The gist is this. We want a full node wallet to be able to solo mine. How can we make this possible? By making another layer and a new coin. If bitcoin is represented as a "1" in the blockchain then a secondary currency could be a "!1". This secondary currency could be inflationary and CPU mineable only by making the uPoW large number factorization. So the uPoW miner would make a special transaction on the blockchain something like (!uPoW "merkle root of bitcoin block" "any nonce" "prime factors"). Basically this proves that the person factored a large number that was based on the hash of his chosen nonce and the merkle root (the merkle root is needed so they can't give themselves an easy number to factor). Miners would see this transaction, verify they indeed did everything right, and create a transaction in the next block giving the uPoW miner !1.
This would be good for bitcoin since it requires actual bitcoin to make these transactions so adds demand, and also gives non-pro miners something to earn at a reasonable pace. The factoring of a 101 digit large number takes about 2 hours on a top of the line CPU.
What's the benefit? Mining should not be an end to itself. So far it only looks like this would clog up the Bitcoin blockchain with !1 transactions. First by uPoW miners sending their uPoW transaction, then by miners sending their !1 reward to uPoW miners. Since we're talking about people being able to solo mine again, this would be thousands of nodes spamming the network with hundreds of transactions per block, receiving hundreds of transactions back. Not exactly an upside.