Before revision:  We conjecture that if the state X(k) is positive for k less than or equal to N in response to a "distinguished path" v*(k) which we define, then for all admissible paths v(k), positivity of the state  is also guaranteed .
After revision:  We conjecture that if the state X(k) is positive for k less than or equal to N in response to a "distinguished path" v*(k) which we define, then for all admissible paths v(k), positivity of the state equation ceases to be meaningful after some finite time. Finally, this paper also includes a conjecture which says that for the "gap" interval \alpha_- \leq \alpha \leq \alpha_+, state positivity is also guaranteed .