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

One observation test

Convention sheet and frozen data › One observation test · lines 524–545

X-A-conv@1#eq:fandxi

Define the nonzero real bump

ψ (x) = ⎩ ⎨ ⎧ exp (1 - \frac{1}{1 - 64 r ( x ) ^{2}}), 0, r (x) < 1/8, r (x) \geq 1/8, N = \int_{M} ψ (x) d^{4} x > 0.

Freeze

f = \frac{ψ}{N} \in C_{c}^{\infty} (O), ξ_{*} = ψ \partial_{1} \in g_{U} .

The same $f$ , $g$ , $ξ_{*}$ , and regulator are used throughout the obstruction witness. In particular, the gauge algebra is not chosen from the kernel of the regulator defect.

Displayed formulas in this passage

X-A-conv@1#eq:fandxi · line 537
$f = \frac{ψ}{N} \in C_{c}^{\infty} (O), ξ_{*} = ψ \partial_{1} \in g_{U} .$
unlabeled · line 527
$ψ (x) = ⎩ ⎨ ⎧ exp (1 - \frac{1}{1 - 64 r ( x ) ^{2}}), 0, r (x) < 1/8, r (x) \geq 1/8, N = \int_{M} ψ (x) d^{4} x > 0.$

Nearby in this section

scope: Frozen contract