You are correct in that 13.8 Brix has a SG of 1.056.
What I meant was a Refractometer Brix reading of 6.3 (on your phosphoric acid solution). That is, the Brix reading on the Refractometer when you test your diluted acid. If you give your acid about an eight to one dilution with distilled water, you should get something close to that. By tweaking with either more water or more concentrated acid, you ought to be able to hit 6.3 on the refractometer. Then, as a check, you can test the density with your hydrometer and you should be close to 1.056.
Strictly speaking, Brix is a scale for density where a solution that has a density of pure water is defined as 0 and a solution that has a density of a 10% sucrose solution in water is defined as 10. Many of the refractometers used by homebrewers are calibrated with the Brix scale. They do not measure density, but refractivity, or the refractive index of the sample. I use the term "Refractometer Brix" to mean the Brix reading of such a refractometer. So, when I say the phosphoric acid has a Refractometer Brix of 6.3, I am saying the refractive index of the phosphoric is equal to the refractive index of a sucrose solution with a density of 6.3 Brix. I'll admit, it is a bit sloppy short-hand, but it works for me and I hope most people can understand what I mean.
To add to the confusion, some refractometers will also read in Specific Gravity. I had one of these and I got rid of it. I was always getting confused between the refractometer reading and the density. In my notes, a reading noted as Brix is the reading off the refractometer and a reading written as a SG (such as 1.056) is taken with a hydrometer. Of course, I will convert, so I may have a beer that my notes say had an OG of 13.8 Brix (1.054), which means I measured with my refractometer and converted to SG (using a correction factor of 1.04 because I am measuring wort and not sucrose).