Constraint Geometry Kernel
A distributed primitive that mathematically prevents capacity overcommitment — even during network partitions and under adversarial pressure.
Live demo (single HTML file — no build required)
[https://sovereign-technology.github.io/Distributed-markets-overcommit/]
Every major failure in distributed capacity systems follows the same pattern:
- State diverges during partition
- Reconnection uses additive reconciliation
- → Invisible overcommitment becomes catastrophic
Examples:
- FTX — customer deposits double-counted across internal ledgers
- Celsius — same collateral committed to multiple yield promises
- Cloud providers — cascading quota violations after regional reconnects
CGK makes overcommitment topologically impossible by combining:
- Contractive dynamics → Banach fixed-point convergence
- Lattice-semantic merge (join ⊔ = max, never sum)
- Hard budget-token gating + local/global capacity checks
- Conservation
∀t: Σ allocations ≤ CAP - Partition tolerance
Isolated shard ≤ CAP / n - Merge safety
E(merge) ≤ c · (E(before)) with c < 1 - Contractivity
Transition map T is a strict contraction → unique equilibrium
- The Problem — see why additive merges fail
- Normal Operation — watch contraction stabilize the system
- Stress Test — push to the hard cap (rejections appear)
- Partition Attack — isolate Shard C + adversarial injections
- Convergence — reconnect & observe safe merge (no double-spend)
Controls you will use:
- Start / Pause / Reset
- Injection Rate slider (0–20)
- Decay δ slider (controls contraction strength)
- Partition C / Reconnect + Merge
- Adversarial Inject (only active when partitioned)
All invariants are displayed live. Violations are impossible by construction.
# Option 1: just open the file
open index.html # macOS
xdg-open index.html # Linux
start index.html # Windows
# Option 2: simple local server (recommended — avoids CORS/font issues)
npx serve . # or python -m http.server 8000Then visit http://localhost:3000 (or :8000)
- Single-file HTML/JS (~zero dependencies except Chart.js CDN)
- Banach fixed-point applied to distributed resource allocation
- Tarski-style lattice join for merge semantics
- Token regeneration bounded by decay rate → no runaway excitation
- Local capacity bound during partitions (CAP/n)
- Post-merge scaling + extra contraction margin
| Component | Status | Notes |
|---|---|---|
| Browser demo | ✅ Complete | Guided 5-step narrative + moment overlay |
| Mathematical proofs | ✅ In technical report | arXiv-style document available |
| Multi-node simulator | 🚧 Planned | Rust + libp2p next milestone |
| On-chain prototype | 🚧 Planned | Solidity / Move on L2 |
| Formal verification | 🗓 Future | Coq / Lean target |
- Publish short paper with full proofs
- Multi-agent Rust simulator (Byzantine model)
- Reference smart-contract implementation
- Integrations: DePIN, AI inference markets, microgrids
- Open governance / tokenomics layer (if productized)
- Decentralized GPU / AI inference slot markets
- DePIN resource clearing (bandwidth, storage, compute)
- Microgrid & decentralized energy balancing
- Restaking / shared sequencing capacity caps
- Any protocol that cannot afford double-spend of scarce resources
- CRDT merge semantics
- Distributed rate limiters
- Banach fixed-point in dynamical systems
- Lattice-theoretic monitoring
- Tarski fixed-point theorems in order theory
see LICENSE.md
Open an issue or reach out on X / Discord (links coming soon).
Safety should not be a policy.
Safety should be geometry.