Definition: Q1 closure used in this paper

Q1 closure means:

1. a complete gauge-fixed free multiplet and its quadratic action;

2. a specified coupled operator domain on compact spacetime tests;

3. normalized retarded and advanced inverse matrices, including auxiliary and ghost sectors;

4. proved support and wavefront bounds;

5. a nonempty, explicitly normalized Hadamard contraction class with its remaining smooth freedom declared.

It does not include physical state positivity, nonlocal lapse-product admission, spatial-tail estimates for that insertion, or an interacting Ward identity.