Proving that a block is valid

Each block satisfies the equation

Σ outputs - Σ inputs = Σ kernel + offset * G + 60e9 * H

which can be seen is a small variation on the equation for the entire transaction history [1], which has no inputs and the UTXO set as outputs.

No; they’re all Pedersen commitments, but only the kernels are represented as public keys, because they are Pedersen commitments to a zero value.

Correct. It would be nice if they’re shown just like inputs and outputs are.

[1] Oneliner Grin: Σ utxo = Σ kernel + offset * G + height * 60 * H

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