Manuscript Em02-B@1 · Em02-B-v1.tex · section · 1347253e

Localization

Localization · lines 101–134

The five-cone mass at fixed rescaled resolution, not a refinement in $ϵ$ , gives residual $- 4.17 \times 1 0^{- 8}$ against $c_{R}$ at $ϵ = 0.25, 0.125, 0.0625$ .

The $47$ chart residual at those scales stays near $- 1.12 \times 1 0^{- 5}$ on an $81$ -node mesh. Holding $ϵ = 0.1$ and refining the mesh gives

nodes	scaled integral	residual against $c_{47}$
$21$	$0.150316797673$	$- 1.342 \times 1 0^{- 4}$
$41$	$0.150407097916$	$- 4.393 \times 1 0^{- 5}$
$81$	$0.150439836944$	$- 1.119 \times 1 0^{- 5}$

The residual shrinks as the mesh is refined. That supports grid bias. It does not by itself prove the bias model; it is the check the previous note lacked.

For $H = 1 + 0.3 T$ , the scaled probe equals $0.3 \int_{0}^{\infty} t^{2} b_{0} (2 t^{2}) d t = 0.14179675523330723$ exactly, before quadrature error. The trapezoidal values are $0.141796588567$ , $0.141796421900$ , and $0.141796088567$ . The drift is consistent with amplification of a small cone-mass error after subtraction, not with failure of the localization identity.