The requested alternative needs qualification

An indefinite gauge-fixed fiber pairing does not by itself obstruct positivity on the physical gauge quotient. Conversely, positivity of one scalar or tensor subsector does not construct a state on the complete quotient. These distinctions matter in linearized Einstein–Klein–Gordon theory Hack.

We explicitly decline to announce a full physical state for the unspecified $W_{\mathcal{B}}$. Instead, we prove:

1. an exact obstruction to positivity for an explicitly constructed representative in the same native class;

2. exact local subtraction;

3. unconditional compact-source rod-response tails;

4. a conditional one-sided covariance-tail theorem with its hypothesis stated as a genuine additional infrared requirement;

5. an unconditional two-rod commutator obstruction.

This is a complete mathematical audit of the stated data. It is not a complete native Q2 state-and-tail package.