Not able to understand the brances of liquidity calculation in LiquidityMath

[Riceee69]

Hello, I was comparing the liquidity amount calculation branches in LiquidityMath::getLiquidityForAmounts with the liquidity minting branches in UniswapV3Pool::mint and I think there are discrepancies in the behavior of both?

From what I understand is Uniswap’s tick ranges are [lower, upper) so the price range of a range excludes the tick price of the upper tick and includes the tick price of the lower range for the range?

But when we are calculating liquidity in the first branch we use the condition if (sqrtPriceX96 <= sqrtPriceAX96) so does this not conflict with the liquidity mintings first branch if (slot0_.tick < lowerTick). If the condition is sqrtPriceX96 = sqrtPriceAX96, then doesn't that mean the current tick is pointing to the lowerTick input by the user so shouldn't the calculation be in range. i.e. calculate for both amount0 and amount1? So shouldn't the condition be if (sqrtPriceX96 < sqrtPriceAX96)?

Similar Issue with the second branch as well, If I understand the concept properly shouldn't it be else if (sqrtPriceX96 < sqrtPriceBX96) and not else if (sqrtPriceX96 <= sqrtPriceBX96) since when the price is = upper tick price we jump to the next range?

Can someone please help me with this? Much appreciated!