Analysis manuscript: small area error, different limits: changed case
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Changed case: a displaced signed transition
On J=[0,1], set c=1/3. Let K(x)=−1 for x≤c and K(x)=1 for x>c. Define gₙ(x)=−1 for x≤c, gₙ(x)=−1+6n(x−c) for c≤x≤c+1/(3n), and gₙ(x)=1 afterward. Rebuild the integral-distance argument rather than just renaming the original formulas: compute ∫J gₙ, ∫J |gₙ−K| and d₁(gₙ,gₘ) for m≥n; prove no continuous integral-distance limit exists; and give a uniform-Cauchy obstruction. For continuous w with ||w||∞≤3, derive a measurement-error bound. A reviewer should change the location, height or width for independent transfer; this displayed case and solution are public guidance.
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