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what is the 6th phase of matter?

liquid,solid,gas,plasma,bose einstein condensate ..____?

I believe that you mean "States".

A "phase" is domain of a thermodynamical variable where Gibbs Free Energy is analytic (does not contain a singularity in the mathematical sense).

I would give the FIVE as...

SOLID: cysteine solids, amorphous solids,
LIQUIDS:
GAS:
PLASMA:
DEGENERATE MATERIALS (containing Bose-Einstein condensates -- which is a super fluid, metallic Hydrogen, white dwarf matter, super dense nucleon matter)

This last category is a "catch all" and contains Bose glass and other odd quantum materials.

Personally, I don't find a need for further classification. I am not radically opposed to considering further classifications, but these five contain all of the extant states (that I know about--and since more are being discovered "everyday" that may change). I view this like Biological Domains--you need a really really good reason to "open up" another category.

This is somewhat a matter (no pun) of personal taste and semantics, so I certainly understand differing views on this one.

-Fred