Agreed on the edit.

So we can see that profitable PoW is not bounded either if k is unbounded, but you can argue that UNprofitable PoW is not bounded at any k > 0. But the retort is that difficulty in my UNprofitable PoW design will not be limited to a difficulty which makes the cost of mining precisely equal to the block rewards, and thus the difficulty the attacker is facing is unbounded which is not the case in Satoshi's PoW design where difficulty is bounded by profitability of the marginal miners.

I asked you wait for the white paper, but there is a hint to you for you to chomp on interim time.

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