The most straightforward representation of spectral envelopes are the filter coefficients , which are the output of the estimation, be it the cepstral coefficients ci (section 3.3 ff.), or one of the LPC coefficients ai, ki (section 3.2). They are the most precise representation possible.
They are stable, but not local. The non-locality is due to the fact that they essentially represent a spectral envelope in time-domain (by one of different possible filter models), so changing one coefficient will change the envelope's value at multiple frequencies.
Because the changes one wishes to effect will be specified in the frequency-domain, they are also not easy to manipulate.
They do certainly fulfill the space requirement (only order pvalues), but are costly in evaluation for additive synthesis, since p cosines have to be evaluated for each frequency at which we desire to know the amplitude of the envelope. For subtractive synthesis, however, they are efficient, since they can directly be used for fast time-domain filtering.
They can not at all be specified manually.