Manuscript X-A-conv@1 · X-A-conv.tex · theorem · c76fffa3

Theorem: The defect survives evaluation on the switched solution

The switched scalar solution and the same obstruction › Scalar covariance proved for the actual action · lines 1653–1675 · proof included or linked

X-A-conv@1#thm:evaluatedgap

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Take $ρ_{0} = x^{1}$ , the fixed $f, ξ_{*}$ , and the pure-gauge metric jet obtained by pulling back the flat metric. Then the difference between the first evaluated relational coefficient and its flat value is

\int f Φ_{g}^{[1]} = c_{ε} > 0.

Proof. Lemma lem:scalarcov gives

ρ_{1, g} = X_{ξ_{*}} ρ_{0} = ψ .

Lemma lem:preflight gives

X_{w} ρ_{0} = S_{ε} ψ .

Equation (eq:evalone) and Lemma lem:positivegap give the result.

Displayed formulas in this passage

unlabeled · line 1659
$\int f Φ_{g}^{[1]} = c_{ε} > 0.$
unlabeled · line 1666
$ρ_{1, g} = X_{ξ_{*}} ρ_{0} = ψ .$
unlabeled · line 1670
$X_{w} ρ_{0} = S_{ε} ψ .$

Nearby in this section

section: Scalar covariance proved for the actual action
lemma: Lemma: Scalar density covariance on the frozen plateau
section: Scalar covariance proved for the actual action
section: Scalar covariance proved for the actual action