising Hamiltonian is identical to the MaxCut of the underlying graph, requiring no algorithmic modification or approximation. Any QUBO instance reduces in polynomial time to a MaxCut instance on an augmented graph (Barahona et al., 1988). The remaining three families use the same engine with an adapted final phase.
Vktor Spectral vs Quantum Machines
MaxCut is the standard benchmark for QAOA (Quantum Approximate Optimization Algorithm). The largest quantum processors today (IBM Condor, 1,121 qubits) cannot run QAOA beyond a few hundred variables — decoherence destroys quantum states before convergence.
| Quantum machine | Vktor Spectral | |
|---|---|---|
| Max instance solved | ~100–200 variables | 20,000 variables |
| Decoherence | Fundamental limit | Nonexistent |
| Error correction | Millions of physical qubits | None |
| Infrastructure | Cryogenics, vacuum, shielding | Laptop, room temperature |
| Cost per run | $10,000+ (cloud) | <$0.01 (electricity) |
Beyond a few hundred variables, quantum computation collapses. Vktor Spectral solves 20,000 variables on a fanless laptop in under 17 minutes.
The mathematical foundations of Sqant Chat (post-quantum encryption, native semantic retrieval, spectral solver) are developed under the Vktor brand.
vktor.io →