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HBD is not dollar backed or bitcoin backed, it is Hive Backed Dollar- or Hive Blockchain Dollar. Here is what should happen. If the dollar drops, the value flows back to HIVE. If Bitcoin rises, Hive also rises, either because users sell HBD or because inversely BTC rises when the US dollar falls. Either way, the internal swap mechanism is for "a dollar worth" either direction now.

If we back with USD are we not closer to the regulators?

Not with usd in the bank, but some other stable like USDC or maybe preferebly DAI