The Coordinate System: Ticks and sqrtPriceX96

Key takeaway: V3 stores price as sqrtPriceX96 — the square root of price in Q64.96 fixed point — because swap math is linear in sqrt(P) (Δy = L * Δ(sqrt(P))), and it indexes price space with ticks, where tick i means price 1.0001^i. TickMath converts between the two with hardcoded magic constants (provided; you use it, you do not retype it). You implement the safety rails around the coordinate system: LiquidityMath.addDelta with V3's terse 'LS'/'LA' overflow checks inside an unchecked block, tickSpacingToMaxLiquidityPerTick which caps per-tick liquidity so the pool-wide uint128 can never overflow, and checkTicks with the 'TLU'/'TLM'/'TUM' range validation every mint and burn passes through.

What You Are Building

Before you can build pools, you need V3's coordinate system: how price is stored, how price space is indexed, and the invariants that keep both inside safe bounds. In this section the heavy artillery — TickMath, with its 20 magic constants — is provided in full. Your job is the surrounding safety layer: LiquidityMath.addDelta, tickSpacingToMaxLiquidityPerTick, and tick-range validation. Small functions, but every mint, burn, and swap in the rest of the module runs through them.