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Manuscript XX-B@1 · XX-B.tex · section · 56d708a5

The target actually constructed

Target, mathematical inputs, and scope › The target actually constructed · lines 143–173

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XX-A froze an explicit original-rod lapse variant on a power-law Einstein–scalar background XXA. This paper constructs its free gauge-fixed field input. It does not reconstruct an unavailable interacting calculation.

The target consists of:

  1. the coupled metric–scalar action Hessian and a fixed gauge-fixing realization;

  2. the auxiliary and ghost sectors, including their signs and normalization;

  3. retarded and advanced inverses on compact spacetime tests;

  4. a normalized Hadamard contraction matrix on that same free field system;

  5. the classical principal-symbol comparison with the independently displayed original-rod lapse.

Here “normalized contraction” means a specified field-equation and graded canonical-commutation normalization with a stated microlocal singularity class. It does not mean a positive physical state or a chosen cosmological vacuum.

The original rods are derived coordinate functionals. They do not appear as additional propagating variables in the invariant bulk action. Their spatial inverse is supplied separately. Consequently, “original-rod Green distributions” must not mean that the Newton inverse is replaced by a retarded spacetime inverse.