The far-field contribution to vortex stretching at a high-vorticity point can be bounded by an unsigned Calderón-Zygmund singular-integral estimate. We separate this bound into the quantity it bounds and the quantity it uses to bound it, and measure both by direct summation of the contracted Biot-Savart stretching integral on direct numerical simulation data, as functions of the outer integration radius $R$. Across forced isotropic turbulence at Taylor-scale Reynolds numbers ${\mathrm{Re}}_{\lambda }\approx 433$, 611, and 1300, the unsigned capacity—the magnitude the estimate permits—grows approximately logarithmically in $R$, whereas the realized signed magnitude—what the same integral actually delivers—grows with only $10–19\%$ of the capacity slope. The empirical tightness $C_{\mathrm{far}}=\left|{\sigma }_{\mathrm{far}}\right|/{\sigma }_{\mathrm{far}}^{\mathrm{abs}}$ therefore decreases by $21–39\%$ over $R/\eta =25-60$, with block-bootstrap confidence intervals excluding zero at both median and extreme-vorticity targets. This decline is robust: it is unchanged when target classes are defined by a threshold pooled across all sampled cutouts rather than locally, it survives a sixth-order finite-difference recomputation of the full pipeline, and it is insensitive to the inner cutoff. The looseness of the bound is thus a radius-dependent margin, not a fixed factor. Expressed as the dimensionless tightness rather than the dimensional capacity, the curves nearly collapse across the threefold range in ${\mathrm{Re}}_{\lambda }$. The realized far field is dynamically substantial: the magnitude ratio $|{\sigma }_{\mathrm{far}}|/|{\sigma }_{\mathrm{total}}|$ reaches 0.50 at median targets and 0.44–0.48 in the extreme-vorticity tail at $R/\eta =60$, so by the triangle inequality the contribution complementary to the measured far-field band has a magnitude at least approximately half of the total at the median and at least $52–56\%$ at the most intense events, with the far field a near-equal partner at the largest measured radius. Cancellation is systematically weaker at extreme-vorticity targets than at the median: the tail-to-median tightness ratio is 1.2–1.7 and grows with radius, so the sign organization that suppresses the far field weakens precisely at the events most relevant to amplification. A per-shell cancellation diagnostic shows that the looseness is already present within individual radial shells and strengthens with radius in both intensity classes.

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• Homogeneous turbulence
• Isotropic turbulence