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This Viglione paper looks interesting, but it isn't about bitcoin, per se. The author is taking advantage of bitcoin's properties as a globally available asset, to study how different institutions affect pricing. Bitcoin is ideal for this because it has such low transactions costs (like transportation, for instance) that it should be able to move across borders very easily.
What's important to realize about this paper is that it's about the differences in bitcoin prices across countries (price premia), not about bitcoin's actual purchasing power.
So, inflation being found to be insignificant, doesn't mean that bitcoin doesn't appreciate with inflation. It means that bitcoin doesn't appreciate disproportionately to inflation: i.e. the price premium doesn't increase with inflation.
Here's a nice excerpt from the conclusion of the paper:
Standard finance theory would suggest inter-market price differences exist because of microstructure characteristics like trading volume and bid-ask spreads. These factors do explain part of the price differences, but there is a missing piece to the puzzle that seems to be explained by proxies to a variety of economic freedom measures that cause large enough frictions to limit arbitrage.
The "mystery" being investigate is why there are cross-border price differences in an asset like Bitcoin, when the naive expectation would be that arbitrage would quickly resolve those differences.