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How many places are actually going to honor this thing
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Any scuba store should honor any nitrox certification.
Most stores these days bank EAN 32 anyway. They used to bank EAN 36 back in the heyday of IANTD. Currently the heyday is PADI, SSI, and GUE. And each of these emphasizes the EAN 32 over the other popular choices of EAN 36, EAN 50, or EAN 25.
Therefore you can be sure a GUE certification is recognized virtually anywhere.
The due diligence requirement of the store owner and management for insurance purposes is to check your certification and have you record it and log your nitrox purchases. You can do that nicely with a GUE card as well as any other, for EAN 32.
"DIR" and "Hogarthian" are somewhat interchangable. Whereas GUE is the agency-organization that trained and certified you. The terms DIR and Hogarthian have been around for awhile. Whereas GUE would have been chosen and put on some sort of legal application to some state business agency to create an organization or association, and therefore GUE is now a name, like NAUI or SSI or PADI etc.
But DIR or Hogarthian would be hard to use as names, since they are fairly ubiquitous.
Some people only associate DIR with GUE, but DIR can be and has been many things. The latest differentiation is now currently between GUE-DIR and AG-DIR, as the evolution continues.