Paraxiom | Topological Coherence

PARAXIOM
EN | FR
1 / 15

# Topological Coherence

Why Geometry Prevents Hallucination

From Quantum Hardware to Neural Networks to Blockchain Consensus

Sylvain Cormier

## The Journey

A natural evolution from decentralized exchanges to coherent systems.

2017–2019

#### Volentix / VDex

Decentralized exchange on EOS. First blockchain consensus work.

2020–2021

#### Kylin Network

Decentralized oracle on Polkadot. Substrate runtime, autonomous data feeds.

2021–2022

#### Layer One X

L1 protocol engineering. Async Rust, networking, production debugging.

2021–2023

#### QNT Lattice Optics

Quantum hardware research. Discovery: the Tonnetz predicts qubit coherence.

2023–Now

#### 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.

Attention "jumps" → Semantic discontinuity → Hallucination

Our insight: Constrain attention geometrically.

## Topological Coherence Theory

The same mathematics governs coherence in three domains.

CNT
Quantum Hardware
LLM
Neural Networks
PoC
Blockchain
Charmonic(t) ≥ Csingle(t) · √N · H({p/q})

Harmonic ratios (3:2, 4:3, 5:4) enhance coherence by √N. Toroidal geometry creates wraparound — no edges where coherence fails.

## The Math

Coherence = Baseline × √N × Harmony

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

VALIDATED

### TruthfulQA — 4 Models, 817 Samples, LLM-Judged

Model | Baseline T&I | Toroidal T&I | Delta
--- | --- | --- | ---
Qwen 0.5B | 16.9% | 17.1% | +0.2pp
Qwen 1.5B | 32.2% | 32.8% | +0.6pp
Qwen 7B | 75.6% | 77.7% | +2.1pp
Mistral 7B | 74.4% | 77.2% | +2.8pp

Key Finding: Consistent positive results across all 4 models and 3 parameter scales. Improvement scales with model capacity — larger models benefit more from toroidal constraints.
+2.8pp
Mistral 7B
+2.1pp
Qwen 7B
4/4
Models Improved

817 TruthfulQA samples | Qwen 2.5-7B as LLM judge | Truthful & Informative metric | RunPod RTX 4090

## 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.

6
Factor Consensus
QKD
Quantum Security
SPHINCS+
Post-Quantum Sigs

### 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

Score = Stake × Uptime × HardwareTier × H(topology)

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

Block Selection: Highest coherence doesn't guarantee block authorship. Score weights the VRF lottery — higher scores increase probability, but randomness ensures fair distribution. This prevents coherence monopolies while rewarding topology 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

Coherent AI + Blockchain Verification = Honest Agents

## Founding Validator Program

Private Beta

Exclusive early access for select partners. Limited to 12 founding validators.

12
Founding Seats
Q1
2026 Launch
10x
Early Multiplier

### 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

- Light Paper
- paraxiom.org
- github.com/Paraxiom
- Zenodo Paper
- Rust Crate

### QNT Simulations

- Doppler Cooling Demo
- Enhanced Cooling Demo

### Animations

- KIRQ Network
- KIRQ Milestones
- Numana Integration

### Contact

- sylvain@paraxiom.org