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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.

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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.

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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.

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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.