A bit more doc on pruning and validation

doc/pruning.md

@@ -41,3 +41,38 @@ receiving or keeping all the data.
 * When a new node joins the network, it may temporarily behave as a partially
 validating node to make it available for use faster, even if it ultimately becomes
 a fully validating node.
+
+# Validation of Fully Pruned State
+
+Pruning needs to remove as much data as possible while keeping all the
+guarantees of a full MimbleWimble-style validation. This is necessary to keep
+a pruning node state's sane, but also on first fast sync, where only the
+minimum amount of data is sent to a new node.
+
+The full validation of the chain state requires that:
+
+* All kernel signatures verify against their public keys.
+* The sum of all UTXO commitments, minus the supply is a valid public key (can
+be used to sign the empty string).
+* The sum of all kernel pubkeys equals the sum of all UTXO commitments, minus
+the supply.
+* The root hashes of the UTXO PMMR, the range proofs PMMR and the kernels MMR
+match a block header with a valid Proof of Work chain.
+* All range proofs are valid.
+
+In addition, while not necessary to validate the full chain state, to be able
+to accept and validate new blocks additional data is required:
+
+* The output features and switch commitments, making the full output data
+necessary for all UTXOs.
+
+At minimum, this requires the following data:
+
+* The block headers chain.
+* All kernels, in order of inclusion in the chain. This also allows the
+reconstruction of the kernel MMR.
+* All unspent outputs.
+* The UTXO MMR and the range proof MMR (to learn the hashes of pruned data).
+
+Note that further pruning could be obtained by requiring the validation of
+only a subset of the range proofs, chosen randomly by the validating node.