Noise scaling and sky-subtraction requirements for ULSB detection. Left: fractional uncertainty as a function of total integration time. Random noise decreases as σ_rand ∝ t^−1/2, while intrinsic sky variability imposes a systematic floor σ_sys = kf_var. For a representative per-exposure uncertainty σ₀ = 1% at t₀ = 5 min and intrinsic sky variability f_var = 2% (Figure 2), an illustrative leakage factor k = 0.1 produces a systematic floor σ_sys = 0.2%. The crossover time t_cross = 125 min marks the transition to a systematics-limited regime, beyond which additional integration yields diminishing returns unless sky subtraction is improved. Right: required sky-subtraction fidelity to detect a target signal S_sig against a sky background S_sky. The required leakage factor is k_req = (S_sig/S_sky)/f_var, and detection requires k < k_req. For typical dark-sky continuum levels (S_sky ∼ 7 × 10⁻¹⁸ erg cm⁻² s⁻¹ arcsec⁻² Å⁻¹), detecting 10⁻¹⁹ requires k ≲ 0.7, whereas detecting 10⁻²⁰ requires k ≲ 0.07, corresponding to suppression of more than 90% of the intrinsic sky variability.