Phase separation of personalities

${\Phi }_i$ is considered phase separated if the sum of probabilities of all tuples of the form $(\mathbb{P},r_{ideal})$ , when evaluated by language model, preferentially map into the space ${\Phi }_i$ :

$Pr(\varphi (\mathcal{P},r_{ideal})\in {\Phi }_i)>{\sum }_{j=1,j\ne i}^{N}Pr(\varphi (\mathcal{P},r_{ideal})\in {\Phi }_j)$

$Pr(o_{ideal}\in {\Phi }_i)>{\sum }_{j=1,j\ne i}^{N}Pr(o_{ideal}\in {\Phi }_j)$

If we are using ${\mathcal{P}}_i,r_i$ and it produces an output that is not in ${\Phi }_i$ (ie. $\varphi ({\mathcal{P}}_i,r_j)\notin {\Phi }_i$) then we experience an “identity break.” This is a case where the identity of the language model is overridden due to either stochastic chance (high temperature) or the input prompt $r_j$ containing some information that ${\mathcal{P}}_i$ cannot access. This will modify ${\mathcal{M}}_i$ such that ${\mathcal{P}}_i\to {\mathcal{P}}_{i+1}$

Personality recovery is possible though:

1. Reset ${\mathcal{P}}_{i+1}\to {\mathcal{P}}_i$ (Chaperone protein basically resetting folding)
2. Modify ${\mathcal{P}}_{i+1}\to {\mathcal{P}}_i^{‘}$ via localized changes (Local remodeling through an isomerase)
3. Prompt using $r_i$ to remodel $\mathcal{M}\text{ and }\mathcal{I}$ (Post-translational modification)