In one example in accordance with the present disclosure, a system comprises a first memory module and a first memory integrity monitoring processor, embedded to the first memory module, to receive a second hash corresponding to a second memory module. The second hash includes a second sequence number for reconstruction of a final hash value and the second hash is not sequentially a first number in a sequence for reconstruction of the final hash value. The first processor may receive a third hash corresponding to a third memory module. The third hash includes a third sequence number for reconstruction of the final hash value and the third hash is received after the second hash. The first processor may determine if the second hash can be combined with the third hash, combine the second hash and third hash into a partial hash reconstruct the final hash value using the partial hash.