> ## Documentation Index
> Fetch the complete documentation index at: https://docs.qu.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# Coincident Blocks

> How merge-mined blocks are used to transfer state across blockchains in Quai Network.

## The Natural Bridges Between Chains

Imagine rolling dice and occasionally getting lucky enough to win multiple games at once. That's essentially what coincident blocks are - mining solutions that satisfy multiple blockchain requirements simultaneously.

**What Makes Them Special:**

* **No extra work required**: They occur naturally through normal mining
* **Mathematically guaranteed**: Not reliant on validators or committees
* **Perfect synchronization**: Chains stay connected through pure probability

**How They Enable Cross-Chain Transactions:**
When a coincident block occurs, it creates an unbreakable mathematical link between chains. This link serves as a trustless bridge, allowing assets and data to move between chains without any intermediary.

## The Mathematics of Luck

**Simple Analogy:**

* Zone difficulty: Need to roll a 6
* Region difficulty: Need to roll two 6s
* Prime difficulty: Need to roll three 6s

Sometimes you roll three 6s when you only needed one - that's a coincident block!

**Probability Table:**

| How "Lucky" Was the Block?      | Chance of Occurrence |
| ------------------------------- | -------------------- |
| Slightly lucky (1 extra zero)   | 50%                  |
| Pretty lucky (2 extra zeros)    | 25%                  |
| Very lucky (3 extra zeros)      | 12.5%                |
| Extremely lucky (4 extra zeros) | 6.25%                |

**Why This Matters:**
Unlike other multi-chain systems that rely on committees, validators, or complex protocols, Quai's cross-chain bridges are created by pure mathematics. No trust required - just probability.

## How Coincident Blocks Work

**Key Principles:**

1. **Hierarchy matters**: Prime blocks are always coincident (they satisfy all chains)
2. **Independence preserved**: Zones can produce blocks without waiting
3. **Atomic validity**: A block must be valid everywhere or nowhere
4. **Perfect synchronization**: All chains append coincident blocks simultaneously

**The Chain Hierarchy:**

* **Prime blocks**: Always coincident (like a master key opening all locks)
* **Region blocks**: Coincident with their zones
* **Zone blocks**: Usually independent, occasionally coincident

**Why Different Block Times?**

* Prime: \~20 seconds (slow but ultra-secure)
* Region: \~10 seconds (balanced)
* Zone: \~5 seconds (fast for users)

This design ensures zones can operate quickly while still maintaining periodic synchronization through coincident blocks.

## Running a Node

**Minimum Requirement - A "Slice":**
The smallest node a miner can run is a slice node. To participate trustlessly, you need:

* The prime chain (global coordination)
* One region chain (regional coordination)
* One zone chain (where transactions happen)

This "slice" gives you everything needed to verify transactions without trusting anyone else.

**The Beauty of the System:**
Coincident blocks create a trustless, automatic, and mathematically guaranteed way for multiple blockchains to stay synchronized and share security - all through the natural randomness of mining.