There are 4 combinations from the 6-stick that need testing against. If you number the atoms 1 to 6, these are 123, 234, 345 and 456 for consecutive atom matches. The original 6-stick is copied such that combinations 234 and 345 are created and joined to the front of the original 6-stick which contains 123 and 456. Aside this, another 12-stick consisting of 4 copies of the 3-stick is made. These sticks are fed side-by-side into the 'Woodchipper' top 2 quint glyph slots.

Below this, a single salt atom is taken to the side and later passed across to the output area near the gold. The Berlo Wheel and main testing wheel next to it continously cycle the 6 different unmatching combinations of the 4 elemental atoms against the atoms from the test sticks (plus 2 unavoidable matching combinations by the nature of the wheel - but this is ok as it gives a little extra time for other things like the 12-sticks' creation).  Any non-match in the test stick atoms will create a quint which is then later destroyed and no atoms are passed along to the left. If the test stick atoms match, no quint is created and the 2 atoms are passed along to the left. If there are 3 pairs matching which are also all from the same group of the 123, 234, 345 or 456 stick testing pairs, the gold and salt atoms are pushed along by the 6-stick created from these 3 pairs; the gold atom being prepped for output on the left and outputted and the salt moved away from being grabbed by its output arm. Otherwise, this single salt atom is outputted. Any loose gold or salt atoms are trashed. After every 3 pairs of stick atoms are tested, the piston arm destroys any 1/3 or 2/3 built stick that was created as it is not part of one of the combinations required. Otherwise (as I found out in earlier tests) you will get gold outputted as part of any combination of atoms in the 6-stick even if they are NOT consecutive...!

If it were possible to have another salt input in another testing wheel (it needs to be there to replace any atoms consumed in creating quints) it would be possible to double the speed of the whole machine by creating a second, inversed symmetrical machine underneath and fiddling a bit with the outputs to make sure golds and salts are in the right places ready to be used or not as the testing proceeds. However, there is only 1 salt input so this concept is difficult to achieve.

Apart from 1 cycle where the testing wheel needs to not move to allow a single salt atom to be taken from the input there for being the potential output if no match, the testing wheel is continuously on a grab/turn/drop 3 instruction repeat so it seems to go as fast as it can and this is the limitation of this machine and method. It still seems pretty slow in terms of cycle count, at least compared to previous computation puzzles. However, for myself, I am pretty happy with what I came up with, especially as I only really started in the second week due to being away from my main PC / place of residence for the 1st week of this final puzzle! Much was done in my head until I was back at my main PC!