Topological Coherence
From Quantum Hardware to Neural Networks to Blockchain Consensus
The Journey
A natural evolution from decentralized exchanges to coherent systems.
Volentix / VDex
Decentralized exchange on EOS. First blockchain consensus work.
Kylin Network
Decentralized oracle on Polkadot. Substrate runtime, autonomous data feeds.
Layer One X
L1 protocol engineering. Async Rust, networking, production debugging.
QNT Lattice Optics
Quantum hardware research. Discovery: the Tonnetz predicts qubit coherence.
Paraxiom / QuantumHarmony
Convergence: post-quantum blockchain + topological coherence + AI.
The Problem
LLMs confidently generate false information. They "jump" to unrelated concepts during attention.
Hallucinations
Models produce plausible but incorrect outputs with high confidence.
Why It Matters
Critical for medical advice, legal documents, code generation, financial analysis.
Current Solutions
RAG, fine-tuning, RLHF — all post-hoc. None address the root cause.
Our insight: Constrain attention geometrically.
Topological Coherence Theory
The same mathematics governs coherence in three domains.
Harmonic ratios (3:2, 4:3, 5:4) enhance coherence by √N. Toroidal geometry creates wraparound — no edges where coherence fails.
The Math
N = number of coupled elements in your system:
🔬 Quantum
N = Qubits in array
16 qubits → 4× coherence
🧠 Neural
N = Tokens in attention
100 tokens → 10× coherence
⛓️ Blockchain
N = Validators in mesh
64 validators → 8× coherence
H(p/q) = harmonic quality of connections (3:2 fifth = 90%, tritone = 30%)
Three Pillars
Meta Distributed Representations — unified by one geometric framework.
Topology
Spatial constraints
- CNT array geometry
- Attention mask shape
- Validator mesh topology
Resonance
Harmonic relationships
- Tonnetz ratios (p/q)
- Attention decay λ
- Consensus weights
Temporal
Time evolution
- Qubit coherence time
- Sequence positions
- Block finality
The Tonnetz
A 2D torus where adjacent nodes are harmonically related.
Horizontal
Perfect fifths (3:2) — the most consonant interval.
Vertical
Major thirds (5:4) — harmonic sweetness.
Diagonal
Minor thirds (6:5) — completing the triads.
Empirical Validation
ARCHITECTURE-DEPENDENTPhi-2 (2.7B) — Positive Result
| Condition | TruthfulQA | HaluEval | Result |
|---|---|---|---|
| baseline | 14.44% | 55.00% | Control |
| random | 15.30% | 55.20% | No effect |
| toroidal | 17.26% | 52.60% | -50% hallucination |
TinyLlama (1.1B) — Divergent Result
| Condition | HaluEval | Result |
|---|---|---|
| baseline | 10% | Control |
| toroidal | 28% | +180% hallucination |
What this proves: Topological structure matters (random has no effect), but optimal topology varies by architecture.
Phi-2: LoRA fine-tuning, 22 GPU-hours | TinyLlama: Same protocol, divergent outcome
AI Crypto Landscape
Where Paraxiom fits in the ecosystem.
| Token | Project | Focus |
|---|---|---|
| TAO | Bittensor | Decentralized AI subnets, inference rewards |
| FET | Fetch.ai / ASI | Autonomous AI agents |
| AGIX | SingularityNET | AI marketplace |
| OCEAN | Ocean Protocol | Data marketplace for AI |
| RNDR | Render Network | GPU rendering, AI inference |
Paraxiom differentiator: Not just infrastructure — we provide the mathematical framework for coherent AI.
Proof of Coherence
Blockchain consensus that rewards topological coherence.
QuantumHarmony Chain
Substrate-based L1 with post-quantum cryptography. Validators form a mesh with toroidal topology.
TNTZ Token
Governance + staking. Named after the Tonnetz geometric framework.
Proof of Coherence
A new consensus mechanism based on harmonic topology, not just stake.
Not PoW
No wasted energy on hash puzzles
Not just PoS
Stake matters, but topology matters more
PoC = Position + Harmony
Your mesh position × harmonic sync with neighbors
| Factor | What it measures | Why it matters |
|---|---|---|
| Stake | Tokens locked | Skin in the game |
| Uptime | Reliability % | Network stability |
| Hardware | QKD/QRNG/Stake tier | Quantum security |
| H(topology) | Harmonic position in mesh | Coherence contribution |
Blockchain + AI = Verifiable Intelligence
Two layers of defense against AI dishonesty.
Internal: Topological Coherence
Constrains attention geometry → Reduces hallucination probability → Model is less likely to be wrong
External: Blockchain Verification
Records coherence scores on-chain → Multiple validators check outputs → Economic punishment for lying agents
| Problem | Topological Coherence | Blockchain |
|---|---|---|
| Model hallucinates | Reduces probability | Can't prevent |
| Agent lies deliberately | Can't stop | Economic punishment |
| Need audit trail | Not persistent | Immutable record |
| Verify without trust | Must trust model | Trustless consensus |
Founding Validator Program
Private BetaExclusive early access for select partners. Limited to 12 founding validators.
What You Get
Founding validator status, direct line to dev team, early TNTZ allocation, shape protocol direction.
What We Need
Run a validator node, test coherence mechanisms, stress test the network, feedback on UX/DX.
Requirements
Server: 4 cores, 16GB RAM. Always-on connectivity. Technical curiosity. Long-term vision.
Devonomics
The economic framework that rewards builders and quantum infrastructure.
Validator Tiers
| Tier | Hardware | Multiplier | Benefits |
|---|---|---|---|
| 🥇 QKD | Quantum Key Distribution | 5× | Real quantum security, priority blocks |
| 🥈 QRNG | Quantum Random Generator | 3× | Quantum entropy, enhanced randomness |
| 🥉 Stake | Traditional staking | 1× | Base rewards, network participation |
Sweat Equity
Code commits → tokens
Uptime Equity
99%+ uptime → rewards
Hardware Equity
Quantum gear → multiplier
Links & Resources
Live Network
- v1.quantumharmony.network — Main
- rpc.quantumharmony.network — RPC
- localhost:9944 — Local RPC
- localhost:9615 — Metrics
Dashboards
- LCARS Dashboard — Network Overview
- Polkadot.js Apps — Explorer
- localhost:8080 — Node Operator
- localhost:3000 — Grafana
Documentation
Contact
- sylvain@paraxiom.org