Real quadratic mass in the shifted initial-time strip

The shifted trace estimate is expressed as an ordinary space-time integral for the subsequent weighted cutoff estimate.

theorem ESS.bu_short_shifted_real_trace_strip_tendsto_zero (scale R : ℝ) (hscale : 0 < scale) (hscale1 : scale ≤ 1) (hR : 0 < R) (w : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3) (Dw : CKN.Foundation.Parabolic.ParabolicPoint → Fin 3 → CKN.Foundation.Parabolic.Vec3) (D2w : CKN.Foundation.Parabolic.ParabolicPoint → Fin 3 → Fin 3 → CKN.Foundation.Parabolic.Vec3) (Dtw : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3) (hcont : ContinuousOn w ({x : CKN.Foundation.Parabolic.Vec3 | 0 < x 2} ×ˢ Set.Ico 0 1)) (hinit : ∀ (x : CKN.Foundation.Parabolic.Vec3), 0 < x 2 → w (x, 0) = 0) (hweak : CKN.HasSpaceTimeWeakDerivs {x : CKN.Foundation.Parabolic.Vec3 | 0 < x 2} (Set.Ioo 0 1) w Dw D2w Dtw) (hL2 : ∀ S ⊆ CKN.spaceTimeSet {x : CKN.Foundation.Parabolic.Vec3 | 0 < x 2} (Set.Ioo 0 1), Bornology.IsBounded S → ∫⁻ (z : CKN.Foundation.Parabolic.ParabolicPoint) in S, ‖Dw z‖ₑ ^ 2 + ‖D2w z‖ₑ ^ 2 + ‖Dtw z‖ₑ ^ 2 < ⊤) : Filter.Tendsto (fun (ε : ℝ) => (∫ (q : CKN.Foundation.Parabolic.Vec3 × ℝ) in buShortTraceBall R ×ˢ Set.Ioc (1 / 2 + ε) (1 / 2 + 2 * ε), CKN.Foundation.Parabolic.vec3EuclideanNorm (buAffineField (-scale ^ 2 / 2) scale w (CKN.Foundation.Parabolic.parabolicHomeomorph.symm q)) ^ 2) / ε ^ 2) (nhdsWithin 0 (Set.Ioi 0)) (nhds 0)

The shifted field has vanishing normalized real quadratic mass on the bounded trace ball as its lower-time strip shrinks.