What is fixed and what remains a choice

The predecessor XX-B supplies a complete gauge-fixed free operator and a nonempty class of algebraic Hadamard contractions XXB. It does not supply one uniquely selected physical covariance, a physical quotient state, or global spatial estimates for an arbitrary member of that class.

The present manuscript keeps:

1. the same invariant action and on-shell background;

2. the same matter-scalar lapse, clock calibration, positive classical branch, and factorial expansion;

3. the same slice-harmonic original rods and decaying spatial boundary condition;

4. the same gauge condition, action-Hessian normalization, causal commutator, and compact-test field domains.

The equations needed for the proofs are reproduced below. No unavailable text of XX-A is represented as having been inspected.

A fixed representative is denoted $W_{\mathcal{B}}$. The normalized Hadamard class is denoted ${\mathfrak{W}}_{\mathcal{B}}$. Membership in the class does not assert positivity, subsidiary invariance, decay, or existence of the Newton compositions. A change within the class is a new normalization choice, not a verification of the original representative.