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If I understand correctly, all cross-chain transfers in the destination network are fixed every block in the parachainsystems.set_validation_date extrinsic in horizontal_messages property.

Is there any way to parse this data into human form? Is there a description of the data structure?

For example, here is Karura set_validation_date with not empty horizontal_messages from Kintsugi (paraId 2092):

"data":"000210010400010200b1200608000c00070010a5d4e80a1300010200b1200608000c00070010a5d4e8010700f2052a010d0100040001010042c37a8f52d17c05bd1f5f4d7b751daae60841b6554bdbc043dd5319fbc5c21b"
"sent_at":13514596

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The horizontal messages are a BTreeMap<Paraid, Vec<InboundHrmpMessage>>. You can find the InboundHrmpMessage declaration here. The data field you then need to parse as versioned xcm message.

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