How light wallets build k_image without spend key? Leave a comment

How light wallets build k_image (I) without spend key? How i understand when we accepted transaction to our wallet by comparison (Pi and P!i), then we need build k_image to write it to our table. How i know

X = Hs(sec_view_key,(tx_pub from extra), index) + secret_spend_key
I = XHp(Pi)

But walllets do not require spend key to server, then they somehow find out.
Yes they give list of k_images for client to detect correct out, but how they get it?

And conditional XMRwallet don`t check k_images in their client, and don’t request spend key to server, but show correct balance, how?

If we have a split sum, will we have the same k_image?

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