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onchain/UNISWAP_V3_MATH.md

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 # Uniswap V3 Math - Critical Learnings
 
+## Critical Implementation Details
+
+### Price Representation in KRAIKEN
+- `_priceAtTick(tick)` returns **price²** in X96 format, NOT regular price or sqrtPrice
+- This is intentional: price² = (sqrtPrice)² / 2^96
+- Used for ETH requirement calculations in floor positioning
+- To get regular price from price²: take sqrt and shift left by 48 bits
+- VWAP stores price² for volume-weighted averaging
+
+### ETH Scarcity vs Abundance
+- **Scarcity**: Floor ETH < Outstanding KRAIKEN * VWAP price → Floor moves to extreme ticks (140k+)
+- **Abundance**: Sufficient ETH → Floor placed near VWAP tick
+- Extreme floor positions (tick 141,200+) are CORRECT behavior in scarcity scenarios
+- Scarcity protects protocol solvency by making KRAIKEN very cheap (ETH expensive)
+
 ## Token Ordering and Price Representation
 
 ### Price Direction Reference Table