Full-limit failure for the circular arc

As T sweeps continuously, the blow-down never settles — uniform convergence fails for the full family.
Stage
j = 3
Tj
rj = Tj/Tj+1
λ = T / Tj+1
0.250
Arc radius R/λ
4.00
Arc extent θλ
0.50π
‖ℓT−γ‖
0.000
H₂[ℓT] / Z
0.000
Presets:
R = 1.0
θ = 2.00π (full circle)
Speed factor: 0.18

1. Blow-down ℓT(u) in V1

Dashed grey: target arc γ. Solid: current blow-down. The curve only agrees with γ at the isolated instants T = Tj.
target γ (dashed) current blow-down ℓT ghosts at previous Tj

2. Sup-norm error ‖ℓT − γ‖

The error drops to zero at each Tj but climbs back immediately — the sawtooth never flattens.

3. Depth-two component H₂[ℓT]

Dashed green: target value −(R²/2)(θ − sin θ). The central coordinate overshoots the target at intermediate scales before returning at each Tj.
target H₂[γ] (dashed) current H₂[ℓT]