Manuscript IX-D@3 · IX-D-v3.tex · assumption · 3ad4586e

Assumption: Copied analytical calibration

Release conventions and inherited inputs › Geometry and actual functionals · lines 397–427

IX-D@3#ass:calibration, IX-D@3#eq:rate

For the prescribed regulator placement,

T_{ε}^{ρ} = 2 K_{ε} (x, y) K_{ε} (x^{'}, y) D_{ε} (x - x^{'}) .

There are $u_{μ}^{ρ}, r \in D^{'} (X)$ with

u_{μ}^{ρ} = U_{m} + (κ_{ρ} + lo g μ) r, u_{μ}^{ρ_{a}} - u_{μ}^{ρ_{b}} = c_{ab} r, c_{ab} \in R .

For each compact $K_{0} \subset X$ ,

⟨ T_{ε}^{ρ} - lo g ((μ ε)^{- 1}) r - u_{μ}^{ρ}, Φ ⟩ \leq C_{K_{0}} ε (1 + ∣ lo g ε ∣) p_{K_{0}, 64} (Φ) .

The estimate includes compacts meeting $Rel \cap Δ_{13}$ , where $Rel = supp r$ and $Δ_{13} = {x = x^{'}}$ . Parent conversion is exactly $c_{ab} r$ , with no additional normal derivative, nonconstant weight, or intersection term. The parent distributions are dagger symmetric.

These are the analytical premises reported through IX-Free and IX-Free-2, including their stated dependence on IX-B and VII-D IXFree,IXFreeTwo,IXB,VIID.

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IX-D@3#eq:rate · line 410
$⟨ T_{ε}^{ρ} - lo g ((μ ε)^{- 1}) r - u_{μ}^{ρ}, Φ ⟩ \leq C_{K_{0}} ε (1 + ∣ lo g ε ∣) p_{K_{0}, 64} (Φ) .$
unlabeled · line 400
$T_{ε}^{ρ} = 2 K_{ε} (x, y) K_{ε} (x^{'}, y) D_{ε} (x - x^{'}) .$
unlabeled · line 405
$u_{μ}^{ρ} = U_{m} + (κ_{ρ} + lo g μ) r, u_{μ}^{ρ_{a}} - u_{μ}^{ρ_{b}} = c_{ab} r, c_{ab} \in R .$

Assumption: Copied analytical calibration

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