> Consciousness is defined as the fraction of an object's inherent description that an observer correctly believes to be true.

Here it's a belief, but in other places it's referring to a relationship between objects and belief (i.e. a ratio). In either case this isn't sufficient to account for the hard problem. It's just building a framework and using the word 'Consciousness' as one of the labels. Any definition of consciousness should account for why we have a subjective perspective that unrolls through time and has qualia.

Also "belief" implies subjectivity, which imlpies a conscious entity, so any use of "belief" is circular here.

An information theoretic approach would tackle this with Shannon entropy and Turing machines, for example.