Question: Is the proof-of-work mint rate path dependent (i.e. does it depend on both current and past difficulty?); (or does it only depend on current difficulty?)
Question: Assuming the mint rate is path dependent, if someone was to take huge hashing power online and offline repeatedly (say one week online; one week offline; repeat), would this process progressively drive down the mint rate?
No memory involved, only current proof-of-work difficulty determines mint: mint = 9999 / (difficulty ** 0.25)
But the difficulty is a running average, correct? IMHO, that may explain the large oscillations we've seen: Someone with huge hashing power hashes for 3-4 days and waits for a few days, for the difficulty to cool down, rinse and repeat. It's rational: In the beginning the huge hashing power is more effective since the difficulty weighting takes into account prior times for lower diff. These leads to a situation where the baseline of miners effectively pays for the efficiency gain in mining of the large entity miner...

When the large-entity miner stops, the casual miner now enjoys lowering mining difficulty levels too without any cost aswell though.
The reason we're seeing the oscillations is, that as soon as it becomes more profitable to mine PPC compared to BTC, people move over. It's like pool-hopping, but, on a currency level.