Manuscript XIII-B@1 · XIII-B.tex · section · b8a5c0f5

The witness remains a boundary

Prerequisite sheet and convention audit › The witness remains a boundary · lines 481–504

XIII-B@1#eq:witness

For XII-F's detecting data, the supplied value is

Δ_{ξ} O (u_{*}) = - 8 \int f (t, x) \int_{0}^{t} (t - s)^{2} a (s) d s d^{4} x < 0.

The parameter is compact, (CP) holds, and the initial configuration lies on the complete free shell but outside the detected cancellation subclass XIIF. The factor $8$ and the cylinder integral are copied. No binary normalization is chosen after this witness, and the witness is not inserted into an odd Ward identity.

The retained action boundary is

S_{grav, D} = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3} d^{4} x .

Gravitational interaction vertices are omitted from the selected calculation, not from the action XIIC.

Displayed formulas in this passage

XIII-B@1#eq:witness · line 484
$Δ_{ξ} O (u_{*}) = - 8 \int f (t, x) \int_{0}^{t} (t - s)^{2} a (s) d s d^{4} x < 0.$
unlabeled · line 497
$S_{grav, D} = S_{EH} + κ \int (σ_{ε} - 1) ℓ_{3} d^{4} x .$