Understanding BalancerV2 is Overlay's launch point, I did happen to be rooting around in Uniswap's periphery repo and encountered this library for ascertaining liquidity amounts between particular price points.
https://github.com/Uniswap/v3-periphery/blob/main/contracts/libraries/LiquidityAmounts.sol
I wanted to catalogue this discussion due to a curiosity about what this library might mean for a formalism built around UniV3.
Where we currently have this as the Overlay market's measure for the market liquidity,
_marketLiquidity = ethIs0
? ( uint256(_liquidity) << 96 ) / _sqrtPrice
: FullMath.mulDiv(uint256(_liquidity), _sqrtPrice, X96);
According to this library, it could be augmented to read liquidity between between specific tick boundaries.
Perhaps this lends more security to a formalism built around uni v3?
Tabling this out of curiosity for potential future development.