Manuscript IV@1 · IV.tex · section · 351cb2d7

Witness, limit boundary, and controls

Cutoff ledger: Model 3 › Witness, limit boundary, and controls · lines 3695–3727

The compact curvature current $J_{ψ}$ is conserved. Its classical support is exterior to the uncut compact scalar preparation on a short slab. The scalar momentum cutoff does not preserve that exact support statement. Only the compact curvature pairing is transferred by coherent expectation convergence, allowing one finite $Λ$ to be fixed.

With $ν = ∥ z_{*} ∥^{2}$ ,

E_{M}^{(3)} = 2 C_{Λ} ν^{2} + 5 ν + 4 [e^{- ν} n > M \sum (n + 2)^{2} \frac{ν ^{n}}{n !}]^{1/2} .

Theorem thm:model3 gives

Δ p_{M} \geq c_{3} - \frac{τ λ}{2} E_{M}^{(3)} .

The scalar vacuum is compared with a scalar coherent state. At $λ = 0$ , or when $T$ is explicitly replaced by zero, both probabilities are $1/2$ .

Neither the $Λ$ -expectation argument nor the $M$ -tail bound supplies an unregulated metric instrument. The cubic $S_{t_{0}} (R T (ϕ)) ϕ$ is not represented by these kernels.

Figures fig:exterior-curvature-witness and fig:model3-record-controls separate the classical support certificate from the regulated record and its controls.

Displayed formulas in this passage

unlabeled · line 3705
$E_{M}^{(3)} = 2 C_{Λ} ν^{2} + 5 ν + 4 [e^{- ν} n > M \sum (n + 2)^{2} \frac{ν ^{n}}{n !}]^{1/2} .$
unlabeled · line 3711
$Δ p_{M} \geq c_{3} - \frac{τ λ}{2} E_{M}^{(3)} .$