Manuscript XX-A@1 · XX-A.tex · section · 3a586110
Required inverses and contraction data
Quantum field input: the operators that are specified and those that remain missing › Required inverses and contraction data · lines 1147–1174
The lemma assumes a physical ; it does not construct one for the present coupled system. Nor does local Hadamard behavior impose the weighted spatial-tail bounds needed for the rods.
| Slot | Specified here | Still required |
|---|---|---|
| Q1 | Background, complete unfixed linearized equations, graded quadratic gauge-fixing candidate | Checked coupled realization, inverses, normalization, and gauge-compatible contraction identities |
| Q2 | Required singularity, field-equation, and positivity tests | Selected state or suitable parametrix and spatial-tail bounds |
The first unclosed quantum gate is Q1. It is not bypassed by calling a quadratic action a covariance.